New results on robust exponential stability of integral delay systems
NASA Astrophysics Data System (ADS)
Melchor-Aguilar, Daniel
2016-06-01
The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov-Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
Ye, Qian; Cui, Baotong
2010-06-01
This paper aims to analyze global robust exponential stability in the mean square sense of stochastic discrete-time genetic regulatory networks with stochastic delays and parameter uncertainties. Comparing to the previous research works, time-varying delays are assumed to be stochastic whose variation ranges and probability distributions of the time-varying delays are explored. Based on the stochastic analysis approach and some analysis techniques, several sufficient criteria for the global robust exponential stability in the mean square sense of the networks are derived. Moreover, two numerical examples are presented to show the effectiveness of the obtained results.
NASA Astrophysics Data System (ADS)
Liu, Puchen; Yi, Fengqi; Guo, Qiang; Yang, Jun; Wu, Wei
2008-04-01
To avoid the unstable phenomena caused by time delays and perturbations, we investigate the sufficient conditions to ensure the global exponential robust stability with a convergence rate for the reaction-diffusion neural networks with S-type distributed delays. Because S-type distributed delays lead to some difficulty, we also introduce a new generalized Halanay inequality and a novel method-system-approximation method into the qualitative research of neural networks. Moreover, the sufficient criteria provided here, which are rather accessible and feasible, have wider adaptive range.
Zhu, Quanxin; Cao, Jinde
2010-08-01
This paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays and known or unknown parameters. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the mixed time delays under consideration comprise both time-varying delays and continuously distributed delays. To the best of the authors' knowledge, till now, the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper. The main objective of this paper is to fill this gap. By constructing a novel Lyapunov-Krasovskii functional, and using some new approaches and techniques, several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square. The results presented in this paper generalize and improve many known results. Finally, two numerical examples and their simulations are given to show the effectiveness of the theoretical results.
Exponentially Stabilizing Robot Control Laws
NASA Technical Reports Server (NTRS)
Wen, John T.; Bayard, David S.
1990-01-01
New class of exponentially stabilizing laws for joint-level control of robotic manipulators introduced. In case of set-point control, approach offers simplicity of proportion/derivative control architecture. In case of tracking control, approach provides several important alternatives to completed-torque method, as far as computational requirements and convergence. New control laws modified in simple fashion to obtain asymptotically stable adaptive control, when robot model and/or payload mass properties unknown.
Liu, Pin-Lin
2013-11-01
This paper investigates a class of delayed cellular neural networks (DCNN) with time-varying delay. Based on the Lyapunov-Krasovski functional and integral inequality approach (IIA), a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Unlike previous methods, the upper bound of the delay derivative is taken into consideration, even if larger than or equal to 1. It is proven that results obtained are less conservative than existing ones. Four numerical examples illustrate efficacy of the proposed methods.
Robust Variable Selection with Exponential Squared Loss.
Wang, Xueqin; Jiang, Yunlu; Huang, Mian; Zhang, Heping
2013-04-01
Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are [Formula: see text] and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower non-causal selection rate. Furthermore, we re-analyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods.
Robust exponential acceleration in time-dependent billiards.
Gelfreich, Vassili; Rom-Kedar, Vered; Shah, Kushal; Turaev, Dmitry
2011-02-18
A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. The class includes ergodic billiards with a piston that moves adiabatically and is removed adiabatically in a periodic fashion. The phenomenon is robust: deformations that keep the chaotic character of the billiard retain the exponential energy growth. The growth rate is found analytically and is, thus, controllable. Numerical simulations corroborate the analytic predictions with good precision. The acceleration mechanism has a natural thermodynamical interpretation and is applied to a hot dilute gas of repelling particles.
NASA Astrophysics Data System (ADS)
Mao, Yanbing; Zhang, Hongbin
2014-05-01
This paper deals with stability and robust H∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov-Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.
Circuit design and exponential stabilization of memristive neural networks.
Wen, Shiping; Huang, Tingwen; Zeng, Zhigang; Chen, Yiran; Li, Peng
2015-03-01
This paper addresses the problem of circuit design and global exponential stabilization of memristive neural networks with time-varying delays and general activation functions. Based on the Lyapunov-Krasovskii functional method and free weighting matrix technique, a delay-dependent criteria for the global exponential stability and stabilization of memristive neural networks are derived in form of linear matrix inequalities (LMIs). Two numerical examples are elaborated to illustrate the characteristics of the results. It is noteworthy that the traditional assumptions on the boundness of the derivative of the time-varying delays are removed.
Exponential Stability of Complex-Valued Memristive Recurrent Neural Networks.
Wang, Huamin; Duan, Shukai; Huang, Tingwen; Wang, Lidan; Li, Chuandong
2017-03-01
In this brief, we establish a novel complex-valued memristive recurrent neural network (CVMRNN) to study its stability. As a generalization of real-valued memristive neural networks, CVMRNN can be separated into real and imaginary parts. By means of M -matrix and Lyapunov function, the existence, uniqueness, and exponential stability of the equilibrium point for CVMRNNs are investigated, and sufficient conditions are presented. Finally, the effectiveness of obtained results is illustrated by two numerical examples.
On exponential stability of gravity driven viscoelastic flows
NASA Astrophysics Data System (ADS)
Jiang, Fei; Wu, Guochun; Zhong, Xin
2016-05-01
We investigate stability of an equilibrium state to a nonhomogeneous incompressible viscoelastic fluid driven by gravity in a bounded domain Ω ⊂R3 of class C3. First, we establish a critical number κC, which depends on the equilibrium density and the gravitational constant, and is a threshold of the elasticity coefficient κ for instability and stability of the linearized perturbation problem around the equilibrium state. Then we prove that the equilibrium state is exponential stability provided that κ >κC and the initial disturbance quantities around the equilibrium state satisfy some relations. In particular, if the equilibrium density ρ bar is a Rayleigh-Taylor (RT) type and ρbar‧ is a constant, our result strictly shows that the sufficiently large elasticity coefficient can prevent the RT instability from occurrence.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C. H.
1993-01-01
This report presents a robust control design using strictly positive realness for second-order dynamic systems. The robust strictly positive real controller allows the system to be stabilized with only acceleration measurements. An important property of this design is that stabilization of the system is independent of the system parameters. The control design connects a virtual system to the given plant. The combined system is positive real regardless of system parameter uncertainty. Then any strictly positive real controllers can be used to achieve robust stability. A spring-mass system example and its computer simulations are presented to demonstrate this controller design.
Robust Stabilizing Compensators for Flexible Structures with Collocated Controls
NASA Technical Reports Server (NTRS)
Balakrishman, A. V.
1996-01-01
For flexible structures with collocated rate and attitude sensors/actuators, we characterize compensator transfer functions which guarantee modal stability even when stiffness/inertia parameters are uncertain. While the compensators are finite-dimensional, the structure models are allowed to be infinite-dimensional (continuum models), with attendant complexity of the notion of stability; thus exponential stability is not possible and the best we can obtain is strong stability. Robustness is interpreted essentially as maintaining stability in the worst case. The conditions require that the compensator transfer functions be positive real and use is made of the Kalman-Yakubovic lemma to characterize them further. The concept of positive realness is shown to be equivalent to dissipativity in infinite dimensions. In particular we show that for a subclass of compensators it is possible to make the system strongly stable as well as dissipative in an appropriate energy norm.
Non-exponential Stabilization of Linear Time-invariant Systems by Time-varying Controllers
NASA Astrophysics Data System (ADS)
Inoue, Masaki; Wada, Teruyo; Ikeda, Masao
This paper proposes non-exponential stabilization of linear time-invariant systems by linear time-varying controllers. We consider state feedback and dynamic output feedback to make the states of the closed-loop systems decay non-exponentially. We first introduce a non-exponential stability concept that the state of a time-varying system converges to the origin with a bound provided by a desired function. Then, we give non-exponential stabilizability conditions and time-varying controllers to achieve the desired behavior of the closed-loop systems. By the proposed methods, we can realize various non-exponential behaviors, which may improve control performance.
Robust stabilization of the Space Station
NASA Technical Reports Server (NTRS)
Wie, Bong
1991-01-01
A robust H-infinity control design methodology and its application to a Space Station Freedom (SSF) attitude and momentum control problem are presented. This approach incorporates nonlinear multi-parameter variations in the state-space formulation of H-infinity control theory. An application of this robust H-infinity control synthesis technique to the SSF control problem yields remarkable results in stability robustness with respect to moments of inertia variation of about 73 percent in one of the structured uncertainty directions. The performance and stability of this robust H-infinity controller for the SSF are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.
Exponential stability of linear discrete systems with nonconstant matrices and nonconstant delay
NASA Astrophysics Data System (ADS)
Diblík, Josef
2017-07-01
The paper studies the exponential stability and exponential estimation of solutions to linear discrete systems with delay x (k +1 )=A (k )x (k )+B (k )x (k -m (k )), k =0 ,1 ,… where x is an n-dimensional dependent variable, A(k) and B(k) are n×n real matrices, and m(k) ∈ ℕ. Using the method of Lyapunov functions, conditions are derived for exponential stability.
Generalized exponential input-to-state stability of nonlinear systems with time delay
NASA Astrophysics Data System (ADS)
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Semigroup approximation and robust stabilization of distributed parameter systems
NASA Technical Reports Server (NTRS)
Kurdila, A. J.; Fabiano, R.; Strganac, T.; Hsu, S.
1994-01-01
Theoretical results that enable rigorous statements of convergence and exponential stability of Galerkin approximations of LQR controls for infinite dimensional, or distributed parameter, systems have proliferated over the past ten years. In addition, extensive progress has been made over the same time period in the derivation of robust control design strategies for finite dimensional systems. However, the study of the convergence of robust finite dimensional controllers to robust controllers for infinite dimensional systems remains an active area of research. We consider a class of soft-constrained differential games evolving in a Hilbert space. Under certain conditions, a saddle point control can be given in feedback form in terms of a solution to a Riccati equation. By considering a related LQR problem, we can show a convergence result for finite dimensional approximations of this differential game. This yields a computational algorithm for the feedback gain that can be derived from similar strategies employed in infinite dimensional LQR control design problems. The approach described in this paper also inherits the additional properties of stability robustness common to game theoretic methods in finite dimensional analysis. These theoretical convergence and stability results are verified in several numerical experiments.
Phat, V N; Trinh, H
2010-07-01
This paper presents some results on the global exponential stabilization for neural networks with various activation functions and time-varying continuously distributed delays. Based on augmented time-varying Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities. A numerical example is given to illustrate the feasibility of our results.
NASA Astrophysics Data System (ADS)
Xiao, Shuiming; Chen, Huabin
2017-03-01
In this paper, the existence and uniqueness, the exponential stability, and the almost sure exponential stability of mild solution for impulsive stochastic partial functional differential equations with finite delay are considered. Some sufficient conditions are established for our concerned problems, and some existing results are generalized and improved. Finally, an illustrative example is provided to show the feasibility and effectiveness of the obtained results.
Robust Fuzzy Logic Stabilization with Disturbance Elimination
Danapalasingam, Kumeresan A.
2014-01-01
A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design. PMID:25177713
Robust fuzzy logic stabilization with disturbance elimination.
Danapalasingam, Kumeresan A
2014-01-01
A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design.
Zeng, Zhigang; Wang, Jun
2006-05-01
This paper presents new theoretical results on global exponential stability of recurrent neural networks with bounded activation functions and time-varying delays. The stability conditions depend on external inputs, connection weights, and time delays of recurrent neural networks. Using these results, the global exponential stability of recurrent neural networks can be derived, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail.
Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid
2017-01-01
In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.
Robust Stabilization Control for an Electric Bicycle
NASA Astrophysics Data System (ADS)
Kawamura, Takuro; Murakami, Toshiyuki
Recently, bicycles have gained immense popularity because they have high mobility and are an environment-friendly means of transport. However, many people tend to avoid riding a bicycle because it is unstable. In order to solve this problem, stabilization control for a bicycle has been researched. The aim of this study is improvement of the robustness in stabilization control. To achieve this goal, control systems that use a camber angle disturbance observer (CADO) are proposed. Two kinds of CADOs are proposed in this paper, and the performances of these two observers are compared. The proposed control systems provide higher robustness than does the conventional method. The validity of the proposed methods is confirmed by the experimental results.
Song, Xueli; Xin, Xing; Huang, Wenpo
2012-05-01
The paper discusses exponential stability of distributed delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions. By relative nonlinear measure method, some novel criteria are obtained for the uniqueness and exponential stability of the equilibrium point. Our method abandons usual assumptions on global Lipschitz continuity, boundedness and monotonicity of activation functions. Our results are generalization and improvement of some existing ones. Finally, two examples and their simulations are presented to illustrate the correctness of our analysis.
Numerical robust stability estimation in milling process
NASA Astrophysics Data System (ADS)
Zhang, Xiaoming; Zhu, Limin; Ding, Han; Xiong, Youlun
2012-09-01
The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment. In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.
Hamed, Kaveh Akbari; Gregg, Robert D.
2016-01-01
This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and H2 robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:28959117
Adaptive control: Stability, convergence, and robustness
NASA Technical Reports Server (NTRS)
Sastry, Shankar; Bodson, Marc
1989-01-01
The deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers. Chapters are devoted to basic AC approaches, notation and fundamental theorems, the identification problem, model-reference AC, parameter convergence using averaging techniques, and AC robustness. Consideration is given to the use of prior information, the global stability of indirect AC schemes, multivariable AC, linearizing AC for a class of nonlinear systems, AC of linearizable minimum-phase systems, and MIMO systems decouplable by static state feedback.
Lu, Hongtao; Amari, Shun-ichi
2006-09-01
In this paper, we study the global exponential stability of a multitime scale competitive neural network model with nonsmooth functions, which models a literally inhibited neural network with unsupervised Hebbian learning. The network has two types of state variables, one corresponds to the fast neural activity and another to the slow unsupervised modification of connection weights. Based on the nonsmooth analysis techniques, we prove the existence and uniqueness of equilibrium for the system and establish some new theoretical conditions ensuring global exponential stability of the unique equilibrium of the neural network. Numerical simulations are conducted to illustrate the effectiveness of the derived conditions in characterizing stability regions of the neural network.
Cao, Jinde; Wang, Jun
2004-04-01
This paper investigates the absolute exponential stability of a general class of delayed neural networks, which require the activation functions to be partially Lipschitz continuous and monotone nondecreasing only, but not necessarily differentiable or bounded. Three new sufficient conditions are derived to ascertain whether or not the equilibrium points of the delayed neural networks with additively diagonally stable interconnection matrices are absolutely exponentially stable by using delay Halanay-type inequality and Lyapunov function. The stability criteria are also suitable for delayed optimization neural networks and delayed cellular neural networks whose activation functions are often nondifferentiable or unbounded. The results herein answer a question: if a neural network without any delay is absolutely exponentially stable, then under what additional conditions, the neural networks with delay is also absolutely exponentially stable.
On global exponential stability of positive neural networks with time-varying delay.
Hien, Le Van
2017-03-01
This paper presents a new result on the existence, uniqueness and global exponential stability of a positive equilibrium of positive neural networks in the presence of bounded time-varying delay. Based on some novel comparison techniques, a testable condition is derived to ensure that all the state trajectories of the system converge exponentially to a unique positive equilibrium. The effectiveness of the obtained results is illustrated by a numerical example.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1995-01-01
It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper.
Zhao, Shouwei
2011-06-01
A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.
NASA Astrophysics Data System (ADS)
Zhao, Shouwei
2011-06-01
A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.
On exponential stability of linear Levin-Nohel integro-differential equations
NASA Astrophysics Data System (ADS)
Tien Dung, Nguyen
2015-02-01
The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].
An approximation theorem for entire functions of exponential type and stability of zero sequences
Khabibullin, B N
2004-02-28
Let L be an entire function of exponential type in C with indicator function h{sub L}; let {lambda}={l_brace}{lambda}{sub n}{r_brace}, n=1,2,..., be a subsequence of zeros of the entire function of exponential type L{ne}0; let {gamma}={l_brace}{gamma}{sub n}{r_brace} be a complex number sequence and assume that {sigma}{sub n}|1/{lambda}{sub n} - 1/{gamma}{sub n}|<{infinity}. A simple construction of a sequence of entire functions of exponential type {l_brace}L{sub n}{r_brace} transforming {lambda} into a subsequence {gamma} of zeros of an entire function of exponential type G{ne}0 such that h{sub G}=h{sub L} is put forward (an approximation theorem). This result is applied to stability problems of zero sequences and non-uniqueness sequences for spaces of entire functions of exponential type with constraints on the indicators and to the problem of the stability of the completeness property of exponential systems in the space of germs of analytic functions on a compact convex set.
Exponential stability of discrete-time genetic regulatory networks with delays.
Cao, Jinde; Ren, Fengli
2008-03-01
Discrete-time versions of the continuous-time genetic regulatory networks (GRNs) with SUM regulatory functions are formulated and studied in this letter. Sufficient conditions are derived to ensure the global exponential stability of the discrete-time GRNs with delays. An illustrative example is given to demonstrate the effectiveness of the obtained results.
NASA Astrophysics Data System (ADS)
Liu, Lei; Shen, Yi; Jiang, Feng
2012-09-01
This article discusses the exponential stability of nonlinear stochastic delay differential systems (SDDSs) whose coefficients obey the polynomial growth condition. Delay-dependent criteria on almost sure exponential stability and pth moment exponential stability of such SDDSs have been established. By applying some novel techniques, our criteria work for many SDDSs including some cases in which the ℒV operator has a complicated form, which seemingly prevents the existing results from being directly used. The range of order of moment exponential stability and the decay rate can be estimated through the coefficients of the system.
Probabilistic robust stabilization of fractional order systems with interval uncertainty.
Alagoz, Baris Baykant; Yeroglu, Celaleddin; Senol, Bilal; Ates, Abdullah
2015-07-01
This study investigates effects of fractional order perturbation on the robust stability of linear time invariant systems with interval uncertainty. For this propose, a probabilistic stability analysis method based on characteristic root region accommodation in the first Riemann sheet is developed for interval systems. Stability probability distribution is calculated with respect to value of fractional order. Thus, we can figure out the fractional order interval, which makes the system robust stable. Moreover, the dependence of robust stability on the fractional order perturbation is analyzed by calculating the order sensitivity of characteristic polynomials. This probabilistic approach is also used to develop a robust stabilization algorithm based on parametric perturbation strategy. We present numerical examples demonstrating utilization of stability probability distribution in robust stabilization problems of interval uncertain systems.
Hamed, Kaveh Akbari; Gregg, Robert D.
2016-01-01
This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059
Liu, Xiwei; Chen, Tianping
2016-03-01
In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent real-valued system. The network model is described by a continuous-time equation. There are two main differences of this paper with previous works: 1) time delays can be asynchronous, i.e., delays between different nodes are different, which make our model more general and 2) we prove the exponential convergence directly, while the existence and uniqueness of the equilibrium point is just a direct consequence of the exponential convergence. Using three generalized norms, we present some sufficient conditions for the uniqueness and global exponential stability of the equilibrium point for delayed complex-valued neural networks. These conditions in our results are less restrictive because of our consideration of the excitatory and inhibitory effects between neurons; so previous works of other researchers can be extended. Finally, some numerical simulations are given to demonstrate the correctness of our obtained results.
Global exponential stability of delayed competitive neural networks with different time scales.
Lu, Hongtao; He, Zhenya
2005-04-01
A competitive neural network model was recently proposed to describe the dynamics of cortical maps, where there are two types of memories: long-term and short-term memories. Such a network is characterized by a system of differential equations with two types of variables, one models the fast neural activity and the other models the slow modification of synaptic strength. In this paper, we introduce a time delay parameter into the neural network model to characterize the signal transmission delays in real neural systems and the finite switch speed in the circuit implementations of neural networks. Then, we analyze the global exponential stability of the delayed competitive neural networks with different time scales. We allow the model has non-differentiable and unbounded functions, and use the nonsmooth analysis techniques to prove the existence and uniqueness of the equilibrium, and derive a new sufficient condition ensuring global exponential stability of the networks.
Global exponential stability for switched memristive neural networks with time-varying delays.
Xin, Youming; Li, Yuxia; Cheng, Zunshui; Huang, Xia
2016-08-01
This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples. Copyright © 2016 Elsevier Ltd. All rights reserved.
Manivannan, R; Samidurai, R; Cao, Jinde; Alsaedi, Ahmed; Alsaadi, Fuad E
2017-03-01
This paper investigates the problems of exponential stability and dissipativity of generalized neural networks (GNNs) with time-varying delay signals. By constructing a novel Lyapunov-Krasovskii functionals (LKFs) with triple integral terms that contain more advantages of the state vectors of the neural networks, and the upper bound on the time-varying delay signals are formulated. We employ a new integral inequality technique (IIT), free-matrix-based (FMB) integral inequality approach, and Wirtinger double integral inequality (WDII) technique together with the reciprocally convex combination (RCC) approach to bound the time derivative of the LKFs. An improved exponential stability and strictly (Q,S,R)-γ-dissipative conditions of the addressed systems are represented by the linear matrix inequalities (LMIs). Finally, four interesting numerical examples are developed to verify the usefulness of the proposed method with a practical application to a biological network. Copyright © 2016 Elsevier Ltd. All rights reserved.
Computation of robustly stabilizing PID controllers for interval systems.
Matušů, Radek; Prokop, Roman
2016-01-01
The paper is focused on the computation of all possible robustly stabilizing Proportional-Integral-Derivative (PID) controllers for plants with interval uncertainty. The main idea of the proposed method is based on Tan's (et al.) technique for calculation of (nominally) stabilizing PI and PID controllers or robustly stabilizing PI controllers by means of plotting the stability boundary locus in either P-I plane or P-I-D space. Refinement of the existing method by consideration of 16 segment plants instead of 16 Kharitonov plants provides an elegant and efficient tool for finding all robustly stabilizing PID controllers for an interval system. The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example in which the uncertain mathematical model of an experimental oblique wing aircraft is robustly stabilized.
NASA Astrophysics Data System (ADS)
Tao, Qiang; Yang, Ying; Yao, Zheng-an
2017-10-01
An initial-boundary value problem for Hall-magnetohydrodynamics in one space dimension with general large initial data is investigated. We establish uniform pointwise positive lower and upper bounds of the density, which are independent of any length of time. Based on the bounds of the density and the skew-symmetric structure of the Hall term, we derive the global existence, uniqueness and exponential stability of strong solutions.
Xu, Changjin; Li, Peiluan; Pang, Yicheng
2016-12-01
In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).
Stagnation-point flow and heat transfer over an exponentially shrinking sheet: A stability analysis
NASA Astrophysics Data System (ADS)
Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah
2016-06-01
Numerical solutions for the stagnation-point flow and heat transfer over an exponentially shrinking sheet have been investigated. The governing boundary layer equations are transformed into an ordinary differential equation using a non-similar transformation. By using the bvp4c solver in MATLAB, the results of the equations can be solved numerically. Numerical results indicate that in certain parameter, the non-unique solutions for the velocity and the temperature do exist. A linear stability analysis shows that only one solution is linearly stable otherwise is unstable. Then, the stability analysis is performed to identify which solution is stable between the two non-unique solutions.
Yang, Shiju; Li, Chuandong; Huang, Tingwen
2016-03-01
The problem of exponential stabilization and synchronization for fuzzy model of memristive neural networks (MNNs) is investigated by using periodically intermittent control in this paper. Based on the knowledge of memristor and recurrent neural network, the model of MNNs is formulated. Some novel and useful stabilization criteria and synchronization conditions are then derived by using the Lyapunov functional and differential inequality techniques. It is worth noting that the methods used in this paper are also applied to fuzzy model for complex networks and general neural networks. Numerical simulations are also provided to verify the effectiveness of theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.
The Role of a Steepness Parameter in the Exponential Stability of a Model Problem. Numerical Aspects
NASA Astrophysics Data System (ADS)
Todorovic, N.
2011-06-01
The Nekhoroshev theorem considers quasi integrable Hamiltonians providing stability of actions in exponentially long times. One of the hypothesis required by the theorem is a mathematical condition called steepness. Nekhoroshev conjectured that different steepness properties should imply numerically observable differences in the stability times. After a recent study on this problem (Guzzo et al. 2011, Todorovic et al. 2011) we show some additional numerical results on the change of resonances and the diffusion laws produced by the increasing effect of steepness. The experiments are performed on a 4-dimensional steep symplectic map designed in a way that a parameter smoothly regulates the steepness properties in the model.
Robust stabilization, robust performance, and disturbance attenuation for uncertain linear systems
NASA Technical Reports Server (NTRS)
Wang, Yeih J.; Shieh, Leang S.; Sunkel, John W.
1992-01-01
This paper presents a linear quadratic regulator approach to the robust stabilization, robust performance, and disturbance attenuation of uncertain linear systems. The state-feedback designed systems provide both the robust stability with optimal performance and the disturbance attenuation with H-infinity-norm bounds. The proposed approach can be applied to matched and/or mismatched uncertain linear systems. For a matched uncertain linear system, it is shown that the disturbance attenuation robust-stabilizing controllers with or without optimal performance always exist and can be easily determined without searching; whereas, for a mismatched uncertain linear system, the introduced tuning parameters greatly enhance the flexibility of finding the disturbance-attenuation robust-stabilizing controllers.
Wavelet Filtering to Reduce Conservatism in Aeroservoelastic Robust Stability Margins
NASA Technical Reports Server (NTRS)
Brenner, Marty; Lind, Rick
1998-01-01
Wavelet analysis for filtering and system identification was used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins was reduced with parametric and nonparametric time-frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data was used to reduce the effects of external desirableness and unmodeled dynamics. Parametric estimates of modal stability were also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. F-18 high Alpha Research Vehicle aeroservoelastic flight test data demonstrated improved robust stability prediction by extension of the stability boundary beyond the flight regime.
On-Line Robust Modal Stability Prediction using Wavelet Processing
NASA Technical Reports Server (NTRS)
Brenner, Martin J.; Lind, Rick
1998-01-01
Wavelet analysis for filtering and system identification has been used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins is reduced with parametric and nonparametric time- frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. The F-18 High Alpha Research Vehicle aeroservoelastic flight test data demonstrates improved robust stability prediction by extension of the stability boundary beyond the flight regime. Guidelines and computation times are presented to show the efficiency and practical aspects of these procedures for on-line implementation. Feasibility of the method is shown for processing flight data from time- varying nonstationary test points.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-07-01
In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations. Copyright © 2016 Elsevier Ltd. All rights reserved.
Generic super-exponential stability of elliptic equilibrium positions for symplectic vector fields
NASA Astrophysics Data System (ADS)
Niederman, Laurent
2013-11-01
In this article, we consider linearly stable elliptic fixed points (equilibrium) for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. We will focus on the neighborhood of elliptic fixed points but the case of linearly stable isotropic reducible invariant tori in a Hamiltonian system should be similar. More specifically, Morbidelli and Giorgilli have proved a result of stability over superexponentially long times if one considers an analytic Lagrangian torus, invariant for an analytic Hamiltonian system, with a diophantine translation vector which admits a sign-definite torsion. Then, the solutions of the system move very little over times which are super-exponentially long with respect to the inverse of the distance to the invariant torus. The proof proceeds in two steps: first one constructs a high-order Birkhoff normal form, then one applies the Nekhoroshev theory. Bounemoura has shown that the second step of this construction remains valid if the Birkhoff normal form linked to the invariant torus or the elliptic fixed point belongs to a generic set among the formal series. This is not sufficient to prove this kind of super-exponential stability results in a general setting. We should also establish that the most strongly non resonant elliptic fixed point or invariant torus in a Hamiltonian system admits Birkhoff normal forms fitted for the application of the Nekhoroshev theory. Actually, the set introduced by Bounemoura is already very large but not big enough to ensure that a typical Birkhoff normal form falls into this class. We show here that this property is satisfied generically in the sense of the measure (prevalence) through infinite-dimensional probe spaces (that is, an infinite number of parameters chosen at random) with methods similar to those developed in a paper of Gorodetski, Kaloshin and Hunt in another setting.
Yielding Elastic Tethers Stabilize Robust Cell Adhesion
Whitfield, Matt J.; Luo, Jonathon P.; Thomas, Wendy E.
2014-01-01
Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds. PMID:25473833
NASA Astrophysics Data System (ADS)
Grobbelaar-Van Dalsen, Marié
2015-08-01
This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.
Exponential stabilization for sampled-data neural-network-based control systems.
Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian
2014-12-01
This paper investigates the problem of sampled-data stabilization for neural-network-based control systems with an optimal guaranteed cost. Using time-dependent Lyapunov functional approach, some novel conditions are proposed to guarantee the closed-loop systems exponentially stable, which fully use the available information about the actual sampling pattern. Based on the derived conditions, the design methods of the desired sampled-data three-layer fully connected feedforward neural-network-based controller are established to obtain the largest sampling interval and the smallest upper bound of the cost function. A practical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.
Zhou, Liqun; Zhang, Yanyan
2016-01-01
In this paper, a class of recurrent neural networks with multi-proportional delays is studied. The nonlinear transformation transforms a class of recurrent neural networks with multi-proportional delays into a class of recurrent neural networks with constant delays and time-varying coefficients. By constructing Lyapunov functional and establishing the delay differential inequality, several delay-dependent and delay-independent sufficient conditions are derived to ensure global exponential periodicity and stability of the system. And several examples and their simulations are given to illustrate the effectiveness of obtained results.
NASA Astrophysics Data System (ADS)
Louihi, M.; Hbid, M. L.
2007-05-01
In this paper we are concerned with the exponential asymptotic stability of the solution of a class of differential equations with state dependent delays. Our approach is based on the Crandall-Liggett approximation and the properties of semigroups.
Zhang, Guodong; Shen, Yi
2015-11-01
This paper is concerned with the global exponential stability on a class of delayed neural networks with state-dependent switching. Under the novel conditions, some sufficient criteria ensuring exponential stability of the proposed system are obtained. In particular, the obtained conditions complement and improve earlier publications on conventional neural networks with continuous or discontinuous right-hand side. Numerical simulations are also presented to illustrate the effectiveness of the obtained results.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1994-01-01
Nonlinear control using feedback linearization or inverse dynamics for robotic manipulators yields good results in the absence of modeling uncertainty. However, modeling uncertainties due to unknown joint friction coefficients and payload variations can give rise to undesirable characteristics when these control systems are implemented. It is shown how passivity concepts can be used to supplement the feedback linearization control design technique, in order to make it robust with respect to the uncertain effects mentioned above. Results are obtained for space manipulators with freely floating base; however, they are applicable to fixed base manipulators as well. The controller guarantees asymptotic tracking of the joint variables. Closed-loop simulation results are illustrated for planar space manipulators for cases where uncertainty exists in friction modeling and payload inertial parameters.
Robust stability of positive switched systems with dwell time
NASA Astrophysics Data System (ADS)
Liu, Jinjin; Zhang, Kanjian; Wei, Haikun
2016-08-01
This paper studies robust stability of positive switched systems (PSSs) with polytopic uncertainties in both discrete-time and continuous-time contexts. By using multiple linear copositive Lyapunov functions, a sufficient condition for stability of PSSs with dwell time is addressed. Being different from time-invariant multiple linear copositive Lyapunov functions, the Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. Then, robust stability of PSSs with polytopic uncertainties is solved. All conditions are solvable via linear programming. Finally, illustrative examples are given to demonstrate the validity of the proposed results.
Robust Stabilization, Robust Performance, and Disturbance Attenuation for Uncertain Linear Systems
1992-01-01
the following Riccati equation: [ - ] B Tp+!I+ 1 CTC+Q=O. (7) Then, a disturbance-attenuation robust- stabilizing control law is given by u(t) = K z(t...disturbance-attenuation robust- stabilizing control law with the attenuation constant 6 is given by u(t) = K x(t), where K = -- BT P with 7> 1/2... stabilizing control law with the attenuation constant 6 is given by u(t) = K z(t), where K = -7 BT P with 7> - 1/2. Furthermore, the state-feedback
Robust Stabilization of a Class of passive Nonlinear Systems
NASA Technical Reports Server (NTRS)
Joshi, Suresh M.; Kelkar, Atul G.
1996-01-01
The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.
Absolute exponential stability of recurrent neural networks with generalized activation function.
Xu, Jun; Cao, Yong-Yan; Sun, Youxian; Tang, Jinshan
2008-06-01
In this paper, the recurrent neural networks (RNNs) with a generalized activation function class is proposed. In this proposed model, every component of the neuron's activation function belongs to a convex hull which is bounded by two odd symmetric piecewise linear functions that are convex or concave over the real space. All of the convex hulls are composed of generalized activation function classes. The novel activation function class is not only with a more flexible and more specific description of the activation functions than other function classes but it also generalizes some traditional activation function classes. The absolute exponential stability (AEST) of the RNN with a generalized activation function class is studied through three steps. The first step is to demonstrate the global exponential stability (GES) of the equilibrium point of original RNN with a generalized activation function being equivalent to that of RNN under all vertex functions of convex hull. The second step transforms the RNN under every vertex activation function into neural networks under an array of saturated linear activation functions. Because the GES of the equilibrium point of three systems are equivalent, the next stability analysis focuses on the GES of the equilibrium point of RNN system under an array of saturated linear activation functions. The last step is to study both the existence of equilibrium point and the GES of the RNN under saturated linear activation functions using the theory of M-matrix. In the end, a two-neuron RNN with a generalized activation function is constructed to show the effectiveness of our results.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-09-01
This paper investigates the stability problem for a class of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. By employing the idea of vector Lyapunov function, M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point. When the impulsive effects are not considered, several sufficient conditions are also given to guarantee the existence, uniqueness and global exponential stability of equilibrium point. Two examples are given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results.
Robust stability analysis of uncertain switched linear systems with unstable subsystems
NASA Astrophysics Data System (ADS)
Yu, Qiang; Wu, Baowei
2015-05-01
The problem of robust stability for switched linear systems with all the subsystems being unstable is investigated. Unlike the most existing results in which each switching mode in the system is asymptotically stable, the subsystems may be unstable in this paper. A necessary condition of stability for switched linear systems is first obtained with certain hypothesis. Then, under two assumptions, sufficient conditions of exponential stability for both deterministic and uncertain switched linear systems are presented by using the invariant subspace theory and average dwell time method. Moreover, we further develop multiple Lyapunov functions and propose a method for constructing multiple Lyapunov functions for the considered switched linear systems with certain switching law. Several examples are included to show the effectiveness of the theoretical findings.
Wehbe, Ali; Youssef, Wael
2010-10-15
In this paper, we study the energy decay rate for the elastic Bresse system in one-dimensional bounded domain. The physical system consists of three wave equations. The two wave equations about the rotation angle and the longitudinal displacement are damped by two locally distributed feedbacks at the neighborhood of the boundary. Then indirect damping is applied to the equation for the transverse displacement of the beam through the coupling terms. We will establish the exponential stability for this system in the case of the same speed of propagation in the equation for the vertical displacement and the equation for the rotation angle of the system. When the wave speeds are different, nonexponential decay rate is proved and a polynomial-type decay rate is obtained. The frequency domain method and the multiplier technique are applied.
Robust stability analysis of linear systems with parametric uncertainty
NASA Astrophysics Data System (ADS)
Zhai, Ding; Zhang, Qing-Ling; Liu, Guo-Yi
2012-09-01
This article is concerned with the problem of robust stability analysis of linear systems with uncertain parameters. By constructing an equivalent system with positive uncertain parameters and using the properties of these parameters, a new stability analysis condition is derived. Due to making use of the properties of uncertain parameters, the new proposed method has potential to give less conservative results than the existing approaches. A numerical example is given to illustrate the effectiveness of the proposed method.
Use of a genetic algorithm to analyze robust stability problems
Murdock, T.M.; Schmitendorf, W.E.; Forrest, S.
1990-01-01
This note resents a genetic algorithm technique for testing the stability of a characteristic polynomial whose coefficients are functions of unknown but bounded parameters. This technique is fast and can handle a large number of parametric uncertainties. We also use this method to determine robust stability margins for uncertain polynomials. Several benchmark examples are included to illustrate the two uses of the algorithm. 27 refs., 4 figs.
Xi, Qiang
2016-01-01
In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results.
Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts
NASA Technical Reports Server (NTRS)
Gupta, Sandeep
1996-01-01
Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.
Robustness for slope stability modelling under deep uncertainty
NASA Astrophysics Data System (ADS)
Almeida, Susana; Holcombe, Liz; Pianosi, Francesca; Wagener, Thorsten
2015-04-01
Landslides can have large negative societal and economic impacts, such as loss of life and damage to infrastructure. However, the ability of slope stability assessment to guide management is limited by high levels of uncertainty in model predictions. Many of these uncertainties cannot be easily quantified, such as those linked to climate change and other future socio-economic conditions, restricting the usefulness of traditional decision analysis tools. Deep uncertainty can be managed more effectively by developing robust, but not necessarily optimal, policies that are expected to perform adequately under a wide range of future conditions. Robust strategies are particularly valuable when the consequences of taking a wrong decision are high as is often the case of when managing natural hazard risks such as landslides. In our work a physically based numerical model of hydrologically induced slope instability (the Combined Hydrology and Stability Model - CHASM) is applied together with robust decision making to evaluate the most important uncertainties (storm events, groundwater conditions, surface cover, slope geometry, material strata and geotechnical properties) affecting slope stability. Specifically, impacts of climate change on long-term slope stability are incorporated, accounting for the deep uncertainty in future climate projections. Our findings highlight the potential of robust decision making to aid decision support for landslide hazard reduction and risk management under conditions of deep uncertainty.
Sun, Yeong-Jeu; Wu, Yu-Biaw; Wang, Ching-Cheng
2013-06-01
In this study, the concept of global exponential ε-stabilization is introduced and the robust stabilization for a class of nonlinear systems with single input is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, a feedback control is proposed to realize the global stabilization of such nonlinear systems with any pre-specified exponential convergence rate. The guaranteed exponential convergence rate can be also correctly estimated. This result can be straightforwardly applicable to some famous chaotic systems. Besides, it will be proven that a single and linear control, with lower dimensions than that of the states, can realize the global exponential stability of some famous chaotic systems. Finally, comparisons of our main results with recently published results as well as numerical examples with circuit realization are provided to show the effectiveness and superiority of the obtained results.
NASA Astrophysics Data System (ADS)
Sun, Yeong-Jeu; Wu, Yu-Biaw; Wang, Ching-Cheng
2013-06-01
In this study, the concept of global exponential ɛ-stabilization is introduced and the robust stabilization for a class of nonlinear systems with single input is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, a feedback control is proposed to realize the global stabilization of such nonlinear systems with any pre-specified exponential convergence rate. The guaranteed exponential convergence rate can be also correctly estimated. This result can be straightforwardly applicable to some famous chaotic systems. Besides, it will be proven that a single and linear control, with lower dimensions than that of the states, can realize the global exponential stability of some famous chaotic systems. Finally, comparisons of our main results with recently published results as well as numerical examples with circuit realization are provided to show the effectiveness and superiority of the obtained results.
Decentralized adaptive control of robot manipulators with robust stabilization design
NASA Technical Reports Server (NTRS)
Yuan, Bau-San; Book, Wayne J.
1988-01-01
Due to geometric nonlinearities and complex dynamics, a decentralized technique for adaptive control for multilink robot arms is attractive. Lyapunov-function theory for stability analysis provides an approach to robust stabilization. Each joint of the arm is treated as a component subsystem. The adaptive controller is made locally stable with servo signals including proportional and integral gains. This results in the bound on the dynamical interactions with other subsystems. A nonlinear controller which stabilizes the system with uniform boundedness is used to improve the robustness properties of the overall system. As a result, the robot tracks the reference trajectories with convergence. This strategy makes computation simple and therefore facilitates real-time implementation.
Robust stability of diamond families of polynomials with complex coefficients
NASA Technical Reports Server (NTRS)
Xu, Zhong Ling
1993-01-01
Like the interval model of Kharitonov, the diamond model proves to be an alternative powerful device for taking into account the variation of parameters in prescribed ranges. The robust stability of some kinds of diamond polynomial families with complex coefficients are discussed. By exploiting the geometric characterizations of their value sets, we show that, for the family of polynomials with complex coefficients and both their real and imaginary parts lying in a diamond, the stability of eight specially selected extreme point polynomials is necessary as well as sufficient for the stability of the whole family. For the so-called simplex family of polynomials, four extreme point and four exposed edge polynomials of this family need to be checked for the stability of the entire family. The relations between the stability of various diamonds are also discussed.
Zhang, Guodong; Shen, Yi
2015-07-01
This paper is concerned with the global exponential stabilization of memristor-based chaotic neural networks with both time-varying delays and general activation functions. Here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new sufficient conditions ensuring exponential stabilization of memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the proposed results here are easy to verify and they also extend the earlier publications. Finally, numerical simulations illustrate the effectiveness of the obtained results.
Zeng, Zhigang; Wang, Jun
2006-12-01
This paper presents new theoretical results on the global exponential stability of recurrent neural networks with bounded activation functions and bounded time-varying delays in the presence of strong external stimuli. It is shown that the Cohen-Grossberg neural network is globally exponentially stable, if the absolute value of the input vector exceeds a criterion. As special cases, the Hopfield neural network and the cellular neural network are examined in detail. In addition, it is shown that criteria herein, if partially satisfied, can still be used in combination with existing stability conditions. Simulation results are also discussed in two illustrative examples.
Gong, Weiqiang; Liang, Jinling; Cao, Jinde
2015-10-01
In this paper, based on the matrix measure method and the Halanay inequality, global exponential stability problem is investigated for the complex-valued recurrent neural networks with time-varying delays. Without constructing any Lyapunov functions, several sufficient criteria are obtained to ascertain the global exponential stability of the addressed complex-valued neural networks under different activation functions. Here, the activation functions are no longer assumed to be derivative which is always demanded in relating references. In addition, the obtained results are easy to be verified and implemented in practice. Finally, two examples are given to illustrate the effectiveness of the obtained results.
Robust stabilization of rotor-active magnetic bearing systems
NASA Astrophysics Data System (ADS)
Li, Guoxin
Active magnetic bearings (AMBs) are emerging as a beneficial technology for high-speed and high-performance suspensions in rotating machinery applications. A fundamental feedback control problem is robust stabilization in the presence of uncertain destabilizing mechanisms in aeroelastic, hydroelastic dynamics, and AMB feedback. As rotating machines are evolving in achieving high speed, high energy density, and high performance, the rotor and the support structure become increasingly flexible, and highly coupled. This makes rotor-AMB system more challenging to stabilize. The primary objective of this research is to develop a systematic control synthesis procedure for achieving highly robust stabilization of rotor-AMB systems. Of special interest is the stabilization of multivariable systems such as the AMB supported flexible rotors and gyroscopic rotors, where the classical control design may encounter difficulties. To this end, we first developed a systematic modeling procedure. This modeling procedure exploited the best advantages of technology developed in rotordynamics and the unique system identification tool provided by the AMBs. A systematic uncertainty model for rotor-AMB systems was developed, eliminating the iterative process of selecting uncertainty structures. The consequences of overestimation or underestimation of uncertainties were made transparent to control engineers. To achieve high robustness, we explored the fundamental performance/robustness limitations due to rotor-AMB system unstable poles. We examined the mixed sensitivity performance that is closely related to the unstructured uncertainty. To enhance transparency of the synthesis, we analyzed multivariable controllers from classical control perspectives. Based on these results, a systematic robust control synthesis procedure was established. For a strong gyroscopic rotor over a wide speed range, we applied the advanced gain-scheduled synthesis, and compared two synthesis frameworks in
Impact of pilots' biodynamic feedthrough on rotorcraft by robust stability
NASA Astrophysics Data System (ADS)
Quaranta, Giuseppe; Masarati, Pierangelo; Venrooij, Joost
2013-09-01
The coupling of rotorcraft dynamics with the dynamics of one of the main systems devoted to its control, the pilot, may lead to several peculiar phenomena, known as Rotorcraft-Pilot Couplings (RPCs), all characterized by an abnormal behavior that may jeopardize flight safety. Among these phenomena, there is a special class of couplings which is dominated by the biodynamic behavior of the pilot's limbs that close the loop between the vibrations and the control inceptors in the cockpit. Leveraging robust stability analysis, the inherently uncertain pilot biodynamics can be treated as the uncertain portion of a feedback system, making analytical, numerical or graphical determination of proneness to RPC possible by comparing robust stability margins of helicopter models with experimental Biodynamic Feedthrough (BDFT) data. The application of the proposed approach to collective bounce is exemplified using simple analytical helicopter and pilot models. The approach is also applied to detailed helicopter models and experimental BDFT measurement data.
NASA Astrophysics Data System (ADS)
Lu, Junjie; She, Zhikun
2016-11-01
In this paper, we investigate sufficient and necessary conditions of uniform local exponential stability (ULES) for the discrete-time nonlinear switched system (DTNSS). We start with the definition of T-step common Lyapunov functions (CLFs), which is a relaxation of traditional CLFs. Then, for a time-varying DTNSS, by constructing such a T-step CLF, a necessary and sufficient condition for its ULES is provided. Afterwards, we strengthen it based on a T-step Lipschitz continuous CLF. Especially, when the system is time-invariant, by the smooth approximation theorem, the Lipschitz continuity condition of T-step CLFs can further be replaced by continuous differentiability; and when the system is time-invariant and homogeneous, due to the extension of Weierstrass approximation theorem, T-step continuously differentiable CLFs can even be strengthened to be T-step polynomial CLFs. Furthermore, three illustrative examples are additionally used to explain our main contribution. In the end, an equivalence between time-varying DTNSSs and their corresponding linearisations is discussed.
Yang, Xinsong; Cui, Xiangzhao; Long, Yao
2009-09-01
A class of cellular neural networks difference equation with delays and impulses are considered. Sufficient conditions for the existence and global exponential stability of periodic solution are obtained by using contraction mapping theorem and inequality techniques. The results of this paper are completely new. A numerical example and its simulations are offered to show the effectiveness of our new results.
Li, Bing; Li, Yongkun; Zhang, Xuemei
2016-01-01
In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).
Zhang, Wei; Huang, Tingwen; He, Xing; Li, Chuandong
2017-11-01
In this study, we investigate the global exponential stability of inertial memristor-based neural networks with impulses and time-varying delays. We construct inertial memristor-based neural networks based on the characteristics of the inertial neural networks and memristor. Impulses with and without delays are considered when modeling the inertial neural networks simultaneously, which are of great practical significance in the current study. Some sufficient conditions are derived under the framework of the Lyapunov stability method, as well as an extended Halanay differential inequality and a new delay impulsive differential inequality, which depend on impulses with and without delays, in order to guarantee the global exponential stability of the inertial memristor-based neural networks. Finally, two numerical examples are provided to illustrate the efficiency of the proposed methods. Copyright © 2017 Elsevier Ltd. All rights reserved.
Impossibility of unconditional stability and robustness of diffusive acceleration schemes
Azmy, Y.Y.
1998-01-01
The authors construct a problem for which exists no preconditioner with a cell-centered diffusion coupling stencil that is unconditionally stable and robust. In particular they consider an asymptotic limit of the Periodic Horizontal Interface (PHI) configuration wherein the cell height in both layers approaches zero like {sigma}{sup 2} while the total cross section varies like a in one layer and like 1/{sigma} in the other layer. In such case they show that the conditions for stability and robustness of the flat eigenmodes of the iteration residual imply instability of the modes flat in the y-dimension and rapidly varying in the x-dimension. This paper is important for radiation transport studies.
Ma, Yingdong; Lu, Junguo; Chen, Weidong
2014-03-01
This paper investigates the robust stability and stabilization of fractional order linear systems with positive real uncertainty. Firstly, sufficient conditions for the asymptotical stability of such uncertain fractional order systems are presented. Secondly, the existence conditions and design methods of the state feedback controller, static output feedback controller and observer-based controller for asymptotically stabilizing such uncertain fractional order systems are derived. The results are obtained in terms of linear matrix inequalities. Finally, some numerical examples are given to validate the proposed theoretical results. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Zhang, Ancai; Qiu, Jianlong; She, Jinhua
2014-02-01
This paper concerns the existence and exponential stability of periodic solution for the high-order discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. First, we present the criteria for the existence of periodic solution based on the continuation theorem of coincidence degree theory and the Young's inequality, and then we give the criteria for the global exponential stability of periodic solution by using a non-Lyapunov method. After that, we give a numerical example that demonstrates the effectiveness of the theoretical results. The criteria presented in this paper are easy to verify. In addition, the proposed analysis method is easy to extend to other high-order neural networks.
Implementation of Robust Stability Augmentation Systems for a Blimp
NASA Astrophysics Data System (ADS)
Mo, Yong-Hwan; Kawashima, Mitsutoyo; Goto, Norihiro
This paper applies robust control techniques to a blimp. The project “Mine Detection System Using Blimps” is in progress. The aim of the project is the development of a practical technique for the autonomous detection of landmines and their positions. In order for a blimp to perform observation and detection, precise flight path control is needed. The error resulting from modeling a real system cannot be avoided, however accurate the model is. In order to aim for realistic control, robust control can compensate model uncertainty. In the two-motion models presented (experimental model and analytical model), it was found that since the yawing motion mode is unstable, lateral-directional movement becomes unstable. This paper proposes a robust stability augmentation system for the yawing motion of the blimp developed for the project. The numerical simulation presents a comparison between a Kharitonov theory controller and a H∞ theory controller. The experimental results show that control of the blimp using a H∞ controller is more suitable for the project objective. An emphasis is placed on implementation of the controller.
NASA Astrophysics Data System (ADS)
Arthi, G.; Park, Ju H.; Jung, H. Y.
2016-03-01
In this paper, we establish the results on existence and uniqueness of mild solution of impulsive neutral stochastic integrodifferential equations driven by a fractional Brownian motion. Further, by using an impulsive integral inequality, some novel sufficient conditions are derived to ensure the exponential stability of mild solution in the mean square moment. The results are obtained by utilizing the fractional power of operators and the semigroup theory. Finally, an example is presented to demonstrate the effectiveness of the proposed result.
Wag, Meng; Qiu, Jianbin; Chadli, Mohammed; Wang, Mao
2016-12-01
This paper investigates the problem of exponential stabilization for sampled-data Takagi-Sugeno (T-S) fuzzy control systems with packet dropouts. An input delay approach is adopted to model the sample-and-hold behavior with a time-varying delayed control input, and a switched system approach is proposed to model the data-missing phenomenon. On this basis, the sampled-data T-S fuzzy control system with packet dropouts is modeled as a switched T-S fuzzy system with time-varying delay. The objective is to design a sampled-data fuzzy controller to guarantee the exponential stability of the resulting closed-loop system. Based on a new piecewise time-dependent Lyapunov functional, a novel sufficient condition is derived for the existence of exponentially stabilizing sampled-data fuzzy controllers. All the solutions to the problem are formulated in the form of linear matrix inequalities. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.
Huang, Haiying; Du, Qiaosheng; Kang, Xibing
2013-11-01
In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results.
NASA Astrophysics Data System (ADS)
Zhong, Kai; Zhu, Song; Yang, Qiqi
2016-11-01
In recent years, the stability problems of memristor-based neural networks have been studied extensively. This paper not only takes the unavoidable noise into consideration but also investigates the global exponential stability of stochastic memristor-based neural networks with time-varying delays. The obtained criteria are essentially new and complement previously known ones, which can be easily validated with the parameters of system itself. In addition, the study of the nonlinear dynamics for the addressed neural networks may be helpful in qualitative analysis for general stochastic systems. Finally, two numerical examples are provided to substantiate our results.
Robust enzyme design: bioinformatic tools for improved protein stability.
Suplatov, Dmitry; Voevodin, Vladimir; Švedas, Vytas
2015-03-01
The ability of proteins and enzymes to maintain a functionally active conformation under adverse environmental conditions is an important feature of biocatalysts, vaccines, and biopharmaceutical proteins. From an evolutionary perspective, robust stability of proteins improves their biological fitness and allows for further optimization. Viewed from an industrial perspective, enzyme stability is crucial for the practical application of enzymes under the required reaction conditions. In this review, we analyze bioinformatic-driven strategies that are used to predict structural changes that can be applied to wild type proteins in order to produce more stable variants. The most commonly employed techniques can be classified into stochastic approaches, empirical or systematic rational design strategies, and design of chimeric proteins. We conclude that bioinformatic analysis can be efficiently used to study large protein superfamilies systematically as well as to predict particular structural changes which increase enzyme stability. Evolution has created a diversity of protein properties that are encoded in genomic sequences and structural data. Bioinformatics has the power to uncover this evolutionary code and provide a reproducible selection of hotspots - key residues to be mutated in order to produce more stable and functionally diverse proteins and enzymes. Further development of systematic bioinformatic procedures is needed to organize and analyze sequences and structures of proteins within large superfamilies and to link them to function, as well as to provide knowledge-based predictions for experimental evaluation.
NASA Astrophysics Data System (ADS)
Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan
2016-11-01
Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.
Lack of exponential stability to Timoshenko system with viscoelastic Kelvin-Voigt type
NASA Astrophysics Data System (ADS)
Malacarne, Andréia; Muñoz Rivera, Jaime Edilberto
2016-06-01
We study the Timoshenko systems with a viscoelastic dissipative mechanism of Kelvin-Voigt type. We prove that the model is analytical if and only if the viscoelastic damping is present in both the shear stress and the bending moment. Otherwise, the corresponding semigroup is not exponentially stable no matter the choice of the coefficients. This result is different to all others related to Timoshenko model with partial dissipation, which establish that the system is exponentially stable if and only if the wave speeds are equal. Finally, we show that the solution decays polynomially to zero as {t^{-1/2}} , no matter where the viscoelastic mechanism is effective and that the rate is optimal whenever the initial data are taken on the domain of the infinitesimal operator.
NASA Astrophysics Data System (ADS)
Kong, Huihui; Li, Hai-Liang; Liang, Chuangchuang; Zhang, Guojing
2017-10-01
The initial boundary value problem for the compressible barotropic Navier-Stokes equations is investigated in the case that the initial density has a jump discontinuity across an interior closed curve in two-dimensional bounded domain. If the initial data is a small perturbation of the constant state and the interior closed curve is near a circle inside the domain, the global existence and large time behavior of the piecewise strong solution is shown, in particular, the jump of the fluid density across the convecting curve decays exponentially in time.
NASA Astrophysics Data System (ADS)
Liu, Wenjun
2014-11-01
In this paper, we consider a wave equation with space variable coefficients. Due to physical considerations, a distributed delay damping is acted on the part of the boundary. Under suitable assumptions, we prove the exponential stability of the energy based on the use of Riemannian geometry method, the perturbed energy argument, and some observability inequalities. From the applications point of view, our results may provide some qualitative analysis and intuition for the researchers in fields such as engineering, biophysics, and mechanics. And the method is rather general and can be adapted to other evolution systems with variable coefficients (e. g. elasticity plates) as well.
NASA Astrophysics Data System (ADS)
Zhang, Jianlin
2017-04-01
In this paper, we study a large time behavior of the global spherically or cylindrically symmetric solutions in H 1 for the compressible viscous radiative and reactive gas in multi-dimension with large initial data. Precisely, if the initial data are spherically symmetric or cylindrically symmetric, the smallness of initial data is not needed. The main concern of the present paper is to investigate the exponential stability of a solution toward the stationary solution as time goes to infinity. We obtain the uniform positive lower and upper bounds of the density by using different methods.
The 32nd CDC: Robust stabilizer synthesis for interval plants using Nevanlina-pick theory
NASA Technical Reports Server (NTRS)
Bhattacharya, Saikat; Keel, L. H.; Bhattacharyya, S. P.
1989-01-01
The synthesis of robustly stabilizing compensators for interval plants, i.e., plants whose parameters vary within prescribed ranges is discussed. Well-known H(sup infinity) methods are used to establish robust stabilizability conditions for a family of plants and also to synthesize controllers that would stabilize the whole family. Though conservative, these methods give a very simple way to come up with a family of robust stabilizers for an interval plant.
The Parameterization of All Robust Stabilizing Simple Repetitive Controllers
NASA Astrophysics Data System (ADS)
Yamada, Kou; Sakanushi, Tatsuya; Ando, Yoshinori; Hagiwara, Takaaki; Murakami, Iwanori; Takenaga, Hiroshi; Tanaka, Hiroshi; Matsuura, Shun
The modified repetitive control system is a type of servomechanism for the periodic reference input. That is, the modified repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or an uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plant does not include time-delay, transfer functions from the periodic reference input to the output and from the disturbance to the output have infinite numbers of poles. When transfer functions from the periodic reference input to the output and from the disturbance to the output have infinite numbers of poles, it is difficult to specify the input-output characteristic and the disturbance attenuation characteristic. From the practical point of view, it is desirable that the input-output characteristic and the disturbance attenuation characteristic are easily specified. In order to specify the input-output characteristic and the disturbance attenuation characteristic easily, transfer functions from the periodic reference input to the output and from the disturbance to the output are desirable to have finite numbers of poles. From this viewpoint, Yamada et al. proposed the concept of simple repetitive control systems such that the controller works as a modified repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. In addition, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. However, the method by Yamada et al. cannot be applied for the plant with uncertainty. The purpose of this paper is to propose the parameterization of all robust stabilizing simple repetitive controllers for the plant with uncertainty.
A design method for robust stabilizing simple repetitive control systems
NASA Astrophysics Data System (ADS)
Yamada, Kou; Takenaga, Hiroshi; Tanaka, Hiroshi
2007-12-01
The modified repetitive control system is a type of servomechanism for the periodic reference input. That is, the modified repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plants does not includes time-delay, the transfer function from the periodic reference input to the output and that from the disturbance to the output have an infinite number of poles. When the transfer function from the periodic reference input to the output and that from the disturbance to the output have an infinite number of poles, it is difficult to specify the input-output characteristic and the disturbance attenuation characteristic. From the practical point of view, it is desirable that the input-output characteristic and the disturbance attenuation characteristic are easily specified. In order to specify the input-output characteristic and the disturbance attenuation characteristic easily, the transfer function from the periodic reference input to the output and that from the disturbance to the output are desirable to have a finite number of poles. Yamada et al. proposed the concept of simple repetitive control systems such that the controller works as a modified repetitive controller and the transfer function from the periodic reference input to the output and that from the disturbance to the output have a finite number of poles. In addition, Yamada et al. clarified the parametrization of all stabilizing simple repetitive controllers. However the method by Yamada et al. cannot be applied for the plant with uncertainty. The purpose of this paper is to propose the parametrization of all robust stabilizing simple repetitive controllers for the plant with uncertainty.
Liang, X B; Si, J
2001-01-01
This paper investigates the existence, uniqueness, and global exponential stability (GES) of the equilibrium point for a large class of neural networks with globally Lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations. The provided sufficient condition for GES is mild and some conditions easily examined in practice are also presented. The GES of neural networks in the case of locally Lipschitz continuous activations is also obtained under an appropriate condition. The analysis results given in the paper extend substantially the existing relevant stability results in the literature, and therefore expand significantly the application range of neural networks in solving optimization problems. As a demonstration, we apply the obtained analysis results to the design of a recurrent neural network (RNN) for solving the linear variational inequality problem (VIP) defined on any nonempty and closed box set, which includes the box constrained quadratic programming and the linear complementarity problem as the special cases. It can be inferred that the linear VIP has a unique solution for the class of Lyapunov diagonally stable matrices, and that the synthesized RNN is globally exponentially convergent to the unique solution. Some illustrative simulation examples are also given.
NASA Technical Reports Server (NTRS)
Blackwell, C. C.
1987-01-01
A relevant facet of the application of Lyapunov gradient-generated robust control to unstable linear autonomous plants is explored. It is demonstrated that if the plant, the output, and the nominal stabilizing control satisfy certain conditions, then the robust component alone stabilizes the nominal plant. An example characterized by two zero eigenvalues and two negative real value poles is presented. These results assure that the robust component will fulfill the role of nominal stabilization successfully so long as the possible magnitude of the robust component can overcome the contribution of the instability to positiveness of the Lyapunov rate.
NASA Astrophysics Data System (ADS)
Li, Yongkun; Liu, Chunchao; Zhu, Lifei
2005-03-01
By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence and stability of periodic solution for shunting inhibitory cellular neural networks (SICNNs) with delays x˙ij(t)=-aij(t)xij(t)-∑Bkl∈Nr(i,j)Bijkl(t)fij(xkl(t))xij(t)-∑Ckl∈Nr(i,j)Cijkl(t)gij(xkl(t-τkl))xij(t)+Lij(t).
Analysis and synthesis of HVDC controls for robust stability of power systems
Venkataraman, S.; Khammash, M.H.; Vittal, V.
1995-11-01
High Voltage DC (HVDC) links have controllable characteristics with potential for affecting system stability. This paper follows the robustness methodology procedure to analyze the stability robustness of HVDC controls in power systems over a range of operating conditions. A novel method to design power system controllers using the robustness methodology is also proposed. Numerical results for a sample test-system are obtained and compared with those obtained by conventional techniques.
Li, Hongfei; Jiang, Haijun; Hu, Cheng
2016-03-01
In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.
Apalara, Tijani A.; Messaoudi, Salim A.
2015-06-15
In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question.
Robustness of fuzzy logic power system stabilizers applied to multimachine power system
Hiyama, Takashi . Dept. of Electrical Engineering and Computer Science)
1994-09-01
This paper investigates the robustness of fuzzy logic stabilizers using the information of speed and acceleration states of a study unit. The input signals are the real power output and/or the speed of the study unit. Non-linear simulations show the robustness of the fuzzy logic power system stabilizers. Experiments are also performed by using a micro-machine system. The results show the feasibility of proposed fuzzy logic stabilizer.
Robust stability and performance of time-delay control systems.
Keviczky, L; Bányász, Cs
2007-04-01
Most of the optimal and adaptive regulators assume an a priori known time delay. The time-delay mismatch can cause unwanted instability. Influence of this uncertainty is investigated in connection with the required performance and robustness.
Probability-based stability robustness assessment of controlled structures
Field, R.V. Jr.; Voulgaris, P.G.; Bergman, L.A.
1996-01-01
Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst-case analyses. These traditional methods include the use of the structured singular value, as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. In this paper an attempt to view controller robustness as a probability measure is presented. The probability of failure due to parametric uncertainty is estimated using first-order reliability methods (FORM). It is demonstrated that this method can provide quite accurate results on the probability of failure of actively controlled structures. Moreover, a comparison of this method to a suitability modified structured singular value robustness analysis in a probabilistic framework is performed. It is shown that FORM is the superior analysis technique when applied to a controlled three degree-of-freedom structure. In addition, the robustness qualities of various active control design schemes such as LQR, H{sub 2}, H {sub oo}, and {mu}-synthesis is discussed in order to provide some design guidelines.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Li, Zhihong; Liu, Lei; Zhu, Quanxin
2016-12-01
This paper studies the mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. By using the vector Lyapunov function and property of M-matrix, two generalized Halanay inequalities are established. By means of the generalized Halanay inequalities, sufficient conditions are also obtained, which can ensure the exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. Two numerical examples are given to illustrate the efficiency of the derived results.
Robust stabilization of marginally stable positive-real systems
NASA Technical Reports Server (NTRS)
Joshi, Suresh M.; Gupta, Sandeep
1994-01-01
This paper investigates the stability of the negative feedback interconnection to two positive-real systems which have poles in the closed left-half of the complex plane. A new definition of marginally strict positive real systems is introduced, and sufficient conditions are obtained for the stability of the feedback interconnection of such systems, using the Lyapunov method. The conditions obtained have direct applications to dynamic dissipative controllers for flexible spacecraft and are the least restrictive ones published to date.
Linear Quantum Systems: Non-Classical States and Robust Stability
2016-06-29
basic importance to develop analysis and design methods that take uncertainty into account. Specifically, in the area of robust control for linear...show that the series product, which serves as an algebraic rule for connecting state-based input–output systems, is intimately related to the...Approved for public release: distribution unlimited. 7 commutation and anticommutation relations of the underlying algebra SU(n). Refereed Conference
Linear Quantum Systems: Non-Classical States and Robust Stability
2016-06-29
basic importance to develop analysis and design methods that take uncertainty into account. Specifically, in the area of robust control for linear...We show that the series product, which serves as an algebraic rule for connecting state-based input–output systems, is intimately related to the...Approved for public release: distribution unlimited. 7 commutation and anticommutation relations of the underlying algebra SU(n). Refereed
Wang, Dongshu; Huang, Lihong
2014-03-01
In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen-Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results. Copyright © 2013 Elsevier Ltd. All rights reserved.
NASA Technical Reports Server (NTRS)
Ryan, R.
1993-01-01
Robustness is a buzz word common to all newly proposed space systems design as well as many new commercial products. The image that one conjures up when the word appears is a 'Paul Bunyon' (lumberjack design), strong and hearty; healthy with margins in all aspects of the design. In actuality, robustness is much broader in scope than margins, including such factors as simplicity, redundancy, desensitization to parameter variations, control of parameter variations (environments flucation), and operational approaches. These must be traded with concepts, materials, and fabrication approaches against the criteria of performance, cost, and reliability. This includes manufacturing, assembly, processing, checkout, and operations. The design engineer or project chief is faced with finding ways and means to inculcate robustness into an operational design. First, however, be sure he understands the definition and goals of robustness. This paper will deal with these issues as well as the need for the requirement for robustness.
An improved robust stability result for uncertain neural networks with multiple time delays.
Arik, Sabri
2014-06-01
This paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.
Stability and robustness of metal-supported SOFCs
NASA Astrophysics Data System (ADS)
Tucker, Michael C.; Lau, Grace Y.; Jacobson, Craig P.; DeJonghe, Lutgard C.; Visco, Steven J.
Tubular metal-supported SOFCs with YSZ electrolyte and electrodes comprising porous YSZ backbone and infiltrated Ni and LSM catalysts are operated at 700 °C. Tolerance to five complete anode redox cycles and five very rapid thermal cycles is demonstrated. The power output of a cell with as-infiltrated Ni anode degrades rapidly over 15 h operation. This degradation can be attributed primarily to coarsening of the fine infiltrated Ni particles. A cell in which the infiltrated Ni anode is precoarsened at 800 °C before operation at 700 °C shows dramatically improved stability. Stable operation over 350 h is demonstrated.
BenAbdallah, Abdallah; Hammami, Mohamed Ali; Kallel, Jalel
2009-03-05
In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.
Intuitive robust stability metric for PID control of self-regulating processes.
Arbogast, Jeffrey E; Beauregard, Brett M; Cooper, Douglas J
2008-10-01
Published methods establish how plant-model mismatch in the process gain and dead time impacts closed-loop stability. However, these methods assume no plant-model mismatch in the process time constant. The work presented here proposes the robust stability factor metric, RSF, to examine the effect of plant-model mismatch in the process gain, dead time, and time constant. The RSF is presented in two forms: an equation form and a visual form displayed on robustness plots derived from the Bode and Nyquist stability criteria. This understanding of robust stability is reinforced through visual examples of how closed-loop performance changes with various levels of plant-model mismatch. One example shows how plant-model mismatch in the time constant can impact closed-loop stability as much as plant-model mismatch in the gain and/or dead time. Theoretical discussion shows that the impact is greater for small dead time to time constant ratios. As the closed-loop time constant used in Internal Model Control (IMC) tuning decreases, the impact becomes significant for a larger range of dead time to time constant ratios. To complete the presentation, the RSF is used to compare the robust stability of IMC-PI tuning to other PI, PID, and PID with Filter tuning correlations.
Liu, Yanbin; Liu, Mengying; Sun, Peihua
2014-01-01
A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods.
Liu, Mengying; Sun, Peihua
2014-01-01
A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods. PMID:24795535
Quantum Popov robust stability analysis of an optical cavity containing a saturated Kerr medium
NASA Astrophysics Data System (ADS)
Petersen, Ian R.
2017-09-01
This paper applies results of the robust stability of nonlinear quantum systems to a system consisting of an optical cavity containing a saturated Kerr medium. The system is characterised by a Hamiltonian operator that contains a non-quadratic term involving a quartic function of the annihilation and creation operators. A saturated version of the Kerr nonlinearity leads to a sector-bounded nonlinearity that enables a quantum small gain theorem to be applied to this system in order to analyse its stability. Also, a non-quadratic version of a quantum Popov stability criterion is presented and applied to analyse the stability of this system.
Robust stabilization of the Space Station in the presence of inertia matrix uncertainty
NASA Technical Reports Server (NTRS)
Wie, Bong; Liu, Qiang; Sunkel, John
1993-01-01
This paper presents a robust H-infinity full-state feedback control synthesis method for uncertain systems with D11 not equal to 0. The method is applied to the robust stabilization problem of the Space Station in the face of inertia matrix uncertainty. The control design objective is to find a robust controller that yields the largest stable hypercube in uncertain parameter space, while satisfying the nominal performance requirements. The significance of employing an uncertain plant model with D11 not equal 0 is demonstrated.
McCartin, B.J.
1996-12-31
Herein, we discuss a generalization of the semiclassical cubic spline known in the literature as the exponential spline. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain {open_quotes}tension{close_quotes} parameters. We first outline the theoretical underpinnings of the exponential spline. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. We next discuss the numerical computation of the exponential spline. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines. We conclude with a consideration of the broad spectrum of possible uses of exponential splines in the applications. Our primary emphasis is on computational fluid dynamics although the imaginative reader will recognize the wider generality of the techniques developed.
Robust control design with real parameter uncertainty using absolute stability theory. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
How, Jonathan P.; Hall, Steven R.
1993-01-01
The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.
NASA Astrophysics Data System (ADS)
Adnan, N. S. M.; Arifin, N. M.
2017-09-01
In this paper, the steady boundary layer fluid flow with heat transfer over an exponentially shrinking sheet with thermal radiation, partial slip and suction is studied. The similarity transformation was applied to the governing partial differential equations to transform into a set of ordinary differential equations which are then solved numerically using bvp4c function in Matlab. It is reveal that dual solutions exist in our observations. A stability analysis is performed to determine which solution is linearly stable and physically realizable.
Robust Video Stabilization Using Particle Keypoint Update and l1-Optimized Camera Path
Jeon, Semi; Yoon, Inhye; Jang, Jinbeum; Yang, Seungji; Kim, Jisung; Paik, Joonki
2017-01-01
Acquisition of stabilized video is an important issue for various type of digital cameras. This paper presents an adaptive camera path estimation method using robust feature detection to remove shaky artifacts in a video. The proposed algorithm consists of three steps: (i) robust feature detection using particle keypoints between adjacent frames; (ii) camera path estimation and smoothing; and (iii) rendering to reconstruct a stabilized video. As a result, the proposed algorithm can estimate the optimal homography by redefining important feature points in the flat region using particle keypoints. In addition, stabilized frames with less holes can be generated from the optimal, adaptive camera path that minimizes a temporal total variation (TV). The proposed video stabilization method is suitable for enhancing the visual quality for various portable cameras and can be applied to robot vision, driving assistant systems, and visual surveillance systems. PMID:28208622
Robust Video Stabilization Using Particle Keypoint Update and l₁-Optimized Camera Path.
Jeon, Semi; Yoon, Inhye; Jang, Jinbeum; Yang, Seungji; Kim, Jisung; Paik, Joonki
2017-02-10
Acquisition of stabilized video is an important issue for various type of digital cameras. This paper presents an adaptive camera path estimation method using robust feature detection to remove shaky artifacts in a video. The proposed algorithm consists of three steps: (i) robust feature detection using particle keypoints between adjacent frames; (ii) camera path estimation and smoothing; and (iii) rendering to reconstruct a stabilized video. As a result, the proposed algorithm can estimate the optimal homography by redefining important feature points in the flat region using particle keypoints. In addition, stabilized frames with less holes can be generated from the optimal, adaptive camera path that minimizes a temporal total variation (TV). The proposed video stabilization method is suitable for enhancing the visual quality for various portable cameras and can be applied to robot vision, driving assistant systems, and visual surveillance systems.
Robust Stability and Performance for Linear Systems with Structured and Unstructured Uncertainties
1990-06-01
Pick Problem in Circuit and System Theory ," Circuir Theory and Appl., vol. 9, pp. 177-187, 1981. [59] E.I. Jury, "Inners and Stability of Dynamic Systems...unstructured uncertainty has been receiving attention much longer and has produced many interesting results, notably the H. theory and the LQG/LTR theory ...stability 6 robustness. It wilL be shown that the aforementioned synthesis task is closely related to singular perturbation theory . The next result
Robust stabilization using LMI techniques of neutral time-delay systems subject to input saturation
NASA Astrophysics Data System (ADS)
El Fezazi, Nabil; El Haoussi, Fatima; Houssaine Tissir, El; Alvarez, Teresa; Tadeo, Fernando
2017-01-01
The robust stabilization of uncertain saturated neutral systems with state delay is solved in this paper: based on a free weighting matrix approach, sufficient conditions are obtained via an LMI formulation. From these conditions, state feedback gains that ensure stability for the largest set of admissible initial conditions can be calculated solving optimization problems with LMI constraints. Some applications of this methodology to feedback control are then presented and compared with previous results in the literature.
Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays
Delgado, Emma; Barreiro, Antonio; Falcón, Pablo; Díaz-Cacho, Miguel
2016-01-01
We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency. PMID:27128914
Karra, Udayarka; Huang, Guoxian; Umaz, Ridvan; Tenaglier, Christopher; Wang, Lei; Li, Baikun
2013-09-01
A novel and robust distributed benthic microbial fuel cell (DBMFC) was developed to address the energy supply issues for oceanographic sensor network applications, especially under scouring and bioturbation by aquatic life. Multi-anode/cathode configuration was employed in the DBMFC system for enhanced robustness and stability in the harsh ocean environment. The results showed that the DBMFC system achieved peak power and current densities of 190mW/m(2) and 125mA/m(2) respectively. Stability characterization tests indicated the DBMFC with multiple anodes achieved higher power generation over the systems with single anode. A computational model that integrated physical, electrochemical and biological factors of MFCs was developed to validate the overall performance of the DBMFC system. The model simulation well corresponded with the experimental results, and confirmed the hypothesis that using a multi anode/cathode MFC configuration results in reliable and robust power generation.
Control design for robust stability in linear regulators: Application to aerospace flight control
NASA Technical Reports Server (NTRS)
Yedavalli, R. K.
1986-01-01
Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.
Robust H∞ stabilization of a hard disk drive system with a single-stage actuator
NASA Astrophysics Data System (ADS)
Harno, Hendra G.; Kiin Woon, Raymond Song
2015-04-01
This paper considers a robust H∞ control problem for a hard disk drive system with a single stage actuator. The hard disk drive system is modeled as a linear time-invariant uncertain system where its uncertain parameters and high-order dynamics are considered as uncertainties satisfying integral quadratic constraints. The robust H∞ control problem is transformed into a nonlinear optimization problem with a pair of parameterized algebraic Riccati equations as nonconvex constraints. The nonlinear optimization problem is then solved using a differential evolution algorithm to find stabilizing solutions to the Riccati equations. These solutions are used for synthesizing an output feedback robust H∞ controller to stabilize the hard disk drive system with a specified disturbance attenuation level.
Wu, Huai-Ning; Cai, Kai-Yuan
2006-06-01
This paper is concerned with the robust-stabilization problem of uncertain Markovian jump nonlinear systems (MJNSs) without mode observations via a fuzzy-control approach. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. The aim is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system (MJFS) is robustly stochastically stable. Based on a stochastic Lyapunov function, a robust-stabilization condition using a mode-independent fuzzy controller is derived for the uncertain MJFS in terms of linear matrix inequalities (LMIs). A new improved LMI formulation is used to alleviate the interrelation between the stochastic Lyapunov matrix and the system matrices containing controller variables in the derivation process. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.
Dubay, R; Kember, G; Lakshminarayan, C V; Pramujati, B
2005-10-01
Discrete-time controller and closed-loop transfer functions were developed for move suppressed lambda and the recently formulated m-shifted multiple-input-multiple-output (MIMO) dynamic matrix control (DMC). Using these transfer functions, robust analyses were conducted for MIMO plants by varying corresponding delay and gain ratios of the system. In all instances, robust plots indicate that the shifted DMC is less sensitive and hence more robust to variations in the plant parameters than move suppressed DMC. It was shown that the design of these MIMO DMC controllers depends on the plant closed-loop performance and overall stability, since the selection of lambda and m directly influences the plant robustness and closed-loop dynamics.
Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach
NASA Technical Reports Server (NTRS)
Pei, Jing; Newsome, Jerry R.
2015-01-01
Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.
Nevsky, A; Alighanbari, S; Chen, Q-F; Ernsting, I; Vasilyev, S; Schiller, S; Barwood, G; Gill, P; Poli, N; Tino, G M
2013-11-15
We have demonstrated a compact, robust device for simultaneous absolute frequency stabilization of three diode lasers whose carrier frequencies can be chosen freely relative to the reference. A rigid ULE multicavity block is employed, and, for each laser, the sideband locking technique is applied. A small lock error, computer control of frequency offset, wide range of frequency offset, simple construction, and robust operation are the useful features of the system. One concrete application is as a stabilization unit for the cooling and trapping lasers of a neutral-atom lattice clock. The device significantly supports and improves the clock's operation. The laser with the most stringent requirements imposed by this application is stabilized to a line width of 70 Hz, and a residual frequency drift less than 0.5 Hz/s. The carrier optical frequency can be tuned over 350 MHz while in lock.
Computational analysis of a stability robustness margin for structured real-parameter perturbations
NASA Technical Reports Server (NTRS)
Wedell, Evan; Chuang, C.-H.; Wie, Bong
1989-01-01
An efficient computational method is presented for stability robustness analysis with structured real-parameter perturbations. A generic model of a class of uncertain dynamical systems is used as an example. The parameter uncertainty is characterized by a real scalar, epsilon. Multilinearity of the closed-loop characteristic polynomial is exploited to permit application of the mapping theorem to calculate the stability robustness margin. It is found that sensitive geometry of the stability boundary in the epsilon, omega-plane renders problematic the calculation of the minimum epsilon as a function of omega. This difficulty is avoided by calculating the minimum distance to the image of the uncertainty domain over omega as a function of epsilon. It is also shown that a certain class of uncertain dynamical systems has the required multilinearity property and are thus amenable to the proposed technique.
Guo, Zhenyuan; Wang, Jun; Yan, Zheng
2013-12-01
This paper addresses the global exponential dissipativity of memristor-based recurrent neural networks with time-varying delays. By constructing proper Lyapunov functionals and using M-matrix theory and LaSalle invariant principle, the sets of global exponentially dissipativity are characterized parametrically. It is proven herein that there are 2(2n(2)-n) equilibria for an n-neuron memristor-based neural network and they are located in the derived globally attractive sets. It is also shown that memristor-based recurrent neural networks with time-varying delays are stabilizable at the origin of the state space by using a linear state feedback control law with appropriate gains. Finally, two numerical examples are discussed in detail to illustrate the characteristics of the results. Copyright © 2013 Elsevier Ltd. All rights reserved.
Xu, Lijun; Jiang, Qi; Gu, Guodong
2016-01-01
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results. PMID:27190502
Jiang, Haijun; Zhang, Long; Teng, Zhidong
2005-11-01
In this paper, we study cellular neural networks with almost periodic variable coefficients and time-varying delays. By using the existence theorem of almost periodic solution for general functional differential equations, introducing many real parameters and applying the Lyapunov functional method and the technique of Young inequality, we obtain some sufficient conditions to ensure the existence, uniqueness, and global exponential stability of almost periodic solution. The results obtained in this paper are new, useful, and extend and improve the existing ones in previous literature.
Xu, Lijun; Jiang, Qi; Gu, Guodong
2016-01-01
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.
Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay
NASA Astrophysics Data System (ADS)
Kalidass, Mathiyalagan; Su, Hongye; Rathinasamy, Sakthivel
2014-02-01
This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.
Robust fuzzy Lyapunov stabilization for uncertain and disturbed Takagi-Sugeno descriptors.
Bouarar, T; Guelton, K; Manamanni, N
2010-10-01
In this paper, new robust H(infinity) controller design methodologies for Takagi-Sugeno (T-S) descriptors is considered. Based on Linear Matrix Inequalities, two different approaches are proposed. The first one involves a "classical closed-loop dynamics" formulation and the second one a "redundancy closed-loop dynamics" approach. The provided conditions are obtained through a fuzzy Lyapunov function candidate and a non-PDC control law. Both the classical and redundancy approaches are compared. It is shown that the latter leads to less conservative stability conditions. The efficiency of the proposed robust control approaches for T-S descriptors as well as the benefit of the redundancy approach are shown through an academic example. Then, to show the applicability of the proposed approaches, the benchmark stabilization of an inverted pendulum on a cart is considered. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Liu, Ping
2013-07-01
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lü and Chen systems are presented to validate the design and analysis.
Flight control application of new stability robustness bounds for linear uncertain systems
NASA Technical Reports Server (NTRS)
Yedavalli, Rama K.
1993-01-01
This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.
Flight control application of new stability robustness bounds for linear uncertain systems
NASA Technical Reports Server (NTRS)
Yedavalli, Rama K.
1993-01-01
This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.
NASA Astrophysics Data System (ADS)
Liang, Yao; Yamaura, Hiroshi; Ouyang, Huajiang
2017-06-01
As friction couples tangential and lateral degrees-of-freedom of a structure at contact interfaces, the resulting asymmetric dynamic system is prone to dynamic instability. Using state-feedback control, such a frictional asymmetric system can be stabilized through assigning the system desirable eigenvalues; but uncertainties in system parameters can cause assigned eigenvalues to deviate from desired locations and thus stability may be lost. This study presents a robust stabilization method that assigns both desirable eigenvalues and their sensitivities and thus render assigned eigenvalues stable and insensitive to perturbations in uncertain contact parameters (the friction coefficient, contact damping, and contact stiffness). This method utilizes receptances of the corresponding symmetric part of the asymmetric system. The optimal control input location is first determined by minimizing the Frobenius norm of the normalized eigen-sensitivity matrix. The normalized eigen-sensitivities indicate that the friction coefficient and contact stiffness intrinsically have similar crucial effects on the stability of the system. To demonstrate the application of the proposed control method, the eigen-sensitivities with respect to only the friction coefficient are assigned. A constrained over-determined least-squares problem is solved to assign both required eigenvalues and eigen-sensitivities. Numerical examples validate the effectiveness of the proposed robust control scheme by Monte Carlo simulations.
Real-Time Stability Margin Measurements for X-38 Robustness Analysis
NASA Technical Reports Server (NTRS)
Bosworth, John T.; Stachowiak, Susan J.
2005-01-01
A method has been developed for real-time stability margin measurement calculations. The method relies on a tailored-forced excitation targeted to a specific frequency range. Computation of the frequency response is matched to the specific frequencies contained in the excitation. A recursive Fourier transformation is used to make the method compatible with real-time calculation. The method was incorporated into the X-38 nonlinear simulation and applied to an X-38 robustness test. X-38 stability margins were calculated for different variations in aerodynamic and mass properties over the vehicle flight trajectory. The new method showed results comparable to more traditional stability analysis techniques, and at the same time, this new method provided coverage that is more complete and increased efficiency.
Robust adaptive spin-axis stabilization of a symmetric spacecraft using two bounded torques
NASA Astrophysics Data System (ADS)
Gui, Haichao; Vukovich, George
2015-12-01
The spin-axis stabilization of an axisymmetric spacecraft by two control torques perpendicular to the symmetry axis is addressed. Two control laws are designed to align the symmetry axis along a desired inertial direction despite the revolution around the symmetry axis. The first controller takes a saturated proportional-derivative form and can stabilize the spin-axis to the desired direction with a priori bounded torques in the absence of modeling uncertainties. In order to achieve better robustness, an adaptive controller is then designed to account for the inertia uncertainties and disturbances, in addition to actuator saturation. Numerical examples are presented to demonstrate the advantageous features of the proposed algorithm compared with conventional spin-axis stabilization methods.
A new delay-independent condition for global robust stability of neural networks with time delays.
Samli, Ruya
2015-06-01
This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.
Redi, M.H.; Diallo, A.; Cooper, W.A.; Fu, G.Y.
2000-01-27
Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal magnetohydrodynamic stability is evaluated as well as energetic particle transport. It is found that tokamak intuition is relevant to understanding the magnetohydrodynamic stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the non-periodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD stability are not anticorrelated in these equilibria, stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties.
Robust numerical phase stabilization for long-range swept-source optical coherence tomography.
Song, Shaozhen; Xu, Jingjiang; Men, Shaojie; Shen, Tueng T; Wang, Ruikang K
2017-05-09
A novel phase stabilization technique is demonstrated with significant improvement in the phase stability of a micro-electromechanical (MEMS) vertical cavity surface-emitting laser (VCSEL) based swept-source optical coherence tomography (SS-OCT) system. Without any requirements of hardware modifications, the new fully numerical phase stabilization technique features high tolerance to acquisition jitter, and significantly reduced budget in computational effort. We demonstrate that when measured with biological tissue, this technique enables a phase sensitivity of 89 mrad in highly scattering tissue, with image ranging distance of up to 12.5 mm at A-line scan rate of 100.3 kHz. We further compare the performances delivered by the phase-stabilization approach with conventional numerical approach for accuracy and computational efficiency. Imaging result of complex signal-based optical coherence tomography angiography (OCTA) and Doppler OCTA indicate that the proposed phase stabilization technique is robust, and efficient in improving the image contrast-to-noise ratio and extending OCTA depth range. The proposed technique can be universally applied to improve phase-stability in generic SS-OCT with different scale of scan rates without a need for special treatment. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks.
Albergante, Luca; Blow, J Julian; Newman, Timothy J
2014-09-02
The gene regulatory network (GRN) is the central decision-making module of the cell. We have developed a theory called Buffered Qualitative Stability (BQS) based on the hypothesis that GRNs are organised so that they remain robust in the face of unpredictable environmental and evolutionary changes. BQS makes strong and diverse predictions about the network features that allow stable responses under arbitrary perturbations, including the random addition of new connections. We show that the GRNs of E. coli, M. tuberculosis, P. aeruginosa, yeast, mouse, and human all verify the predictions of BQS. BQS explains many of the small- and large-scale properties of GRNs, provides conditions for evolvable robustness, and highlights general features of transcriptional response. BQS is severely compromised in a human cancer cell line, suggesting that loss of BQS might underlie the phenotypic plasticity of cancer cells, and highlighting a possible sequence of GRN alterations concomitant with cancer initiation.
Stability of discrete-time networked control systems and its extension for robust H ∞ control
NASA Astrophysics Data System (ADS)
Wang, Peng; Han, Chongzhao; Ding, Baocang
2013-02-01
The stability of discrete-time Networked Control Systems (NCSs) is studied in this article. By introducing some scalars into matrix cross-term bounding technique, we present a new approach for the state feedback controller, with less conservatism, based on the Bilinear Matrix Inequalities (BMIs) and the descriptor model transformation. We further extend the method to robust H ∞ control considering both disturbances and parametric uncertainties. For the BMI problem which is difficult to be solved directly, a modified optimisation algorithm is proposed. The practicability, less conservatism and effectiveness of the results are demonstrated by two examples.
A scheme for theoretical and experimental evaluation of multivariable system stability robustness
NASA Technical Reports Server (NTRS)
Mukhopadhyay, Vivek; Pototzky, Anthony S.; Fox, Matthew E.
1990-01-01
A scheme for theoretical and experimental evaluation of multivariable system stability robustness measures is described. The experimental scheme is based on the estimation of frequency responses from power-spectra analyses of a set of time responses due to sine-sweep excitation at each input and then computation of the appropriate singular values. The procedure can also be used on an open-loop stable system to predict the closed-loop stability before closing the loop. Classical Nyquist diagrams can also be constructed to determine one-loop-at-a-time gain or phase margins. The scheme has been implemented in a wind tunnel test for singular-value evaluation of digital flutter suppression control laws and compared with theory. The singular values at the plant input and output of the actual system and the theoretical model are qualitatively similar but have some discrepancies.
Robust Global Control Strategies for Improvement of Angular Stability using FACTS and HVDC Devices
NASA Astrophysics Data System (ADS)
Agnihotri, P.; Kulkarni, A. M.; Gole, A. M.
2013-05-01
System-wide feedback signals made available by Wide-Area Measurement Systems technology can be used in FACTS/HVDC based controllers for the improvement of angular stability. These global signals can facilitate the efficient use of controller effort to stabilize critical swing modes. This paper introduces a restricted global strategy which involves the use of specific global feedback signals which are available at the HVDC/FACTS locations. The strategy is expected to be robust to changes in the power grid as well as communication uncertainties. This paper presents a heuristic introduction to this strategy using a circuit analogy of a simplified model of a power system. Preliminary results on a small system are also presented.
Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes.
Li, Jinghao; Zhang, Qingling; Yan, Xing-Gang; Spurgeon, Sarah K
2017-09-19
This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.
NASA Astrophysics Data System (ADS)
Rossi, Stefano; Petrelli, Maurizio; Morgavi, Daniele; González-García, Diego; Fischer, Lennart A.; Vetere, Francesco; Perugini, Diego
2017-08-01
The mixing of magmas is a fundamental process in the Earth system causing extreme compositional variations in igneous rocks. This process can develop with different intensities both in space and time, making the interpretation of compositional patterns in igneous rocks a petrological challenge. As a time-dependent process, magma mixing has been suggested to preserve information about the time elapsed between the injection of a new magma into sub-volcanic magma chambers and eruptions. This allowed the use of magma mixing as an additional volcanological tool to infer the mixing-to-eruption timescales. In spite of the potential of magma mixing processes to provide information about the timing of volcanic eruptions its statistical robustness is not yet established. This represents a prerequisite to apply reliably this conceptual model. Here, new chaotic magma mixing experiments were performed at different times using natural melts. The degree of reproducibility of experimental results was tested repeating one experiment at the same starting conditions and comparing the compositional variability. We further tested the robustness of the statistical analysis by randomly removing from the analysed dataset a progressively increasing number of samples. Results highlight the robustness of the method to derive empirical relationships linking the efficiency of chemical exchanges and mixing time. These empirical relationships remain valid by removing up to 80% of the analytical determinations. Experimental results were applied to constrain the homogenization time of chemical heterogeneities in natural magmatic system during mixing. The calculations show that, when the mixing dynamics generate millimetre thick filaments, homogenization timescales of the order of a few minutes are to be expected.
An exponential polynomial observer for synchronization of chaotic systems
NASA Astrophysics Data System (ADS)
Mata-Machuca, J. L.; Martínez-Guerra, R.; Aguilar-López, R.
2010-12-01
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation.
NASA Astrophysics Data System (ADS)
Matone, Marco
2017-09-01
We consider two related formulations for mass generation in the U (1) Higgs-Kibble model and in the Standard Model (SM). In the first formulation there are no scalar self-interactions and, in the case of the SM, the formulation is related to the normal subgroup of G = SU (3) × SU (2) × U (1), generated by (e 2 πi / 3 I , - I ,e πi / 3) ∈ G, that acts trivially on all the fields of the SM. The key step of our construction is to relax the non-negative definiteness condition for the Higgs field due to the polar decomposition. This solves several stringent problems, that we will shortly review, both at the non-perturbative and perturbative level. We will show that the usual polar decomposition of the complex scalar doublet Φ should be done with U ∈ SU (2) /Z2 ≃ SO (3), where Z2 is the group generated by -I, and with the Higgs field ϕ ∈ R rather than ϕ ∈R≥0. As a byproduct, the investigation shows how Elitzur theorem may be avoided in the usual formulation of the SM. It follows that the simplest lagrangian density for the Higgs mechanism has the standard kinetic term in addition to the mass term, with the right sign, and to a linear term in ϕ. The other model concerns the scalar theories with normal ordered exponential interactions. The remarkable property of these theories is that for D > 2 the purely scalar sector corresponds to a free theory.
NASA Astrophysics Data System (ADS)
De la Sen, M.
2008-08-01
This paper discusses linear fractional representations (LFR) of parameter-dependent nonlinear systems with real-rational nonlinearities and point-delayed dynamics. Sufficient conditions for robust global asymptotic stability independent of the delays and the existence of a robust stabilizing gain-scheduled dynamic controller are investigated via linear matrix inequalities. Such inequalities are obtained from the values of the time-derivatives of appropriate Lyapunov functions at all the vertices of the polytope which contains the parametrized uncertainties. The synthesized stabilizing controller consists of an interpolation being performed with the stabilizing controllers at the set of vertices of a certain polytope where the nonlinear-rational parametrization belongs to. Some extensions are also given concerning robust global asymptotic stability dependent of the delays. Numerical examples corroborate the usefulness of the proposed formalism and its applicability to practical related problems.
A Robust Method of Vehicle Stability Accurate Measurement Using GPS and INS
NASA Astrophysics Data System (ADS)
Miao, Zhibin; Zhang, Hongtian; Zhang, Jinzhu
2015-12-01
With the development of the vehicle industry, controlling stability has become more and more important. Techniques of evaluating vehicle stability are in high demand. Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) is a very practical method to get high-precision measurement data. Usually, the Kalman filter is used to fuse the data from GPS and INS. In this paper, a robust method is used to measure vehicle sideslip angle and yaw rate, which are two important parameters for vehicle stability. First, a four-wheel vehicle dynamic model is introduced, based on sideslip angle and yaw rate. Second, a double level Kalman filter is established to fuse the data from Global Positioning System and Inertial Navigation System. Then, this method is simulated on a sample vehicle, using Carsim software to test the sideslip angle and yaw rate. Finally, a real experiment is made to verify the advantage of this approach. The experimental results showed the merits of this method of measurement and estimation, and the approach can meet the design requirements of the vehicle stability controller.
Nominal and robust stability regions of optimization-based PID controllers.
Ou, Linlin; Zhang, Weidong; Gu, Danying
2006-07-01
In recent decades, several optimization-based methods have been developed for the proportional-integral-derivative (PID) controller design, and the common feature of these methods is that the controller has only one adjustable parameter. To keep the closed-loop systems stable is an essential requirement for the optimization-based PID controllers. In almost all these methods, however, no exact stability region for the single adjustable parameter was sketched. In this paper, using the proposed analytical procedure based on the dual-locus diagram technique, explicit stability regions of the optimization-based PID controllers are derived for stable, integrating, and unstable processes with time delay in the nominal and perturbed cases, respectively. It is revealed that the proposed analytical procedure is effective for the determination of the nominal and robust stability regions and it offers simplicity and ease of mathematical calculations over other available stability analysis methods. The results in this paper provide some insight into the tuning of the optimization-based PID controllers.
NASA Astrophysics Data System (ADS)
Feng, Baowei
2017-02-01
This paper is concerned with a class of plate equation with past history and time-varying delay in the internal feedback u_{tt}+α Δ ^2 u-int limits ^t_{-∞}g(t-s)Δ ^2 u(s)ds+μ _1u_t+μ _2u_t(t-τ (t))+f(u)=h(x), defined in a bounded domain of {R}^n (n≥1) with some suitable initial data and boundary conditions. For arbitrary real numbers μ _1 and μ _2, we proved the global well-posedness of the problem. Results on stability of energy are also proved under some restrictions on μ _1, μ _2 and h(x)=0.
What is the weakest topology in which feedback stability is robust?
NASA Astrophysics Data System (ADS)
Vinnicombe, Glenn
2013-11-01
Mathematical theorems in control theory are only of interest in so far as their assumptions relate to practical situations. The space of systems with transfer functions in ?, for example, has many advantages mathematically, but includes large classes of non-physical systems, and one must be careful in drawing inferences from results in that setting. Similarly, the graph topology has long been known to be the weakest, or coarsest, topology in which (1) feedback stability is a robust property (i.e. preserved in small neighbourhoods) and (2) the map from open-to-closed-loop transfer functions is continuous. However, it is not known whether continuity is a necessary part of this statement, or only required for the existing proofs. It is entirely possible that the answer depends on the underlying classes of systems used. The class of systems we concern ourselves with here is the set of systems that can be approximated, in the graph topology, by real rational transfer function matrices. That is, lumped parameter models, or those distributed systems for which it makes sense to use finite element methods. This is precisely the set of systems that have continuous frequency responses in the extended complex plane. For this class, we show that there is indeed a weaker topology; in which feedback stability is robust but for which the maps from open-to-closed-loop transfer functions are not necessarily continuous.
Robustness and cognition in stabilization problem of dynamical systems based on asymptotic methods
NASA Astrophysics Data System (ADS)
Dubovik, S. A.; Kabanov, A. A.
2017-01-01
The problem of synthesis of stabilizing systems based on principles of cognitive (logical-dynamic) control for mobile objects used under uncertain conditions is considered. This direction in control theory is based on the principles of guaranteeing robust synthesis focused on worst-case scenarios of the controlled process. The guaranteeing approach is able to provide functioning of the system with the required quality and reliability only at sufficiently low disturbances and in the absence of large deviations from some regular features of the controlled process. The main tool for the analysis of large deviations and prediction of critical states here is the action functional. After the forecast is built, the choice of anti-crisis control is the supervisory control problem that optimizes the control system in a normal mode and prevents escape of the controlled process in critical states. An essential aspect of the approach presented here is the presence of a two-level (logical-dynamic) control: the input data are used not only for generating of synthesized feedback (local robust synthesis) in advance (off-line), but also to make decisions about the current (on-line) quality of stabilization in the global sense. An example of using the presented approach for the problem of development of the ship tilting prediction system is considered.
A network-centric robust resource allocation strategy for unmanned systems: stability analysis
NASA Astrophysics Data System (ADS)
Bouyoucef, K.; Khorasani, K.
2007-04-01
It is widely understood that communication is a critical technological factor in designing autonomous unmanned networks consisting of a large number of heterogeneous nodes that may be configured in ad-hoc fashions and incorporating intricate architectures. In fact, one of the challenges in this field is to recognize the entire network as a heterogenous collection of physical and information systems with complicated interconnections and interactions. Using high data rates that are essential for real-time interactive command and control systems, these networks require utilization of optimal integration of local feedback loops into a scheduling and resource allocation systems. This integration becomes particularly problematic in presence of latencies and delays. Given that dynamics of a network of unmanned systems could easily become unstable depending on interconnections among nodes, in this paper stability of the resulting time-delayed controlled network based on configuration changes is studied. We also formally investigate sufficient conditions for our proposed robust resource allocation strategies to be able to cope with these interconnections and time-delays in an optimal fashion. Our time-delayed dependent network consists of three nodes that can be configured into different architectures. To model our traffic and network we use a fluid flow model that is of low order and simpler than a detailed Markovian queueing probabilistic model. Using sliding mode-based variable structure control (SM-VSC) techniques that enjoy robustness capabilities, we design on the basis of an inaccurate/uncertain model our proposed robust nonlinear feedback-based control approaches. The results presented are analyzed analytically to guarantee stability of known/unknown time-delayed dependent network of unmanned systems for different configurations.
NASA Astrophysics Data System (ADS)
Shi, Yunde; Longman, Richard W.
2012-06-01
Repetitive control (RC) can be used to design active vibration isolation mounts that aim to cancel the influence of spacecraft vibrations on fine pointing equipment. It can cancel the influence of slight imbalance in momentum wheels, reaction wheels, and CMGs. Because RC aims for zero error, it requires reasonably accurate knowledge of the system dynamics all the way to Nyquist frequency. As a result, special methods are needed to establish robustness to model error. A series of publications have demonstrated a method of averaging a cost function over models to increase the robustness. A previous paper improves on this by adjusting the learning rate as a function of frequency to further improve robustness, but there is still a hard limit on phase error. This paper considers yet one more approach, and all three can be used simultaneously. Here we compromise on the zero tracking error requirement for frequencies that require extra robustness. This allows one to extend this hard limit making RC tolerate larger model errors. A quadratic cost is used that penalizes not just the rate of change of the input function, but also the size of the input function. We first establish how to do this for the sister field of iterative learning control, and then the frequency response characteristics are produced for design of repetitive control. The method can improve tracking error for a frequency interval above the frequency at which one would otherwise have to cut off the learning because of model error. Model uncertainty can be used directly in the design process to produce stable RC laws for any level of uncertainty. The design approach differs from typical earlier work that used a sharp frequency cutoff, and instead uses a minimal amount of attenuation needed to produce stability.
NASA Astrophysics Data System (ADS)
Danik, Yulia
2016-08-01
This paper is dedicated to the robustness analysis of a stabilizing controller for quasi-linear state dependent coefficients discrete systems. The interval parametric uncertainties in the linear part of the system are investigated. The nonlinear stabilizing regulator proposed for such systems is calculated at the average values of the uncertainty parameters and is used for all realizations of the system. The basic idea is that the existence of only weak nonlinearity in the system allows us to study its robustness based on the robustness of the corresponding unperturbed discrete linear system. The robustness conditions are formulated in the form of linear matrix inequalities. Numerical experiments demonstrating the robustness of the closed-loop system are presented.
Wang, Leimin; Shen, Yi; Sheng, Yin
2016-04-01
This paper is concerned with the finite-time robust stabilization of delayed neural networks (DNNs) in the presence of discontinuous activations and parameter uncertainties. By using the nonsmooth analysis and control theory, a delayed controller is designed to realize the finite-time robust stabilization of DNNs with discontinuous activations and parameter uncertainties, and the upper bound of the settling time functional for stabilization is estimated. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.
Anderson, Ericka L; Li, Weizhong; Klitgord, Niels; Highlander, Sarah K; Dayrit, Mark; Seguritan, Victor; Yooseph, Shibu; Biggs, William; Venter, J Craig; Nelson, Karen E; Jones, Marcus B
2016-08-25
As reports on possible associations between microbes and the host increase in number, more meaningful interpretations of this information require an ability to compare data sets across studies. This is dependent upon standardization of workflows to ensure comparability both within and between studies. Here we propose the standard use of an alternate collection and stabilization method that would facilitate such comparisons. The DNA Genotek OMNIgene∙Gut Stool Microbiome Kit was compared to the currently accepted community standard of freezing to store human stool samples prior to whole genome sequencing (WGS) for microbiome studies. This stabilization and collection device allows for ambient temperature storage, automation, and ease of shipping/transfer of samples. The device permitted the same data reproducibility as with frozen samples, and yielded higher recovery of nucleic acids. Collection and stabilization of stool microbiome samples with the DNA Genotek collection device, combined with our extraction and WGS, provides a robust, reproducible workflow that enables standardized global collection, storage, and analysis of stool for microbiome studies.
Anderson, Ericka L.; Li, Weizhong; Klitgord, Niels; Highlander, Sarah K.; Dayrit, Mark; Seguritan, Victor; Yooseph, Shibu; Biggs, William; Venter, J. Craig; Nelson, Karen E.; Jones, Marcus B.
2016-01-01
As reports on possible associations between microbes and the host increase in number, more meaningful interpretations of this information require an ability to compare data sets across studies. This is dependent upon standardization of workflows to ensure comparability both within and between studies. Here we propose the standard use of an alternate collection and stabilization method that would facilitate such comparisons. The DNA Genotek OMNIgene∙Gut Stool Microbiome Kit was compared to the currently accepted community standard of freezing to store human stool samples prior to whole genome sequencing (WGS) for microbiome studies. This stabilization and collection device allows for ambient temperature storage, automation, and ease of shipping/transfer of samples. The device permitted the same data reproducibility as with frozen samples, and yielded higher recovery of nucleic acids. Collection and stabilization of stool microbiome samples with the DNA Genotek collection device, combined with our extraction and WGS, provides a robust, reproducible workflow that enables standardized global collection, storage, and analysis of stool for microbiome studies. PMID:27558918
NASA Technical Reports Server (NTRS)
Garg, Sanjay
1989-01-01
A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.
Hallez, Yannick; Meireles, Martine
2017-09-26
Increasing demand is appearing for the fast, robust prediction of the equation of state of colloidal suspensions, notably with a view to using it as input data to calculate transport coefficients in complex flow solvers. This is also of interest in rheological studies, industrial screening tests of new formulations, and the real-time interpretation of osmotic compression experiments, for example. For charge-stabilized spherical particles, the osmotic pressure can be computed with standard liquid theories. However, this calculation can sometimes be lengthy and/or unstable under some physicochemical conditions, a drawback that precludes its use in multiscale flow simulators. As a simple, fast, and robust replacement, the literature reports estimations of the osmotic pressure that have been built by adding the Carnahan-Starling and the cell model pressures (CSCM model). The first contribution is intended to account for colloid-colloid contacts, and the second, for electrostatic effects. This approximation has not yet been thoroughly tested. In this work, the CSCM is evaluated by comparison with data from experiments on silica particles, Monte Carlo simulations, and solutions of the accurate Rogers-Young integral equation scheme with a hard-sphere Yukawa potential obtained from the extrapolated point-charge renormalization method for a wide range of volume fractions, surface charge densities, and interaction ranges. We find that the CSCM is indeed perfectly adequate in the electrostatically concentrated regime, where it can be used from vanishingly small to high surface charge because there is error cancellation between the Carnahan-Starling and cell model contributions at intermediate charge. The CSCM is thus a nice extension of the cell model to liquid-like dense suspensions, which should find application in the domains mentioned above. However, it fails for dilute suspensions with strong electrostatics. In this case, we show that, and explain why, perturbation
Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks
Albergante, Luca; Blow, J Julian; Newman, Timothy J
2014-01-01
The gene regulatory network (GRN) is the central decision‐making module of the cell. We have developed a theory called Buffered Qualitative Stability (BQS) based on the hypothesis that GRNs are organised so that they remain robust in the face of unpredictable environmental and evolutionary changes. BQS makes strong and diverse predictions about the network features that allow stable responses under arbitrary perturbations, including the random addition of new connections. We show that the GRNs of E. coli, M. tuberculosis, P. aeruginosa, yeast, mouse, and human all verify the predictions of BQS. BQS explains many of the small- and large‐scale properties of GRNs, provides conditions for evolvable robustness, and highlights general features of transcriptional response. BQS is severely compromised in a human cancer cell line, suggesting that loss of BQS might underlie the phenotypic plasticity of cancer cells, and highlighting a possible sequence of GRN alterations concomitant with cancer initiation. DOI: http://dx.doi.org/10.7554/eLife.02863.001 PMID:25182846
NASA Astrophysics Data System (ADS)
Nguyen, Quan M.; Peleg, Avner; Tran, Thinh P.
2015-01-01
We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that the amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with coupled nonlinear Schrödinger equations confirm the predictions of the LV model, and show complete suppression of radiative instability and pulse distortion. This enables stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides.
Practical robust stabilization of PMAC servo drive based on continuous variable structure control
Grcar, B.; Cafuta, P.; Znidaric, M.
1996-12-01
In the paper the two stage control design of a high performance PMAC servo drive is described. In the first stage the nominal PMAC motor model is discussed as an analytical nonlinear system, transformed into the controllable canonical Brunovsky`s forms on the basis of input-output linearization. The influence of the load torque is considered implicitly by introducing the disturbance observer. Due to the sensitivity of the nominal model based control to parameter perturbations the linear tracking control is extended in the second stage by a continuous variable structure stabilizing control derived from Lyapunov`s function of the augmented feedback system. The design of the variable structure control requires no knowledge of the upper bounds of the perturbation function; instead, it considers the variable bounds of the available control signal. Undesired chattering of states and controlled variables are excluded. The introduced two stage control design assures practical robust stabilization for the class of bounded nonlinear perturbations satisfying the matching conditions without affecting the relative degree of the feedback system. Experimental results of the proposed PMAC servo drive control are presented.
NASA Astrophysics Data System (ADS)
Ratschbacher, Lothar; Gallego, Jose; Ghosh, Sutapa; Alavi, Seyed; Alt, Wolfgang; Martinez-Dorantes, Miguel; Meschede, Dieter
2016-04-01
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications. Some of the most promising areas of application of these optical micro-resonators with high finesse and small mode volume are in the field of quantum communication and information. The resonator-enhanced light-matter interaction, for instance, provide basis for the realization of efficient optical interfaces between stationary matter-based quantum nodes and flying single-photon qubits. To date fiber Fabry-Perot cavities have been successfully applied in experiments interfacing single photons with a wide range of quantum systems, including cold atoms, ions and solid state emitters as well as quantum optomechanical experiments. Here we address some important practical questions that arise during the experimental implementation of high finesse fiber Fabry-Perot cavities: How can optimal fiber cavity alignment be achieved and how can the efficiency of coupling light from the optical fibers to the cavity mode and vice versa be characterized? How should optical fiber cavities be constructed and stabilized to fulfill their potential for miniaturization and integration into robust scientific and technological devices that can operate outside of dedicated laboratory environments in the future? The first two questions we answer with an analytic mode matching calculation that relates the alignment dependent fiber-to-cavity mode-matching efficiency to the easily measurable dip in the reflected light power at the cavity resonance. Our general analysis provides a simple recipe for the optimal alignment of fiber Fabry-Perot cavities and moreover for the first time explains the asymmetry in their reflective line shapes. The latter question we explore by investigating a novel, intrinsically rigid fiber cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal
NASA Astrophysics Data System (ADS)
Gayvoronskiy, S. A.; Ezangina, T.; Khozhaev, I.; Gunbo, Lan
2017-01-01
The authors of this article developed the technique of combined parametric synthesis of a linear controller on the basis of the coefficient method and the method of mathematical programming capable of ensuring the maximization of the degree of robust stability of a control system. The article also presents the numerical illustration of the PI controller synthesis of the position stabilization system of an underwater object.
ERIC Educational Resources Information Center
Ishigami, Yoko; Klein, Raymond M.
2015-01-01
The current study examined the robustness, stability, reliability, and isolability of the attention network scores (alerting, orienting, and executive control) when young children experienced repeated administrations of the child version of the Attention Network Test (ANT; Rueda et al., 2004). Ten test sessions of the ANT were administered to 12…
ERIC Educational Resources Information Center
Ishigami, Yoko; Klein, Raymond M.
2015-01-01
The current study examined the robustness, stability, reliability, and isolability of the attention network scores (alerting, orienting, and executive control) when young children experienced repeated administrations of the child version of the Attention Network Test (ANT; Rueda et al., 2004). Ten test sessions of the ANT were administered to 12…
Shi, Wei; Lu, Wensheng; Jiang, Long
2009-10-01
Herein, we reported an efficient and universal protocol to prepare gold nanoparticles capped by a dodecanethiol and cetyltrimethyl ammonium bromide interdigitated bilayer which could be dispersed well in either aqueous or organic solvents without additional phase transfer reagents. The gold nanoparticles were synthesized in a micro-emulsion method with transferring the precursor hydrophobic dodecanethiol-capped gold nanoparticles into cetyltrimethyl ammonium bromide aqueous solution. The advantage of this work consists in controlling the diameter of the core gold nanoparticles by capping of dodecanethiol, obtaining high concentration and robust colloidal stability monodisperse amphiphilic gold nanoparticles of various sizes in 2 nm, 5 nm and 7.5 nm, which is very difficult to realize with other methods as far as we known. Very few change existed in the size and intrinsic optical property during the conversion from the aqueous phase to the organic phase and back to aqueous phase, showing these size-controllable amphiphilic gold nanoparticles can be applied not only in biological labeling and sensing, design of diagnostic and therapeutic due to their aqueous soluble biological compatibility, but also in assembling ordered 2D or 3D superlattice due to their monodispersity and high concentration.
NASA Astrophysics Data System (ADS)
Ngamroo, Issarachai
2010-12-01
It is well known that the superconducting magnetic energy storage (SMES) is able to quickly exchange active and reactive power with the power system. The SMES is expected to be the smart storage device for power system stabilization. Although the stabilizing effect of SMES is significant, the SMES is quite costly. Particularly, the superconducting magnetic coil size which is the essence of the SMES, must be carefully selected. On the other hand, various generation and load changes, unpredictable network structure, etc., cause system uncertainties. The power controller of SMES which is designed without considering such uncertainties, may not tolerate and loses stabilizing effect. To overcome these problems, this paper proposes the new design of robust SMES controller taking coil size and system uncertainties into account. The structure of the active and reactive power controllers is the 1st-order lead-lag compensator. No need for the exact mathematical representation, system uncertainties are modeled by the inverse input multiplicative perturbation. Without the difficulty of the trade-off of damping performance and robustness, the optimization problem of control parameters is formulated. The particle swarm optimization is used for solving the optimal parameters at each coil size automatically. Based on the normalized integral square error index and the consideration of coil current constraint, the robust SMES with the smallest coil size which still provides the satisfactory stabilizing effect, can be achieved. Simulation studies in the two-area four-machine interconnected power system show the superior robustness of the proposed robust SMES with the smallest coil size under various operating conditions over the non-robust SMES with large coil size.
Faydasicok, Ozlem; Arik, Sabri
2013-08-01
The main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition.
NASA Astrophysics Data System (ADS)
Al-Azzawi, Waleed; Al-Akaidi, Marwan
2015-04-01
In this paper, the robust stability analysis of solar wireless networked control systems (SWNCSs) with stochastic time delays and packet dropout is investigated. The robust model predictive controller (RMPC) technique for the SWNCS is discussed using the linear matrix inequality (LMI) technique. Based on the SWNCS model, the RMPC (a full state feedback controller) can be constructed by using the Lyapunov functional method. Both sensor-to-controller and controller-to-actuator time delays of the SWNCS are considered as stochastic variables controlled by a Markov chain. A discrete-time Markovian jump linear system (MJLS) with norm bounded time delay is presented to model the SWNCSs. Conditions for H∞-norm is used to evaluate stability and stabilization of the fundamental systems derived via LMIs formulation. Finally, an illustrative numerical example is given to demonstrate the effectiveness of the proposed techniques.
Theory, computation, and application of exponential splines
McCartin, B.J.
1981-10-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Theory, computation, and application of exponential splines
NASA Technical Reports Server (NTRS)
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
NASA Astrophysics Data System (ADS)
Nechak, Lyes; Berger, Sébastien; Aubry, Evelyne
2013-03-01
This paper is devoted to the stability analysis of uncertain nonlinear dynamic dry friction systems. The stability property of dry friction systems is known to be very sensitive to the variations of friction laws. Moreover, the friction coefficient admits dispersions due to the manufacturing processes. Therefore, it becomes necessary to take this uncertainty into account in the stability analysis of dry friction systems to ensure robust predictions of stable and instable behaviors. The generalized polynomial chaos formalism is proposed to deal with this challenging problem treated in most cases with the prohibitive Monte Carlo based techniques. Two equivalent methods presented here combine the non-intrusive generalized polynomial chaos with the indirect Lyapunov method. Both methods are shown to be efficient in the estimation of the stability and instability regions with high accuracy and high confidence levels and at lower cost compared with the classic Monte Carlo based method.
Jaballi, Ahmed; Sakly, Anis; Hajjaji, Ahmed El
2016-07-01
This paper provides novel sufficient conditions on robust asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy with time-varying delays. The attention is focused on developing new algebraic criteria to break with classical criteria in terms of Linear Matrix Inequalities (LMIs). Firstly, based on the M-matrix proprieties and through l1,∞ induced norms notion, new delay-dependent sufficient conditions are derived to ensure the asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy systems with time-varying delay. Secondly, these results are extended for a class of uncertain discrete-time switched fuzzy systems with time delays, modeled by difference equations. Finally, two numerical examples and practical example (a robot arm) are provided to demonstrate the advantage and the effectiveness of our results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Jin, Q B; Liu, Q; Huang, B
2016-03-01
This paper considers the problem of determining all the robust PID (proportional-integral-derivative) controllers in terms of the gain and phase margins (GPM) for open-loop unstable first order plus time delay (UFOPTD) processes. It is the first time that the feasible ranges of the GPM specifications provided by a PID controller are given for UFOPTD processes. A gain and phase margin tester is used to modify the original model, and the ranges of the margin specifications are derived such that the modified model can be stabilized by a stabilizing PID controller based on Hermite-Biehlers Theorem. Furthermore, we obtain all the controllers satisfying a given margin specification. Simulation studies show how to use the results to design a robust PID controller.
NASA Astrophysics Data System (ADS)
Ripamonti, Francesco; Resta, Ferruccio; Vivani, Andrea
2015-04-01
The aim of this paper is to present two control logics and an attitude estimator for UAV stabilization and remote piloting, that are as robust as possible to physical parameters variation and to other external disturbances. Moreover, they need to be implemented on low-cost micro-controllers, in order to be attractive for commercial drones. As an example, possible applications of the two switching control logics could be area surveillance and facial recognition by means of a camera mounted on the drone: the high computational speed logic is used to reach the target, when the high-stability one is activated, in order to complete the recognition tasks.
Phenomenology of stochastic exponential growth
NASA Astrophysics Data System (ADS)
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Ko, Hsien-Ju; Yu, Wen-Shyong
2004-08-01
In this paper, an approach for robust stability analysis of a digital closed-loop system for digital controller implementations subject to finite word length (FWL) effects is proposed. Uncertainties caused by the roundoff and computational errors subject to FWL effects are expressed in function of mantissa bit number when the mode of floating-point arithmetic is used in the process. Then, based on the Small Gain Theorem and the Bellman-Grownwall Lemma, a sufficient stability criterion for the digital closed-loop system is derived. The eigenvalue sensitivity of the closed-loop system is developed in terms of mixed matrix-2/Frobenius norms. Then, by minimizing this eigenvalue sensitivity and using orthogonal Hermitian transform as well, an optimal similarity transformation can be obtained. By substituting this optimal transformation into the stability criterion, a minimum mantissa bit number used for implementing the stabilizing digital controllers can be determined. The main contributions are that this approach provides an analytical closed-form solution for obtaining the optimal transformation and, in addition to the stability criterion, leads to the implementation of the stabilizing controllers with a lower mantissa bit number when using this optimal one. Finally, detailed numerical design processes and simulation results are used to illustrate the effectiveness of the proposed scheme.
Embaby, Amira M; Saeed, Hesham; Hussein, Ahmed
2016-12-01
Present study underlines an unusual non-cumbersome-powerful strategy for purification of SHG10 keratinolytic alkaline protease from Bacillus licheniformis SHG10 DSM 28096 with robust stability properties. The enzyme was impressively purified to homogeneity with specific activity, purification fold, and yield of 613.82 U mg(-1) , 58.91 and 99%, respectively, via a sequential two-step purification strategy: precipitation with 65% (NH4 )2 SO4 and flow through fractions of DEAE-cellulose DE 53 column. SDS-PAGE conferred a monomeric enzyme with a molecular mass of 30.4 kDa. The enzyme demonstrated optimal activity at pH (10.0-11.0) and at 65 °C. It exhibited full stability at pH (6.0-11.0) over 38 h at 4 °C and at 65 °C for 15 min. Remarkable enhanced enzyme activity (130.15 and 126.37%) was retained in presence of commercial laundry detergents Oxi and Ariel after 1 h, respectively. Organic solvent stability of the enzyme was verified in butanol, ether, acetonitrile, isopropanol, and chloroform. Imposingly, full storage stability (100%) of the enzyme along 1 year in -20 °C was confirmed. Km -Vmax was 0.00174 mM-534.2 mM Sub · min(-1) · mg protein(-1) and 1.266 mg-28.89 mg Sub · h(-1) · mg protein(-1) on N-Suc-Ala-Ala-Pro-Phe-pNA and keratin azure, respectively. Robust stability properties of SHG10 keratinolytic alkaline protease along with rapid-efficient purification underpin its potential commercialization for industrial exploitation.
Stabilization and robustness of non-linear unity-feedback system - Factorization approach
NASA Technical Reports Server (NTRS)
Desoer, C. A.; Kabuli, M. G.
1988-01-01
The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.
Stabilization and robustness of non-linear unity-feedback system - Factorization approach
NASA Technical Reports Server (NTRS)
Desoer, C. A.; Kabuli, M. G.
1988-01-01
The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.
Robust reliable control design for networked control system with sampling communication
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Santra, Srimanta; Mathiyalagan, K.; Su, Hongye
2015-12-01
In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov-Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.
NASA Astrophysics Data System (ADS)
Akcabay, Deniz Tolga; Xiao, Jian; Young, Yin Lu
2017-06-01
The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid-structure interaction (FSI) models. Classically, partitioned fluid and structure solvers are easier to implement compared to monolithic methods; however, partitioned FSI models are vulnerable to numerical ("virtual added mass") instabilities for cases when the solid to fluid density ratio is low and if the flow is incompressible. As a partitioned method, the loosely hybrid coupled (LHC) method, which was introduced and validated in Young et al. (Acta Mech. Sin. 28:1030-1041, 2012), has been successfully used to efficiently and stably model lightweight and flexible structures. The LHC method achieves its numerical stability by, in addition to the viscous fluid forces, embedding potential flow approximations of the fluid induced forces to transform the partitioned FSI model into a semi-implicit scheme. The objective of this work is to derive and validate the numerical stability boundary of the LHC. The results show that the stability boundary of the LHC is much wider than traditional loosely coupled methods for a variety of numerical integration schemes. The results also show that inclusion of an estimate of the fluid inertial forces is the most critical to ensure the numerical stability when solving for fluid-structure interaction problems involving cases with a solid to fluid-added mass ratio less than one.
NASA Astrophysics Data System (ADS)
Akcabay, Deniz Tolga; Xiao, Jian; Young, Yin Lu
2017-08-01
The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid-structure interaction (FSI) models. Classically, partitioned fluid and structure solvers are easier to implement compared to monolithic methods; however, partitioned FSI models are vulnerable to numerical ("virtual added mass") instabilities for cases when the solid to fluid density ratio is low and if the flow is incompressible. As a partitioned method, the loosely hybrid coupled (LHC) method, which was introduced and validated in Young et al. (Acta Mech. Sin. 28:1030-1041, 2012), has been successfully used to efficiently and stably model lightweight and flexible structures. The LHC method achieves its numerical stability by, in addition to the viscous fluid forces, embedding potential flow approximations of the fluid induced forces to transform the partitioned FSI model into a semi-implicit scheme. The objective of this work is to derive and validate the numerical stability boundary of the LHC. The results show that the stability boundary of the LHC is much wider than traditional loosely coupled methods for a variety of numerical integration schemes. The results also show that inclusion of an estimate of the fluid inertial forces is the most critical to ensure the numerical stability when solving for fluid-structure interaction problems involving cases with a solid to fluid-added mass ratio less than one.
ERIC Educational Resources Information Center
Huynh, Huynh; Rawls, Anita
2011-01-01
There are at least two procedures to assess item difficulty stability in the Rasch model: robust z procedure and "0.3 Logit Difference" procedure. The robust z procedure is a variation of the z statistic that reduces dependency on outliers. The "0.3 Logit Difference" procedure is based on experiences in Rasch linking for tests…
ERIC Educational Resources Information Center
Huynh, Huynh; Rawls, Anita
2011-01-01
There are at least two procedures to assess item difficulty stability in the Rasch model: robust z procedure and "0.3 Logit Difference" procedure. The robust z procedure is a variation of the z statistic that reduces dependency on outliers. The "0.3 Logit Difference" procedure is based on experiences in Rasch linking for tests…
An Exceptional Exponential Function
ERIC Educational Resources Information Center
Curgus, Branko
2006-01-01
We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…
Azizi, Sajad
2017-03-10
The robust stability of a class of feedback linearizable minimum-phase nonlinear system, having parametric uncertainties, is investigated in this study. The system in new coordinates is represented to an equivalent formulation after the attempt of feedback linearization. Due to the parametric uncertainties the approximately linearized system entails a norm bounded input nonlinearity such that the equilibrium point condition in error dynamics can not be satisfied. Accordingly, to guarantee the regional asymptotic stability a control synthesis problem is proposed by means of sufficient Linear Matrix Inequalities (LMIs) together with an amended nonlinear control term, derived from the Lyapunov redesign method, which tackles zero steady-state error condition. The numerical examples of a general aviation aircraft's longitudinal dynamics and inverted pendulum are simulated to show the proficiency of the proposed control technique.
Robust stability analysis of a class of neural networks with discrete time delays.
Faydasicok, Ozlem; Arik, Sabri
2012-05-01
This paper studies the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete constant time delays under parameter uncertainties. The class of the neural network considered in this paper employs the activation functions which are assumed to be continuous and slope-bounded but not required to be bounded or differentiable. We conduct a stability analysis by exploiting the stability theory of Lyapunov functionals and the theory of Homomorphic mapping to derive some easily verifiable sufficient conditions for existence, uniqueness and global asymptotic stability of the equilibrium point. The conditions obtained mainly establish some time-independent relationships between the network parameters of the neural network. We make a detailed comparison between our results and the previously published corresponding results. This comparison proves that our results are new and improve and generalize the results derived in the past literature. We also give some illustrative numerical examples to show the effectiveness and applicability of our proposed stability results.
NASA Astrophysics Data System (ADS)
Schaefer, Bradley E.; Dyson, Samuel E.
1996-08-01
A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.
NASA Astrophysics Data System (ADS)
Balint, Stefan; Balint, Agneta M.
2017-01-01
Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].
Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization
NASA Technical Reports Server (NTRS)
Singh, S. N.; Schy, A. A.
1985-01-01
An approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law, u sub d, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, u sub s, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u sub d + u sub s.
Stability and Robustness Analysis Tools for Marine Robot Localization and Mapping Applications
2009-06-01
propeller, and shaft, and sometimes rivets and welds). DIDSON provides a range and bearing measurement associated with each pixel of each image... Springer - Verlag, 1990, pp. 167-193. [22] M. Csorba, Simultaneous Localisation and Map Building, PhD Thesis, University of Oxford, 1997. [23] G... Springer -Verlag, 2003, pp. 361-371. [39] E. Malis, “Stability Analysis of Invariant Visual Servoing and Robutness to Parametric Uncertainties,” A
Robust stabilization of underactuated nonlinear systems: A fast terminal sliding mode approach.
Khan, Qudrat; Akmeliawati, Rini; Bhatti, Aamer Iqbal; Khan, Mahmood Ashraf
2017-01-01
This paper presents a fast terminal sliding mode based control design strategy for a class of uncertain underactuated nonlinear systems. Strategically, this development encompasses those electro-mechanical underactuated systems which can be transformed into the so-called regular form. The novelty of the proposed technique lies in the hierarchical development of a fast terminal sliding attractor design for the considered class. Having established sliding mode along the designed manifold, the close loop dynamics become finite time stable which, consequently, result in high precision. In addition, the adverse effects of the chattering phenomenon are reduced via strong reachability condition and the robustness of the system against uncertainties is confirmed theoretically. A simulation as well as experimental study of an inverted pendulum is presented to demonstrate the applicability of the proposed technique.
Nanoporous membrane robustness / stability in small form factor microfluidic filtration system.
Johnson, Dean G; Pan, Sabrina; Hayden, Andrew; McGrath, James L
2016-08-01
The development of wearable hemodialysis (HD) devices that replace center-based HD holds the promise to improve both outcomes and quality-of-life for patients with end-stage-renal disease (ERD). A prerequisite for these devices is the development of highly efficient membranes that can achieve high toxin clearance in small footprints. The ultrathin nanoporous membrane material developed by our group is orders of magnitude more permeable than conventional HD membranes. We report on our progress making a prototype wearable dialysis unit. First, we present data from benchtop studies confirming that clinical levels of urea clearance can be obtained in a small animal model with low blood flow rates. Second, we report on efforts to improve the mechanical robustness of high membrane area dialysis devices.
ERIC Educational Resources Information Center
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
ERIC Educational Resources Information Center
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Reichert, Malinda D; Lin, Chia-Cheng; Vela, Javier
2014-07-08
Anisotropic II–VI semiconductor nanostructures are important photoactive materials for various energy conversion and optical applications. However, aside from the many available surface chemistry studies and from their ubiquitous photodegradation under continuous illumination, the general chemical reactivity and thermal stability (phase and shape transformations) of these materials are poorly understood. Using CdSe and CdS nanorods as model systems, we have investigated the behavior of II–VI semiconductor nanorods against various conditions of extreme chemical and physical stress (acids, bases, oxidants, reductants, and heat). CdSe nanorods react rapidly with acids, becoming oxidized to Se or SeO2. In contrast, CdSe nanorods remain mostly unreactive when treated with bases or strong oxidants, although bases do partially etch the tips of the nanorods (along their axis). Roasting (heating in air) of CdSe nanorods results in rock-salt CdO, but neither CdSe nor CdO is easily reduced by hydrogen (H2). Another reductant, n-BuLi, reduces CdSe nanorods to metallic Cd. Variable temperature X-ray diffraction experiments show that axial annealing and selective axial melting of the nanorods precede particle coalescence. Furthermore, thermal analysis shows that the axial melting of II–VI nanorods is a ligand-dependent process. In agreement with chemical reactivity and thermal stability observations, silica-coating experiments show that the sharpest (most curved) II–VI surfaces are most active against heterogeneous nucleation of a silica shell. These results provide valuable insights into the fate and possible ways to enhance the stability and improve the use of II–VI semiconductor nanostructures in the fields of optics, magnetism, and energy conversion.
NASA Astrophysics Data System (ADS)
Balasubramaniam, P.; Sathy, R.
2011-02-01
In this paper, the robust asymptotic stability problem is considered for a class of fuzzy Markovian jumping genetic regulatory networks with uncertain parameters and switching probabilities by delay decomposition approach. The purpose of the addressed stability analysis problem is to establish an easy-to-verify condition under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. A new Lyapunov-Krasovskii functional (LKF) is constructed by nonuniformly dividing the delay interval into multiple subinterval, and choosing proper functionals with different weighting matrices corresponding to different subintervals in the LKFs. Employing these new LKFs for the time-varying delays, a new delay-dependent stability criterion is established with Markovian jumping parameters by T-S fuzzy model. Note that the obtained results are formulated in terms of linear matrix inequality (LMI) that can efficiently solved by the LMI toolbox in Matlab. Numerical examples are exploited to illustrate the effectiveness of the proposed design procedures.
Robust nonlinear controller design to improve the stability of a large scale photovoltaic system
NASA Astrophysics Data System (ADS)
Islam, Gazi Md. Saeedul
Recently interest in photovoltaic (PV) power generation systems is increasing rapidly and the installation of large PV systems or large groups of PV systems that are interconnected with the utility grid is accelerating despite their high cost and low efficiency due to environmental issues and depletions of fossil fuels. Most of the photovoltaic (PV) applications are grid connected. Existing power systems may face the stability problems because of the high penetration of PV systems to the grid. Therefore, more stringent grid codes are being imposed by the energy regulatory bodies for grid integration of PV plants. Recent grid codes dictate that PV plants need to stay connected with the power grid during the network faults because of their increased power penetration level. This requires the system to have large disturbance rejection capability to protect the system and provide dynamic grid support. This thesis presents a new control method to enhance the steady-state and transient stabilities of a grid connected large scale photovoltaic (PV) system. A new control coordination scheme is also presented to reduce the power mismatch during the fault condition in order to limit the fault currents, which is one of the salient features of this study. The performance of the overall system is analyzed using laboratory standard power system simulation software PSCAD/EMTDC.
Minakshi, Manickam; Barmi, Maryam J; Jones, Robert T
2017-03-14
Hybrid capacitors can replace or complement batteries, while storing energy through ion adsorption and fast surface redox reactions. There is a growing demand in developing nanostructured materials as electrodes for hybrid systems that can enhance the specific capacitance by ion desolvation in the nanopores. Here, we demonstrate that rescaling the pore diameter with the aid of biopolymer at an optimal level during the synthesis of metal molybdate leads to high capacitance 124 F g(-1) giving robust capacitance retention of 80% over 2000 cycles for a constructed device (activated carbon vs. metal molybdate). The presence of biopolymer (l-glutamic acid) in the metal molybdate acts as a complexing agent of the metal ion while enhancing the mass transport and hence it's improved electrochemical performance. However, XPS and other elemental analyses illustrated no evidence for N doping but traces of other surface functional groups (i.e. C and O) could be present on the molybdate surface. The biopolymer synthetic approach has the advantage of yielding nanostructured material with a relatively narrow pore size distribution controlled by l-glutamic acid. This study will provide a generic route to rescale other metal molybdate, phosphate or oxide counterparts and be an added value to the database.
NASA Astrophysics Data System (ADS)
Requejo, Rubén J.; Camacho, Juan; Cuesta, José A.; Arenas, Alex
2012-08-01
The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.
Collaborative Research: Robust Climate Projections and Stochastic Stability of Dynamical Systems
Ghil, Michael; McWilliams, James; Neelin, J. David; Zaliapin, Ilya; Chekroun, Mickael; Kondrashov, Dmitri; Simonnet, Eric
2011-10-13
The project was completed along the lines of the original proposal, with additional elements arising as new results were obtained. The originally proposed three thrusts were expanded to include an additional, fourth one. (i) The e ffects of stochastic perturbations on climate models have been examined at the fundamental level by using the theory of deterministic and random dynamical systems, in both nite and in nite dimensions. (ii) The theoretical results have been implemented first on a delay-diff erential equation (DDE) model of the El-Nino/Southern-Oscillation (ENSO) phenomenon. (iii) More detailed, physical aspects of model robustness have been considered, as proposed, within the stripped-down ICTP-AGCM (formerly SPEEDY) climate model. This aspect of the research has been complemented by both observational and intermediate-model aspects of mid-latitude and tropical climate. (iv) An additional thrust of the research relied on new and unexpected results of (i) and involved reduced-modeling strategies and associated prediction aspects have been tested within the team's empirical model reduction (EMR) framework. Finally, more detailed, physical aspects have been considered within the stripped-down SPEEDY climate model. The results of each of these four complementary e fforts are presented in the next four sections, organized by topic and by the team members concentrating on the topic under discussion.
Zhong, Xungao; Zhong, Xunyu; Peng, Xiafu
2013-01-01
In this paper, a global-state-space visual servoing scheme is proposed for uncalibrated model-independent robotic manipulation. The scheme is based on robust Kalman filtering (KF), in conjunction with Elman neural network (ENN) learning techniques. The global map relationship between the vision space and the robotic workspace is learned using an ENN. This learned mapping is shown to be an approximate estimate of the Jacobian in global space. In the testing phase, the desired Jacobian is arrived at using a robust KF to improve the ENN learning result so as to achieve robotic precise convergence of the desired pose. Meanwhile, the ENN weights are updated (re-trained) using a new input-output data pair vector (obtained from the KF cycle) to ensure robot global stability manipulation. Thus, our method, without requiring either camera or model parameters, avoids the corrupted performances caused by camera calibration and modeling errors. To demonstrate the proposed scheme's performance, various simulation and experimental results have been presented using a six-degree-of-freedom robotic manipulator with eye-in-hand configurations. PMID:24108426
Zhong, Xungao; Zhong, Xunyu; Peng, Xiafu
2013-10-08
In this paper, a global-state-space visual servoing scheme is proposed for uncalibrated model-independent robotic manipulation. The scheme is based on robust Kalman filtering (KF), in conjunction with Elman neural network (ENN) learning techniques. The global map relationship between the vision space and the robotic workspace is learned using an ENN. This learned mapping is shown to be an approximate estimate of the Jacobian in global space. In the testing phase, the desired Jacobian is arrived at using a robust KF to improve the ENN learning result so as to achieve robotic precise convergence of the desired pose. Meanwhile, the ENN weights are updated (re-trained) using a new input-output data pair vector (obtained from the KF cycle) to ensure robot global stability manipulation. Thus, our method, without requiring either camera or model parameters, avoids the corrupted performances caused by camera calibration and modeling errors. To demonstrate the proposed scheme's performance, various simulation and experimental results have been presented using a six-degree-of-freedom robotic manipulator with eye-in-hand configurations.
Quéro, Anthony; Jousse, Cyril; Lequart-Pillon, Michelle; Gontier, Eric; Guillot, Xavier; Courtois, Bernard; Courtois, Josiane; Pau-Roblot, Corinne
2014-11-01
Plant metabolite profiling is commonly carried out by GC-MS of methoximated trimethylsilyl (TMS) derivatives. This technique is robust and enables a library search for spectra produced by electron ionization. However, recent articles have described problems associated with the low stability of some TMS derivatives. This limits the use of GC-MS for metabolomic studies that need large sets of qualitative and quantitative analyses. The aim of this work is to determine the experimental conditions in which the stability of TMS derivatives could be improved. This would facilitate the analysis of the large-scale experimental designs needed in the metabolomics approach. For good repeatability, the sampling conditions and the storage temperature of samples during analysis were investigated. Multiple injections of one sample from one vial led to high variations while injection of one sample from different vials improved the analysis. However, before injection, some amino acid TMS derivatives were degraded during the storage of vials in the autosampler. Only 10% of the initial quantity of glutamine 3 TMS and glutamate 3 TMS and 66% of α-alanine 2 TMS was detected 48 h after derivatization. When stored at 4 °C until injection, all TMS derivatives remained stable for 12 h; at -20 °C, they remained stable for 72 h. From the integration of all these results, a detailed analytical procedure is thus proposed. It enables a robust quantification of polar metabolites, useful for further plant metabolomics studies using GC-MS. Copyright © 2014 Elsevier B.V. All rights reserved.
A robust stabilization methodology for time domain integral equations in electromagnetics
NASA Astrophysics Data System (ADS)
Pray, Andrew J.
Time domain integral equations (TDIEs) are an attractive framework from which to analyze electromagnetic scattering problems. Casting problems in the time domain enables study of systems with nonlinearities, characterization of transient behavior both at the early and late time, and broadband analysis within a single simulation. Integral equation frameworks have the advantages of restricting the computational domain to the scatterer surface (boundary integral equations) or volume (volume integral equations), implicitly satisfying the radiation boundary condition, and being free of numerical dispersion error. Despite these advantages, TDIE solvers are not widely used by computational practitioners; principally because TDIE solutions are susceptible to late-time instability. While a plethora of stabilization schemes have been developed, particularly since the early 1980s, most of these schemes either do not guarantee stability, are difficult to implement, or are impractical for certain problems. The most promising methods seem to be the space-time Galerkin schemes. These are very challenging to implement as they require the accurate evaluation of 4-dimensional spatial integrals. The most successful recent approach to implementing these schemes has been to approximate a subset of these integrals, and evaluate the remaining integrals analytically. This approach describes the quasi-exact integration methods [Shanker et al. IEEE TAP 2009, Shi et al. IEEE TAP 2011]. The method of [Shanker et al. IEEE TAP 2009] approximates 2 of the 4 dimensions using numerical quadrature. The remaining integrals are evaluated analytically by determining shadow boundaries on the domain of integration. In [Shi et al. IEEE TAP 2011], only 1 dimension is approximated, but the procedure also relies on analytical integration between shadow boundaries. These two characteristics-the need to find shadow boundaries and develop analytical integration rules-prevent these methods from being extended
A robust method to screen detergents for membrane protein stabilization, revisited.
Champeil, Philippe; Orlowski, Stéphane; Babin, Simon; Lund, Sten; le Maire, Marc; Møller, Jesper; Lenoir, Guillaume; Montigny, Cédric
2016-10-15
This report is a follow up of our previous paper (Lund, Orlowski, de Foresta, Champeil, le Maire and Møller (1989), J Biol Chem 264:4907-4915) showing that solubilization in detergent of a membrane protein may interfere with its long-term stability, and proposing a protocol to reveal the kinetics of such irreversible inactivation. We here clarify the fact that when various detergents are tested for their effects, special attention has of course to be paid to their critical micelle concentration. We also investigate the effects of a few more detergents, some of which have been recently advertised in the literature, and emphasize the role of lipids together with detergents. Among these detergents, lauryl maltose neopentyl glycol (LMNG) exerts a remarkable ability, even higher than that of β-dodecylmaltoside (DDM), to protect our test enzyme, the paradigmatic P-type ATPase SERCA1a from sarcoplasmic reticulum. Performing such experiments for one's favourite protein probably remains useful in pre-screening assays testing various detergents. Copyright © 2016 Elsevier Inc. All rights reserved.
Robust design of polyrhythmic neural circuits
NASA Astrophysics Data System (ADS)
Schwabedal, Justus T. C.; Neiman, Alexander B.; Shilnikov, Andrey L.
2014-08-01
Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.
Exponentially fitted symplectic integrator
NASA Astrophysics Data System (ADS)
Simos, T. E.; Vigo-Aguiar, Jesus
2003-01-01
In this paper a procedure for constructing efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the exponential fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge-Kutta-Nyström second-order algebraic exponentially fitted method is developed. We give explicitly the symplecticness conditions for the modified Runge-Kutta-Nyström method. We also give the exponential fitting and trigonometric fitting conditions. Numerical results indicate that the present method is much more efficient than the “classical” symplectic Runge-Kutta-Nyström second-order algebraic method introduced by M.P. Calvo and J.M. Sanz-Serna [J. Sci. Comput. (USA) 14, 1237 (1993)]. We note that the present procedure is appropriate for all near-unimodal systems.
NASA Astrophysics Data System (ADS)
Frye, Michael Takaichi
This dissertation examines the problem of global decentralized control by output feedback for large-scale uncertain nonlinear systems whose subsystems are interconnected not only by their outputs but also by their unmeasurable states. Several innovative techniques will be developed to create decentralized output feedback controllers rendering the closed-loop systems globally asymptotically stable. This is accomplished by extending an output feedback domination design that requires only limited information about the nonlinear system. We will apply our design to lower, upper, and non-triangular nonlinear systems. A time-varying output feedback controller is also constructed for use with large-scale systems that have unknown parameters. Furthermore, a mixed large-scale system consisting of both lower and upper triangular systems is shown to be stabilizable by employing a combined high and low gain domination technique. The significance of our results is that we do not need to have prior information about the nonlinearities of the system. In addition, a new design technique was developed using homogeneous system theory, which allows for the design of nonsmooth controllers and observers to stabilize a class of feedforward system with uncontrollable and unobservable linearization. An example of a large-scale system is a group of autonomous airships performing the function of a temporary mobile cell phone network. An airship mobile cell phone network is a novel solution to the problem of maintaining communication during the advent of extensive damage to the communication infrastructure; be it from a flood, earthquake, hurricane, or terrorist attack. A first principle force-based dynamic model for the Tri-Turbofan Airship was developed and will be discussed in detail. The mathematical model was based on actual flight test data that has been collected at the Gait Analysis and Innovative Technologies Laboratory. This model was developed to research autonomous airship
Nonuniform exponential dichotomies and Lyapunov functions
NASA Astrophysics Data System (ADS)
Barreira, Luis; Dragičević, Davor; Valls, Claudia
2017-05-01
For the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential dichotomy in terms of quadratic Lyapunov sequences. We emphasize that, in sharp contrast with previous results, we consider the general case of possibly noninvertible linear operators, thus requiring only the invertibility along the unstable direction. As an application, we give a simple proof of the robustness of a nonuniform exponential dichotomy under sufficiently small linear perturbations.
Exponential Localization of Photons
NASA Astrophysics Data System (ADS)
Bialynicki-Birula, Iwo
1998-06-01
It is shown that photons can be localized in space with an exponential falloff of the energy density and photodetection rates. The limits of localization are determined by the fundamental Paley-Wiener theorem. A direct mathematical connection between the spatial localization of photons and the decay in time of quantum mechanical systems is established.
Leng, Y; Wang, Z; Tsai, L-K; Leeds, P; Fessler, E B; Wang, J; Chuang, D-M
2015-02-01
Fibroblast growth factor-21 (FGF-21) is a new member of the FGF super-family and an important endogenous regulator of glucose and lipid metabolism. It has been proposed as a therapeutic target for diabetes and obesity. Its function in the central nervous system (CNS) remains unknown. Previous studies from our laboratory demonstrated that aging primary neurons are more vulnerable to glutamate-induced excitotoxicity, and that co-treatment with the mood stabilizers lithium and valproic acid (VPA) induces synergistic neuroprotective effects. This study sought to identify molecule(s) involved in these synergistic effects. We found that FGF-21 mRNA was selectively and markedly elevated by co-treatment with lithium and VPA in primary rat brain neurons. FGF-21 protein levels were also robustly increased in neuronal lysates and culture medium following lithium-VPA co-treatment. Combining glycogen synthase kinase-3 (GSK-3) inhibitors with VPA or histone deacetylase (HDAC) inhibitors with lithium synergistically increased FGF-21 mRNA levels, supporting that synergistic effects of lithium and VPA are mediated via GSK-3 and HDAC inhibition, respectively. Exogenous FGF-21 protein completely protected aging neurons from glutamate challenge. This neuroprotection was associated with enhanced Akt-1 activation and GSK-3 inhibition. Lithium-VPA co-treatment markedly prolonged lithium-induced Akt-1 activation and augmented GSK-3 inhibition. Akt-1 knockdown markedly decreased FGF-21 mRNA levels and reduced the neuroprotection induced by FGF-21 or lithium-VPA co-treatment. In addition, FGF-21 knockdown reduced lithium-VPA co-treatment-induced Akt-1 activation and neuroprotection against excitotoxicity. Together, our novel results suggest that FGF-21 is a key mediator of the effects of these mood stabilizers and a potential new therapeutic target for CNS disorders.
Li, Xiansen; Narayanan, Shankar; Michaelis, Vladimir K; Ong, Ta-Chung; Keeler, Eric G; Kim, Hyunho; McKay, Ian S; Griffin, Robert G; Wang, Evelyn N
2015-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg(2+) ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg,Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the labscale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N2 sorption, (27)Al/(29)Si MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick's 2(nd) law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications.
Leng, Yan; Wang, Zhifei; Tsai, Li-Kai; Leeds, Peter; Fessler, Emily Bame; Wang, Junyu; Chuang, De-Maw
2013-01-01
Fibroblast growth factor-21 (FGF-21) is a new member of the FGF super-family and an important endogenous regulator of glucose and lipid metabolism. It has been proposed as a therapeutic target for diabetes and obesity. Its function in the central nervous system (CNS) remains unknown. Previous studies from our laboratory demonstrated that aging primary neurons are more vulnerable to glutamate-induced excitotoxicity, and that co-treatment with the mood stabilizers lithium and valproic acid (VPA) induces synergistic neuroprotective effects. This study sought to identify molecule(s) involved in these synergistic effects. We found that FGF-21 mRNA was selectively and dramatically elevated by co-treatment with lithium and VPA in primary rat brain neurons. FGF-21 protein levels were also robustly increased in neuronal lysates and culture medium following lithium-VPA co-treatment. Combining glycogen synthase kinase-3 (GSK-3) inhibitors with VPA or histone deacetylase (HDAC) inhibitors with lithium synergistically increased FGF-21 mRNA levels, supporting that synergistic effects of lithium and VPA are mediated via GSK-3 and HDAC inhibition, respectively. Exogenous FGF-21 protein completely protected aging neurons from glutamate challenge. This neuroprotection was associated with enhanced Akt-1 activation and GSK-3 inhibition. Lithium-VPA co-treatment dramatically prolonged lithium-induced Akt-1 activation and augmented GSK-3 inhibition. Akt-1 knockdown markedly decreased FGF-21 mRNA levels, and reduced the neuroprotection induced by FGF-21 or lithium-VPA co-treatment. In addition, FGF-21 knockdown reduced lithium-VPA co-treatment-induced Akt-1 activation and neuroprotection against excitotoxicity. Together, our novel results suggest that FGF-21 is a key mediator of the effects of these mood stabilizers, and a potential new therapeutic target for CNS disorders. PMID:24468826
Li, XS; Narayanan, S; Michaelis, VK; Ong, TC; Keeler, EG; Kim, H; Mckay, IS; Griffin, RG; Wang, EN
2015-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg2+ ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg, Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the lab-scale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N-2 sorption, Al-27/Si-29 MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick's 2nd law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N-2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. (C) 2014 Elsevier Inc. All rights reserved.
Li, Xiansen; Narayanan, Shankar; Michaelis, Vladimir K.; Ong, Ta-Chung; Keeler, Eric G.; Kim, Hyunho; McKay, Ian S.; Griffin, Robert G.; Wang, Evelyn N.
2014-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg2+ ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg,Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the labscale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N2 sorption, 27Al/29Si MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick’s 2nd law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. PMID:25395877
NASA Astrophysics Data System (ADS)
Vachirasricirikul, Sitthidet; Ngamroo, Issarachai; Kaitwanidvilai, Somyot
It is well known that the power system controller designed by H∞ control is complicated, high order and impractical. In power system applications, practical structures such as proportional integral derivative (PID) etc., are widely used, because of their simple structure, less number of tuning parameters and low-order. However, tuning of controller parameters to achieve a good performance and robustness is based on designer's experiences. To overcome this problem, this paper proposes a fixed structure robust H∞ loop shaping control to design Static Var Compensator (SVC) and Automatic Voltage Regulator (AVR) for robust stabilization of voltage fluctuation in an isolated wind-diesel hybrid power system. The structure of the robust controller of SVC and AVR is specified by a PID controller. In the system modeling, a normalized coprime factorization is applied to represent possible unstructured uncertainties in the power system such as variation of system parameters, generating and loading conditions etc. Based on the H∞ loop shaping, the performance and robust stability conditions are formulated as the optimization problem. The particle swarm optimization is applied to solve for PID control parameters of SVC and AVR simultaneously. Simulation studies confirm the control effect and robustness of the proposed control.
Okaru, Alex O.; Abuga, Kennedy O.; Kamau, Franco N.; Ndwigah, Stanley N.; Lachenmeier, Dirk W.
2017-01-01
A simple, isocratic and robust RP-HPLC method for the analysis of azithromycin was developed, validated and applied for the analysis of bulk samples, tablets and suspensions. The optimum chromatographic conditions for separation were established as a mobile phase comprised of acetonitrile-0.1 M KH2PO4 pH 6.5–0.1 M tetrabutyl ammonium hydroxide pH 6.5-water (25:15:1:59 v/v/v/v) delivered at a flow rate of 1.0 mL/min. The stationary phase consisted of reverse-phase XTerra® (250 mm × 4.6 mm i.d., 5 µm particle size) maintained at a temperature of 43 °C with a UV detection at 215 nm. The method was found to be linear in the range 50%–150% (r2 = 0.997). The limits of detection and quantification were found to be 0.02% (20 µg) and 0.078% (78 µg), respectively, with a 100.7% recovery of azithromycin. Degradation products of azithromycin in acidic and oxidative environments at 37 °C were resolved from the active pharmaceutical ingredient and thus the method is fit for the purpose of drug stability confirmation. PMID:28245574
Bapatu, Hanimi Reddy; Maram, Ravi Kumar; Murthy, R Satyanarayana
2015-10-01
A novel, reversed-phase high-performance liquid chromatographic method was developed and validated for the determination of related substances in Plerixafor (PLX) drug substance. PLX is an immunostimulant used to mobilize hematopoietic stem cells in cancer patients. The method is efficient for estimation of all degradation and process-related impurities. The method was developed using the Phenomenex Luna L11 column using the gradient program with mobile phase A and mobile phase B, where mobile phase A consists of pH 2.0 1-heptanesulfonic acid sodium salt buffer and acetonitrile in the ratio of 80:20 (v/v) and mobile phase B consists of pH 2.0 1-heptanesulfonic acid sodium salt buffer and acetonitrile in the ratio of 20:80 (v/v). PLX and its impurities were monitored at 210 nm. The present work is describing the role of ion-pair reagent in the separation of polar compounds. PLX was subjected to various stress conditions of oxidative, acid, base, hydrolytic, thermal, humidity and photolytic degradations. The degradation products were well separated from each other and with the main peak, demonstrating the stability-indicating power of the method. The performance of the method was validated according to the present ICH guidelines for specificity, limit of detection, limit of quantification, linearity, accuracy, precision, ruggedness and robustness.
Exponentiated power Lindley distribution
Ashour, Samir K.; Eltehiwy, Mahmoud A.
2014-01-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data. PMID:26644927
Exponentiated power Lindley distribution.
Ashour, Samir K; Eltehiwy, Mahmoud A
2015-11-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data.
Exponential fitting BDF Runge Kutta algorithms
NASA Astrophysics Data System (ADS)
Vigo-Aguiar, J.; Martín-Vaquero, J.; Ramos, H.
2008-01-01
In other papers, the authors presented exponential fitting methods of BDF type. Now, these methods are used to derive some BDF-Runge-Kutta type formulas (of second-, third- and fourth-order), capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential with parameter A and ordinary polynomials. Theorems of the truncation error reveal the good behavior of the new methods for stiff problems. Plots of their absolute stability regions that include the whole of the negative real axis are provided. Different procedures to find the parameter of the method are proposed, using these techniques there will not be necessary to compute the exponential matrix at each step, even when nonlinear problems are integrated. Numerical examples underscore the efficiency of the proposed codes, especially when they are integrating stiff problems.
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Wright, Charles; Henry, Jon; Burov, Stas; Lin, Yihan; Crosson, Sean; Dinner, Aaron; Scherer, Norbert
2013-03-01
The interplay between growth and division of cells is has been studied in the context of exponential growth of bacterial cells (in suitable conditions) for decades. However, bulk culture studies obscure phenomena that manifest in single cells over many generations. We introduce a unique technology combining microfluidics, single-cell imaging, and quantitative analysis. This enables us to track the growth of single Caulobacter crescentus stalked cells over hundreds of generations. The statistics that we extract indicate a size thresholding mechanism for cell division and a non-trivial scaling collapse of division time distributions at different temperatures. In this talk I shall discuss these observations and a stochastic model of growth and division that captures all our observations with no free parameters.
Forecasting exponential growth and exponential decline: similarities and differences.
Ebersbach, Mirjam; Lehner, Mirjam; Resing, Wilma C M; Wilkening, Friedrich
2008-02-01
Previous research has demonstrated adults' difficulties with explicitly forecasting exponential processes. Exponential growth is usually grossly underestimated, whereas exponential decline is forecast more accurately. By contrast, the present study examined implicit knowledge about exponential processes and how it is affected by function type (growth versus decline) in samples of 7-, 10-, 14-year-olds, and adults (N=80). Different indicators of the quality of forecasts were investigated. As opposed to previous findings, participants of all age groups estimated exponential decline less adequately than exponential growth. This effect could be attributed mainly to the fact that, in relation to fitted exponential functions, the starting value, or intercept, of the function was approximated well for exponential growth but badly with regard to exponential decline. The accuracy of the non-linear component in forecast functions barely differed between function types within the same age group. Furthermore, even 7-year-olds appeared to have a preliminary understanding of exponential processes, while both intercepts and exponents of forecasts became more accurate with age. Theoretical and practical implications are discussed.
NASA Technical Reports Server (NTRS)
Haddad, Wassim M.; Bernstein, Dennis S.
1991-01-01
Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: (1) a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and (2) two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed.
NASA Technical Reports Server (NTRS)
Soo, Han Lee
1991-01-01
Researchers developed a robust control law for slow motions for the accurate trajectory control of a flexible robot. The control law does not need larger velocity gains than position gains, which some researchers need to ensure the stability of a rigid robot. Initial experimentation for the Small Articulated Manipulator (SAM) shows that control laws that use smaller velocity gains are more robust to signal noise than the control laws that use larger velocity gains. Researchers analyzed the stability of the composite control law, the robust control for the slow motion, and the strain rate feedback for the fast control. The stability analysis was done by using a quadratic Liapunov function. Researchers found that the flexible motion of links could be controlled by relating the input force to the flexible signals which are sensed at the near tip of each link. The signals are contaminated by the time delayed input force. However, the effect of the time delayed input force can be reduced by giving a certain configuration to the SAM.
NASA Technical Reports Server (NTRS)
Soo, Han Lee
1991-01-01
Researchers developed a robust control law for slow motions for the accurate trajectory control of a flexible robot. The control law does not need larger velocity gains than position gains, which some researchers need to ensure the stability of a rigid robot. Initial experimentation for the Small Articulated Manipulator (SAM) shows that control laws that use smaller velocity gains are more robust to signal noise than the control laws that use larger velocity gains. Researchers analyzed the stability of the composite control law, the robust control for the slow motion, and the strain rate feedback for the fast control. The stability analysis was done by using a quadratic Liapunov function. Researchers found that the flexible motion of links could be controlled by relating the input force to the flexible signals which are sensed at the near tip of each link. The signals are contaminated by the time delayed input force. However, the effect of the time delayed input force can be reduced by giving a certain configuration to the SAM.
Exponential Boundary Observers for Pressurized Water Pipe
NASA Astrophysics Data System (ADS)
Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel
2015-11-01
This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.
NASA Astrophysics Data System (ADS)
Fermi, Enrico
The Patent contains an extremely detailed description of an atomic pile employing natural uranium as fissile material and graphite as moderator. It starts with the discussion of the theory of the intervening phenomena, in particular the evaluation of the reproduction or multiplication factor, K, that is the ratio of the number of fast neutrons produced in one generation by the fissions to the original number of fast neutrons, in a system of infinite size. The possibility of having a self-maintaining chain reaction in a system of finite size depends both on the facts that K is greater than unity and the overall size of the system is sufficiently large to minimize the percentage of neutrons escaping from the system. After the description of a possible realization of such a pile (with many detailed drawings), the various kinds of neutron losses in a pile are depicted. Particularly relevant is the reported "invention" of the exponential experiment: since theoretical calculations can determine whether or not a chain reaction will occur in a give system, but can be invalidated by uncertainties in the parameters of the problem, an experimental test of the pile is proposed, aimed at ascertaining if the pile under construction would be divergent (i.e. with a neutron multiplication factor K greater than 1) by making measurements on a smaller pile. The idea is to measure, by a detector containing an indium foil, the exponential decrease of the neutron density along the length of a column of uranium-graphite lattice, where a neutron source is placed near its base. Such an exponential decrease is greater or less than that expected due to leakage, according to whether the K factor is less or greater than 1, so that this experiment is able to test the criticality of the pile, its accuracy increasing with the size of the column. In order to perform this measure a mathematical description of the effect of neutron production, diffusion, and absorption on the neutron density in the
OPINION: Safe exponential manufacturing
NASA Astrophysics Data System (ADS)
Phoenix, Chris; Drexler, Eric
2004-08-01
In 1959, Richard Feynman pointed out that nanometre-scale machines could be built and operated, and that the precision inherent in molecular construction would make it easy to build multiple identical copies. This raised the possibility of exponential manufacturing, in which production systems could rapidly and cheaply increase their productive capacity, which in turn suggested the possibility of destructive runaway self-replication. Early proposals for artificial nanomachinery focused on small self-replicating machines, discussing their potential productivity and their potential destructiveness if abused. In the light of controversy regarding scenarios based on runaway replication (so-called 'grey goo'), a review of current thinking regarding nanotechnology-based manufacturing is in order. Nanotechnology-based fabrication can be thoroughly non-biological and inherently safe: such systems need have no ability to move about, use natural resources, or undergo incremental mutation. Moreover, self-replication is unnecessary: the development and use of highly productive systems of nanomachinery (nanofactories) need not involve the construction of autonomous self-replicating nanomachines. Accordingly, the construction of anything resembling a dangerous self-replicating nanomachine can and should be prohibited. Although advanced nanotechnologies could (with great difficulty and little incentive) be used to build such devices, other concerns present greater problems. Since weapon systems will be both easier to build and more likely to draw investment, the potential for dangerous systems is best considered in the context of military competition and arms control.
Vaseem, Mohammad; McKerricher, Garret; Shamim, Atif
2016-01-13
Currently, silver-nanoparticle-based inkjet ink is commercially available. This type of ink has several serious problems such as a complex synthesis protocol, high cost, high sintering temperatures (∼200 °C), particle aggregation, nozzle clogging, poor shelf life, and jetting instability. For the emerging field of printed electronics, these shortcomings in conductive inks are barriers for their widespread use in practical applications. Formulating particle-free silver inks has potential to solve these issues and requires careful design of the silver complexation. The ink complex must meet various requirements, such as in situ reduction, optimum viscosity, storage and jetting stability, smooth uniform sintered films, excellent adhesion, and high conductivity. This study presents a robust formulation of silver-organo-complex (SOC) ink, where complexing molecules act as reducing agents. The 17 wt % silver loaded ink was printed and sintered on a wide range of substrates with uniform surface morphology and excellent adhesion. The jetting stability was monitored for 5 months to confirm that the ink was robust and highly stable with consistent jetting performance. Radio frequency inductors, which are highly sensitive to metal quality, were demonstrated as a proof of concept on flexible PEN substrate. This is a major step toward producing high-quality electronic components with a robust inkjet printing process.
On the Matrix Exponential Function
ERIC Educational Resources Information Center
Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai
2006-01-01
A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.
On the Matrix Exponential Function
ERIC Educational Resources Information Center
Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai
2006-01-01
A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.
Rajchakit, G; Saravanakumar, R; Ahn, Choon Ki; Karimi, Hamid Reza
2017-02-01
This article examines the exponential stability analysis problem of generalized neural networks (GNNs) including interval time-varying delayed states. A new improved exponential stability criterion is presented by establishing a proper Lyapunov-Krasovskii functional (LKF) and employing new analysis theory. The improved reciprocally convex combination (RCC) and weighted integral inequality (WII) techniques are utilized to obtain new sufficient conditions to ascertain the exponential stability result of such delayed GNNs. The superiority of the obtained results is clearly demonstrated by numerical examples.
NASA Astrophysics Data System (ADS)
Wang, Yonggang; Wen, Ting; Park, Changyong; Kenney-Benson, Curtis; Pravica, Michael; Yang, Wenge; Zhao, Yusheng
2016-01-01
The structure stability under high pressure and thermal expansion behavior of Na3OBr and Na4OI2, two prototypes of alkali-metal-rich antiperovskites, were investigated by in situ synchrotron X-ray diffraction techniques under high pressure and low temperature. Both are soft materials with bulk modulus of 58.6 GPa and 52.0 GPa for Na3OBr and Na4OI2, respectively. The cubic Na3OBr structure and tetragonal Na4OI2 with intergrowth K2NiF4 structure are stable under high pressure up to 23 GPa. Although being a characteristic layered structure, Na4OI2 exhibits nearly isotropic compressibility. Negative thermal expansion was observed at low temperature range (20-80 K) in both transition-metal-free antiperovskites for the first time. The robust high pressure structure stability was examined and confirmed by first-principles calculations among various possible polymorphisms qualitatively. The results provide in-depth understanding of the negative thermal expansion and robust crystal structure stability of these antiperovskite systems and their potential applications.
Wang, Yonggang E-mail: yangwg@hpstar.ac.cn; Wen, Ting; Park, Changyong; Kenney-Benson, Curtis; Pravica, Michael; Zhao, Yusheng E-mail: yangwg@hpstar.ac.cn; Yang, Wenge E-mail: yangwg@hpstar.ac.cn
2016-01-14
The structure stability under high pressure and thermal expansion behavior of Na{sub 3}OBr and Na{sub 4}OI{sub 2}, two prototypes of alkali-metal-rich antiperovskites, were investigated by in situ synchrotron X-ray diffraction techniques under high pressure and low temperature. Both are soft materials with bulk modulus of 58.6 GPa and 52.0 GPa for Na{sub 3}OBr and Na{sub 4}OI{sub 2}, respectively. The cubic Na{sub 3}OBr structure and tetragonal Na{sub 4}OI{sub 2} with intergrowth K{sub 2}NiF{sub 4} structure are stable under high pressure up to 23 GPa. Although being a characteristic layered structure, Na{sub 4}OI{sub 2} exhibits nearly isotropic compressibility. Negative thermal expansion was observed at low temperature range (20–80 K) in both transition-metal-free antiperovskites for the first time. The robust high pressure structure stability was examined and confirmed by first-principles calculations among various possible polymorphisms qualitatively. The results provide in-depth understanding of the negative thermal expansion and robust crystal structure stability of these antiperovskite systems and their potential applications.
Faure, Guilhem; Koonin, Eugene V.
2016-01-01
Robustness to destabilizing effects of mutations is thought of as a key factor of protein evolution. The connections between two measures of robustness, the relative core size and the computationally estimated effect of mutations on protein stability (ΔΔG), protein abundance and the selection pressure on protein-coding genes (dN/dS) were analyzed for the organisms with a large number of available protein structures including four eukaryotes, two bacteria and one archaeon. The distribution of the effects of mutations in the core on protein stability is universal and indistinguishable in eukaryotes and bacteria, centered at slightly destabilizing amino acid replacements, and with a heavy tail of more strongly destabilizing replacements. The distribution of mutational effects in the hyperthermophilic archaeon Thermococcus gammatolerans is significantly shifted toward strongly destabilizing replacements which is indicative of stronger constraints that are imposed on proteins in hyperthermophiles. The median effect of mutations is strongly, positively correlated with the relative core size, in evidence of the congruence between the two measures of protein robustness. However, both measures show only limited correlations to the expression level and selection pressure on protein-coding genes. Thus, the degree of robustness reflected in the universal distribution of mutational effects appears to be a fundamental, ancient feature of globular protein folds whereas the observed variations are largely neutral and uncoupled from short term protein evolution. A weak anticorrelation between protein core size and selection pressure is observed only for surface residues in prokaryotes but a stronger anticorrelation is observed for all residues in eukaryotic proteins. This substantial difference between proteins of prokaryotes and eukaryotes is likely to stem from the demonstrable higher compactness of prokaryotic proteins. PMID:25927823
NASA Astrophysics Data System (ADS)
Faure, Guilhem; Koonin, Eugene V.
2015-05-01
Robustness to destabilizing effects of mutations is thought of as a key factor of protein evolution. The connections between two measures of robustness, the relative core size and the computationally estimated effect of mutations on protein stability (ΔΔG), protein abundance and the selection pressure on protein-coding genes (dN/dS) were analyzed for the organisms with a large number of available protein structures including four eukaryotes, two bacteria and one archaeon. The distribution of the effects of mutations in the core on protein stability is universal and indistinguishable in eukaryotes and bacteria, centered at slightly destabilizing amino acid replacements, and with a heavy tail of more strongly destabilizing replacements. The distribution of mutational effects in the hyperthermophilic archaeon Thermococcus gammatolerans is significantly shifted toward strongly destabilizing replacements which is indicative of stronger constraints that are imposed on proteins in hyperthermophiles. The median effect of mutations is strongly, positively correlated with the relative core size, in evidence of the congruence between the two measures of protein robustness. However, both measures show only limited correlations to the expression level and selection pressure on protein-coding genes. Thus, the degree of robustness reflected in the universal distribution of mutational effects appears to be a fundamental, ancient feature of globular protein folds whereas the observed variations are largely neutral and uncoupled from short term protein evolution. A weak anticorrelation between protein core size and selection pressure is observed only for surface residues in prokaryotes but a stronger anticorrelation is observed for all residues in eukaryotic proteins. This substantial difference between proteins of prokaryotes and eukaryotes is likely to stem from the demonstrable higher compactness of prokaryotic proteins.
Faure, Guilhem; Koonin, Eugene V
2015-04-30
Robustness to destabilizing effects of mutations is thought of as a key factor of protein evolution. The connections between two measures of robustness, the relative core size and the computationally estimated effect of mutations on protein stability (ΔΔG), protein abundance and the selection pressure on protein-coding genes (dN/dS) were analyzed for the organisms with a large number of available protein structures including four eukaryotes, two bacteria and one archaeon. The distribution of the effects of mutations in the core on protein stability is universal and indistinguishable in eukaryotes and bacteria, centered at slightly destabilizing amino acid replacements, and with a heavy tail of more strongly destabilizing replacements. The distribution of mutational effects in the hyperthermophilic archaeon Thermococcus gammatolerans is significantly shifted toward strongly destabilizing replacements which is indicative of stronger constraints that are imposed on proteins in hyperthermophiles. The median effect of mutations is strongly, positively correlated with the relative core size, in evidence of the congruence between the two measures of protein robustness. However, both measures show only limited correlations to the expression level and selection pressure on protein-coding genes. Thus, the degree of robustness reflected in the universal distribution of mutational effects appears to be a fundamental, ancient feature of globular protein folds whereas the observed variations are largely neutral and uncoupled from short term protein evolution. A weak anticorrelation between protein core size and selection pressure is observed only for surface residues in prokaryotes but a stronger anticorrelation is observed for all residues in eukaryotic proteins. This substantial difference between proteins of prokaryotes and eukaryotes is likely to stem from the demonstrable higher compactness of prokaryotic proteins.
Otto, M. R.; René de Cotret, L. P.; Stern, M. J.; Siwick, B. J.
2017-01-01
We demonstrate the compression of electron pulses in a high-brightness ultrafast electron diffraction instrument using phase-locked microwave signals directly generated from a mode-locked femtosecond oscillator. Additionally, a continuous-wave phase stabilization system that accurately corrects for phase fluctuations arising in the compression cavity from both power amplification and thermal drift induced detuning was designed and implemented. An improvement in the microwave timing stability from 100 fs to 5 fs RMS is measured electronically, and the long-term arrival time stability (>10 h) of the electron pulses improves to below our measurement resolution of 50 fs. These results demonstrate sub-relativistic ultrafast electron diffraction with compressed pulses that is no longer limited by laser-microwave synchronization. PMID:28852686
Dynamic controller design for exponential synchronization of Chen chaotic system
NASA Astrophysics Data System (ADS)
Park, Ju H.; Lee, S. M.; Kwon, O. M.
2007-07-01
The Letter considers synchronization of Chen chaotic system. The problems of determining the exponential stability and estimating the exponential convergence rate for the synchronization are investigated by employing the Lyapunov functional method and linear matrix inequality (LMI) technique. For this end, a dynamic controller is proposed for the first time and a criterion for existence of the controller is given in terms of LMIs. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Is radioactive decay really exponential?
NASA Astrophysics Data System (ADS)
Aston, P. J.
2012-03-01
Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of 14C can be calibrated over a period of 12550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3000 years are in error, which is generally attributed to past variation in atmospheric levels of 14C. We note that predicted atmospheric variation (assuming exponential decay) does not agree with results from modelling, and that theoretical quantum mechanics does not predict exact exponential decay. We give mathematical arguments that non-exponential decay should be expected for slowly decaying isotopes and explore the consequences of non-exponential decay. We propose an experimental test of this prediction of non-exponential decay for 14C. If confirmed, a foundation stone of current dating methods will have been removed, requiring a radical reappraisal both of radioisotope dating methods and of currently predicted dates obtained using these methods.
Rauk, Adam P; Guo, Kevin; Hu, Yanling; Cahya, Suntara; Weiss, William F
2014-08-01
Defining a suitable product presentation with an acceptable stability profile over its intended shelf-life is one of the principal challenges in bioproduct development. Accelerated stability studies are routinely used as a tool to better understand long-term stability. Data analysis often employs an overall mass action kinetics description for the degradation and the Arrhenius relationship to capture the temperature dependence of the observed rate constant. To improve predictive accuracy and precision, the current work proposes a least-squares estimation approach with a single nonlinear covariate and uses a polynomial to describe the change in a product attribute with respect to time. The approach, which will be referred to as Arrhenius time-scaled (ATS) least squares, enables accurate, precise predictions to be achieved for degradation profiles commonly encountered during bioproduct development. A Monte Carlo study is conducted to compare the proposed approach with the common method of least-squares estimation on the logarithmic form of the Arrhenius equation and nonlinear estimation of a first-order model. The ATS least squares method accommodates a range of degradation profiles, provides a simple and intuitive approach for data presentation, and can be implemented with ease.
Universality in Stochastic Exponential Growth
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.
2014-07-01
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
NASA Astrophysics Data System (ADS)
Ankarali, M. Mert; Saranli, Uluç
2010-09-01
In this paper, we analyze the self-stability properties of planar running with a dissipative spring-mass model driven by torque actuation at the hip. We first show that a two-dimensional, approximate analytic return map for uncontrolled locomotion with this system under a fixed touchdown leg angle policy and an open-loop ramp torque profile exhibits only marginal self-stability that does not always persist for the exact system. We then propose a per-stride feedback strategy for the hip torque that explicitly compensates for damping losses, reducing the return map to a single dimension and substantially improving the robust stability of fixed points. Subsequent presentation of simulation evidence establishes that the predictions of this approximate model are consistent with the behavior of the exact plant model. We illustrate the relevance and utility of our model both through the qualitative correspondence of its predictions to biological data as well as its use in the design of a task-level running controller.
Liu, Xue; Du, Jing; Shao, Yang; Zhao, Shao-Fan; Yao, Ke-Fu
2017-08-31
Metallic core-shell nanostructures have inspired prominent research interests due to their better performances in catalytic, optical, electric, and magnetic applications as well as the less cost of noble metal than monometallic nanostructures, but limited by the complicated and expensive synthesis approaches. Development of one-pot and inexpensive method for metallic core-shell nanostructures' synthesis is therefore of great significance. A novel Cu network supported nanoporous Ag-Cu alloy with an Ag shell and an Ag-Cu core was successfully synthesized by one-pot chemical dealloying of Zr-Cu-Ag-Al-O amorphous/crystalline composite, which provides a new way to prepare metallic core-shell nanostructures by a simple method. The prepared nanoporous Ag-Cu@Ag core-shell alloy demonstrates excellent air-stability at room temperature and enhanced oxidative stability even compared with other reported Cu@Ag core-shell micro-particles. In addition, the nanoporous Ag-Cu@Ag core-shell alloy also possesses robust antibacterial activity against E. Coli DH5α. The simple and low-cost synthesis method as well as the excellent oxidative stability promises the nanoporous Ag-Cu@Ag core-shell alloy potentially wide applications.
Jiang, Yanjun; Liu, Xinlong; Chen, Yafei; Zhou, Liya; He, Ying; Ma, Li; Gao, Jing
2014-02-01
A novel catalytic system of Pickering emulsion stabilized by lipase-containing periodic mesoporous organosilica was constructed (named LP@PE) and used as biocatalyst for biodiesel production. The reaction parameters were optimized and the optimum conditions were as follows: the water fraction 0.65%, molar ratio of ethanol to oleic acid 2:1, immobilized lipase particles 150mg, phosphate buffer pH 7.0 and temperature 30°C. Under these conditions, the maximum biodiesel yield obtained via esterification of oleic acid with ethanol could reach 95.8%. The biodiesel yield could maintain 88.6% after LP@PE was used 15times. The LP@PE was also used in the synthesis of biodiesel from Jatropha curcas oil. The highest yield could reach 87.1% and the yield was 73.0% after 10 cycles. All these results demonstrated that Pickering emulsion system stabilized by immobilized enzyme may possess much potential in many enzymatic industrial applications. Copyright © 2013 Elsevier Ltd. All rights reserved.
Real-Time Exponential Curve Fits Using Discrete Calculus
NASA Technical Reports Server (NTRS)
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Exponential sensitivity of noise-driven switching in genetic networks
NASA Astrophysics Data System (ADS)
Mehta, Pankaj; Mukhopadhyay, Ranjan; Wingreen, Ned
2008-03-01
Cells are known to utilize biochemical noise to probabilistically switch between distinct gene expression states. We demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. However, provided mRNA lifetimes are short, switching can still be accurately simulated using protein-only models of gene expression. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably.
Exponential sensitivity of noise-driven switching in genetic networks
NASA Astrophysics Data System (ADS)
Mehta, Pankaj; Mukhopadhyay, Ranjan; Wingreen, Ned S.
2008-06-01
There is increasing experimental evidence that cells can utilize biochemical noise to switch probabilistically between distinct gene-expression states. In this paper, we demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably. We discuss our results in the context of competence in the bacterium Bacillus subtilis.
Barth, Aline Bergesch; de Oliveira, Gabriela Bolfe; Malesuik, Marcelo Donadel; Paim, Clésio Soldatelli; Volpato, Nadia Maria
2011-08-01
A stability-indicating liquid chromatography method for the determination of the antifungal agent butenafine hydrochloride (BTF) in a cream was developed and validated using the Plackett-Burman experimental design for robustness evaluation. Also, the drug photodegradation kinetics was determined. The analytical column was operated with acetonitrile, methanol and a solution of triethylamine 0.3% adjusted to pH 4.0 (6:3:1) at a flow rate of 1 mL/min and detection at 283 nm. BTF extraction from the cream was done with n-butyl alcohol and methanol in ultrasonic bath. The performed degradation conditions were: acid and basic media with HCl 1M and NaOH 1M, respectively, oxidation with H(2)O(2) 10%, and the exposure to UV-C light. No interference in the BTF elution was verified. Linearity was assessed (r(2) = 0.9999) and ANOVA showed non-significative linearity deviation (p > 0.05). Adequate results were obtained for repeatability, intra-day precision, and accuracy. Critical factors were selected to examine the method robustness with the two-level Plackett-Burman experimental design and no significant factors were detected (p > 0.05). The BTF photodegradation kinetics was determined for the standard and for the cream, both in methanolic solution, under UV light at 254 nm. The degradation process can be described by first-order kinetics in both cases.
Ishigami, Yoko; Klein, Raymond M.
2011-01-01
Ishigami and Klein (2010) showed that scores of the three attention networks (alerting, orienting, and executive control) measured with the two versions of the Attention Network Test (ANT; Fan et al., 2002; Callejas et al., 2005) were robust over 10 sessions of repeated testing even though practice effects were consistently observed especially in the executive network when young adults were tested. The current study replicated their method to examine robustness, stability, reliability, and isolability of the networks scores when older adults were tested with these ANTs. Ten test sessions, each containing two versions of the ANT, were administered to 10 older adults. Participants were asked to indicate the direction of a target arrow, flanked by distractors, presented either above or below the fixation following auditory signals or/and visual cue. Network scores were calculated using orthogonal subtractions of performance in selected conditions. All network scores remained highly significant even after nine previous sessions despite some practice effects in the executive and the alerting networks. Some lack of independence among the networks was found. The relatively poor reliability of network scores with one session of data rises to respectable levels as more data is added. PMID:22110440
Approximating Functions with Exponential Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Linear or Exponential Number Lines
ERIC Educational Resources Information Center
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather…
Quantum properties of exponential states
Luis, Alfredo
2007-05-15
The use of Renyi entropy as an uncertainty measure alternative to variance leads to the study of states with quantum fluctuations below the levels established by Gaussian states, which are the position-momentum minimum uncertainty states according to variance. We examine the quantum properties of states with exponential wave functions, which combine reduced fluctuations with practical feasibility.
Linear or Exponential Number Lines
ERIC Educational Resources Information Center
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather…
Punctuated evolution and robustness in morphogenesis.
Grigoriev, D; Reinitz, J; Vakulenko, S; Weber, A
2014-09-01
This paper presents an analytic approach to the pattern stability and evolution problem in morphogenesis. The approach used here is based on the ideas from the gene and neural network theory. We assume that gene networks contain a number of small groups of genes (called hubs) controlling morphogenesis process. Hub genes represent an important element of gene network architecture and their existence is empirically confirmed. We show that hubs can stabilize morphogenetic pattern and accelerate the morphogenesis. The hub activity exhibits an abrupt change depending on the mutation frequency. When the mutation frequency is small, these hubs suppress all mutations and gene product concentrations do not change, thus, the pattern is stable. When the environmental pressure increases and the population needs new genotypes, the genetic drift and other effects increase the mutation frequency. For the frequencies that are larger than a critical amount the hubs turn off; and as a result, many mutations can affect phenotype. This effect can serve as an engine for evolution. We show that this engine is very effective: the evolution acceleration is an exponential function of gene redundancy. Finally, we show that the Eldredge-Gould concept of punctuated evolution results from the network architecture, which provides fast evolution, control of evolvability, and pattern robustness. To describe analytically the effect of exponential acceleration, we use mathematical methods developed recently for hard combinatorial problems, in particular, for so-called k-SAT problem, and numerical simulations. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Punctuated evolution and robustness in morphogenesis
Grigoriev, D.; Reinitz, J.; Vakulenko, S.; Weber, A.
2014-01-01
This paper presents an analytic approach to the pattern stability and evolution problem in morphogenesis. The approach used here is based on the ideas from the gene and neural network theory. We assume that gene networks contain a number of small groups of genes (called hubs) controlling morphogenesis process. Hub genes represent an important element of gene network architecture and their existence is empirically confirmed. We show that hubs can stabilize morphogenetic pattern and accelerate the morphogenesis. The hub activity exhibits an abrupt change depending on the mutation frequency. When the mutation frequency is small, these hubs suppress all mutations and gene product concentrations do not change, thus, the pattern is stable. When the environmental pressure increases and the population needs new genotypes, the genetic drift and other effects increase the mutation frequency. For the frequencies that are larger than a critical amount the hubs turn off; and as a result, many mutations can affect phenotype. This effect can serve as an engine for evolution. We show that this engine is very effective: the evolution acceleration is an exponential function of gene redundancy. Finally, we show that the Eldredge-Gould concept of punctuated evolution results from the network architecture, which provides fast evolution, control of evolvability, and pattern robustness. To describe analytically the effect of exponential acceleration, we use mathematical methods developed recently for hard combinatorial problems, in particular, for so-called k-SAT problem, and numerical simulations. PMID:24996115
Vasantha, Vivek Arjunan; Junhui, Chen; Ying, Tay Boon; Parthiban, Anbanandam
2015-10-13
Metal nanoparticles (MNps) tend to be influenced by environmental factors such as pH, ionic strength, and temperature, thereby leading to aggregation. Forming stable aqueous dispersions could be one way of addressing the environmental toxicity of MNps. In contrast to the electrolyte-induced aggregation of MNps, novel zwitterionic sulfabetaine polymers reported here act as stabilizers of MNps even under high salinity. Polysulfabetaines exhibited unique solubility and swelling tendencies in brine and deionized water, respectively. The polysulfabetaines derived from methacrylate (PSBMA) and methacrylamide (PSBMAm) also showed reversible salt-responsive and thermoresponsive behaviors as confirmed by cloud-point titration, transmittance, and dynamic light scattering studies. The brine soluble nature was explored for its ability to be used as a capping agents to form metal nanoparticles using formic acid as a reducing agent. Thus, silver and noble metal (gold and palladium) nanoparticles were synthesized. The nanoparticles formed were characterized by UV-vis, XRD, TEM, EDX, and DLS studies. The size of the nanoparticles remained more or less the same even after 2 months of storage in 2 M sodium chloride solution under ambient conditions and also at elevated temperatures as confirmed by light-scattering measurements. The tunable, stimuli-responsive polysulfabetaine-capped stable MNp formed under low (hyposalinity) and hypersalinity could find potential applications in a variety of areas.
Dolev, Danny; Függer, Matthias; Posch, Markus; Schmid, Ulrich; Steininger, Andreas; Lenzen, Christoph
2014-01-01
We present the first implementation of a distributed clock generation scheme for Systems-on-Chip that recovers from an unbounded number of arbitrary transient faults despite a large number of arbitrary permanent faults. We devise self-stabilizing hardware building blocks and a hybrid synchronous/asynchronous state machine enabling metastability-free transitions of the algorithm's states. We provide a comprehensive modeling approach that permits to prove, given correctness of the constructed low-level building blocks, the high-level properties of the synchronization algorithm (which have been established in a more abstract model). We believe this approach to be of interest in its own right, since this is the first technique permitting to mathematically verify, at manageable complexity, high-level properties of a fault-prone system in terms of its very basic components. We evaluate a prototype implementation, which has been designed in VHDL, using the Petrify tool in conjunction with some extensions, and synthesized for an Altera Cyclone FPGA. PMID:26516290
Dolev, Danny; Függer, Matthias; Posch, Markus; Schmid, Ulrich; Steininger, Andreas; Lenzen, Christoph
2014-06-01
We present the first implementation of a distributed clock generation scheme for Systems-on-Chip that recovers from an unbounded number of arbitrary transient faults despite a large number of arbitrary permanent faults. We devise self-stabilizing hardware building blocks and a hybrid synchronous/asynchronous state machine enabling metastability-free transitions of the algorithm's states. We provide a comprehensive modeling approach that permits to prove, given correctness of the constructed low-level building blocks, the high-level properties of the synchronization algorithm (which have been established in a more abstract model). We believe this approach to be of interest in its own right, since this is the first technique permitting to mathematically verify, at manageable complexity, high-level properties of a fault-prone system in terms of its very basic components. We evaluate a prototype implementation, which has been designed in VHDL, using the Petrify tool in conjunction with some extensions, and synthesized for an Altera Cyclone FPGA.
Chen, Shanliang; Shang, Minghui; Wang, Lin; Yang, Zuobao; Gao, Fengmei; Zheng, Jinju; Yang, Weiyou
2017-10-11
Low turn-on fields together with boosted stabilities are recognized as two key factors for pushing forward the implementations of the field emitters in electronic units. In current work, we explored superior flexible field emitters based on single-crystalline 3C-SiC nanowires, which had numbers of sharp edges, as well as corners surrounding the wire body and B dopants. The as-constructed field emitters behaved exceptional field emission (FE) behaviors with ultralow turn-on fields (Eto) of 0.94-0.68 V/μm and current emission fluctuations of ±1.0-3.4%, when subjected to harsh working conditions under different bending cycles, various bending configurations, as well as elevated temperature environments. The sharp edges together with the edges were able to significantly increase the electron emission sites, and the incorporated B dopants could bring a more localized state close to the Fermi level, which rendered the SiC nanowire emitters with low Eto, large field enhancement factor as well as robust current emission stabilities. Current B-doped SiC nanowires could meet all essential requirements for an ideal flexible emitters, which exhibit their promising prospect to be applied in flexible electronic units.
Generalized exponential function and discrete growth models
NASA Astrophysics Data System (ADS)
Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino
2009-07-01
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Application of Krylov exponential propagation to fluid dynamics equations
NASA Technical Reports Server (NTRS)
Saad, Youcef; Semeraro, David
1991-01-01
An application of matrix exponentiation via Krylov subspace projection to the solution of fluid dynamics problems is presented. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.
Robust growth of Escherichia coli.
Wang, Ping; Robert, Lydia; Pelletier, James; Dang, Wei Lien; Taddei, Francois; Wright, Andrew; Jun, Suckjoon
2010-06-22
The quantitative study of the cell growth has led to many fundamental insights in our understanding of a wide range of subjects, from the cell cycle to senescence. Of particular importance is the growth rate, whose constancy represents a physiological steady state of an organism. Recent studies, however, suggest that the rate of elongation during exponential growth of bacterial cells decreases cumulatively with replicative age for both asymmetrically and symmetrically dividing organisms, implying that a "steady-state" population consists of individual cells that are never in a steady state of growth. To resolve this seeming paradoxical observation, we studied the long-term growth and division patterns of Escherichia coli cells by employing a microfluidic device designed to follow steady-state growth and division of a large number of cells at a defined reproductive age. Our analysis of approximately 10(5) individual cells reveals a remarkable stability of growth whereby the mother cell inherits the same pole for hundreds of generations. We further show that death of E. coli is not purely stochastic but is the result of accumulating damages. We conclude that E. coli, unlike all other aging model systems studied to date, has a robust mechanism of growth that is decoupled from cell death.
Abbasi, Hamid; Bennet, Laura; Gunn, Alistair J; Unsworth, Charles P
2017-05-01
Currently, there are no developed methods to detect sharp wave transients that exist in the latent phase after hypoxia-ischemia (HI) in the electroencephalogram (EEG) in order to determine if these micro-scale transients are potential biomarkers of HI. A major issue with sharp waves in the HI-EEG is that they possess a large variability in their sharp wave profile making it difficult to build a compact 'footprint of uncertainty' (FOU) required for ideal performance of a Type-2 fuzzy logic system (FLS) classifier. In this paper, we develop a novel computational EEG analysis method to robustly detect sharp waves using over 30[Formula: see text]h of post occlusion HI-EEG from an equivalent, in utero, preterm fetal sheep model cohort. We demonstrate that initial wavelet transform (WT) of the sharp waves stabilizes the variation in their profile and thus permits a highly compact FOU to be built, hence, optimizing the performance of a Type-2 FLS. We demonstrate that this method leads to higher overall performance of [Formula: see text] for the clinical [Formula: see text] sampled EEG and [Formula: see text] for the high resolution [Formula: see text] sampled EEG that is improved upon over conventional standard wavelet [Formula: see text] and [Formula: see text], respectively, and fuzzy approaches [Formula: see text] and [Formula: see text], respectively, when performed in isolation.
Saad, Ahmed S; Ismail, Nahla S; Soliman, Marwa; Zaazaa, Hala E
2016-01-01
A sensitive and highly selective stability-indicating gradient HPLC method was developed and validated for simultaneous determination of clorsulon (CLO) and ivermectin (IVM) in the presence of their degradation products. The drugs were subjected to different stress conditions, including acid and alkaline hydrolysis, oxidative, thermal, and photolytic forced degradation. The robustness of the proposed method was assessed using the Plackett-Burman experimental design, the factors affecting system performance were defined, and nonsignificant intervals for the significant factors were determined. The separation was carried out on a ZORBAX SB phenyl analytical column (250 × 4.6 mm id, 5 μm particle size), with gradient elution utilizing 10 mM sodium dihydrogen phosphate and acetonitrile as mobile phase. UV detection was performed for CLO and IVM at 254 nm over a concentration range of 4-140 and 5-50 μg/mL, respectively, with mean percentage recoveries of 99.90 ± 1.30 and 98.59 ± 1.16%, respectively. The proposed method was successfully applied to a pharmaceutical dosage form containing the investigated drugs. The results were statistically compared with the official HPLC methods, and no significant differences were found.
Exponential Formulae and Effective Operations
NASA Technical Reports Server (NTRS)
Mielnik, Bogdan; Fernandez, David J. C.
1996-01-01
One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).
Robust stability under additive perturbations
NASA Technical Reports Server (NTRS)
Bhaya, A.; Desoer, C. A.
1985-01-01
A MIMO linear time-invariant feedback system 1S(P,C) is considered which is assumed to be U-stable. The plant P is subjected to an additive perturbation Delta P which is proper but not necessarily stable. It is proved that the perturbed system is U-stable if and only if Delta P(I + Q x Delta P) exp -1 is U-stable.
Teaching about Exponential Growth in Social Studies.
ERIC Educational Resources Information Center
Allen, Rodney F.; LaHart, David E.
1984-01-01
Characteristics of exponential growth which should be taught in social studies classes are listed, and learning activities dealing with exponential growth which can be used in secondary social studies classes are provided. (RM)
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
In ecological networks, network robustness should be large enough to confer intrinsic robustness for tolerating intrinsic parameter fluctuations, as well as environmental robustness for resisting environmental disturbances, so that the phenotype stability of ecological networks can be maintained, thus guaranteeing phenotype robustness. However, it is difficult to analyze the network robustness of ecological systems because they are complex nonlinear partial differential stochastic systems. This paper develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance sensitivity in ecological networks. We found that the phenotype robustness criterion for ecological networks is that if intrinsic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations and environmental disturbances. These results in robust ecological networks are similar to that in robust gene regulatory networks and evolutionary networks even they have different spatial-time scales.
Robust controls with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1993-01-01
This final report summarizes the recent results obtained by the principal investigator and his coworkers on the robust stability and control of systems containing parametric uncertainty. The starting point is a generalization of Kharitonov's theorem obtained in 1989, and its generalization to the multilinear case, the singling out of extremal stability subsets, and other ramifications now constitutes an extensive and coherent theory of robust parametric stability that is summarized in the results contained here.
Observational constraints on exponential gravity
Yang, Louis; Lee, Chung-Chi; Luo, Ling-Wei; Geng, Chao-Qiang
2010-11-15
We study the observational constraints on the exponential gravity model of f(R)=-{beta}R{sub s}(1-e{sup -R/R}{sub s}). We use the latest observational data including Supernova Cosmology Project Union2 compilation, Two-Degree Field Galaxy Redshift Survey, Sloan Digital Sky Survey Data Release 7, and Seven-Year Wilkinson Microwave Anisotropy Probe in our analysis. From these observations, we obtain a lower bound on the model parameter {beta} at 1.27 (95% C.L.) but no appreciable upper bound. The constraint on the present matter density parameter is 0.245<{Omega}{sub m}{sup 0}<0.311 (95% C.L.). We also find out the best-fit value of model parameters on several cases.
Wang, Nianfang; Koh, Sungjun; Jeong, Byeong Guk; Lee, Dongkyu; Kim, Whi Dong; Park, Kyoungwon; Nam, Min Ki; Lee, Kangha; Kim, Yewon; Lee, Baek-Hee; Lee, Kangtaek; Bae, Wan Ki; Lee, Doh C
2017-05-05
We present facile synthesis of bright CdS/CdSe/CdS@SiO2 nanoparticles with 72% of quantum yields (QYs) retaining ca 80% of the original QYs. The main innovative point is the utilization of the highly luminescent CdS/CdSe/CdS seed/spherical quantum well/shell (SQW) as silica coating seeds. The significance of inorganic semiconductor shell passivation and structure design of quantum dots (QDs) for obtaining bright QD@SiO2 is demonstrated by applying silica encapsulation via reverse microemulsion method to three kinds of QDs with different structure: CdSe core and 2 nm CdS shell (CdSe/CdS-thin); CdSe core and 6 nm CdS shell (CdSe/CdS-thick); and CdS core, CdSe intermediate shell and 5 nm CdS outer shell (CdS/CdSe/CdS-SQW). Silica encapsulation inevitably results in lower photoluminescence quantum yield (PL QY) than pristine QDs due to formation of surface defects. However, the retaining ratio of pristine QY is different in the three silica coated samples; for example, CdSe/CdS-thin/SiO2 shows the lowest retaining ratio (36%) while the retaining ratio of pristine PL QY in CdSe/CdS-thick/SiO2 and SQW/SiO2 is over 80% and SQW/SiO2 shows the highest resulting PL QY. Thick outermost CdS shell isolates the excitons from the defects at surface, making PL QY relatively insensitive to silica encapsulation. The bright SiO2-coated SQW sample shows robustness against harsh conditions, such as acid etching and thermal annealing. The high luminescence and long-term stability highlights the potential of using the SQW/SiO2 nanoparticles in bio-labeling or display applications.
NASA Astrophysics Data System (ADS)
Wang, Nianfang; Koh, Sungjun; Jeong, Byeong Guk; Lee, Dongkyu; Kim, Whi Dong; Park, Kyoungwon; Nam, Min Ki; Lee, Kangha; Kim, Yewon; Lee, Baek-Hee; Lee, Kangtaek; Bae, Wan Ki; Lee, Doh C.
2017-05-01
We present facile synthesis of bright CdS/CdSe/CdS@SiO2 nanoparticles with 72% of quantum yields (QYs) retaining ca 80% of the original QYs. The main innovative point is the utilization of the highly luminescent CdS/CdSe/CdS seed/spherical quantum well/shell (SQW) as silica coating seeds. The significance of inorganic semiconductor shell passivation and structure design of quantum dots (QDs) for obtaining bright QD@SiO2 is demonstrated by applying silica encapsulation via reverse microemulsion method to three kinds of QDs with different structure: CdSe core and 2 nm CdS shell (CdSe/CdS-thin); CdSe core and 6 nm CdS shell (CdSe/CdS-thick); and CdS core, CdSe intermediate shell and 5 nm CdS outer shell (CdS/CdSe/CdS-SQW). Silica encapsulation inevitably results in lower photoluminescence quantum yield (PL QY) than pristine QDs due to formation of surface defects. However, the retaining ratio of pristine QY is different in the three silica coated samples; for example, CdSe/CdS-thin/SiO2 shows the lowest retaining ratio (36%) while the retaining ratio of pristine PL QY in CdSe/CdS-thick/SiO2 and SQW/SiO2 is over 80% and SQW/SiO2 shows the highest resulting PL QY. Thick outermost CdS shell isolates the excitons from the defects at surface, making PL QY relatively insensitive to silica encapsulation. The bright SiO2-coated SQW sample shows robustness against harsh conditions, such as acid etching and thermal annealing. The high luminescence and long-term stability highlights the potential of using the SQW/SiO2 nanoparticles in bio-labeling or display applications.
Robust interval-based regulation for anaerobic digestion processes.
Alcaraz-González, V; Harmand, J; Rapaport, A; Steyer, J P; González-Alvarez, V; Pelayo-Ortiz, C
2005-01-01
A robust regulation law is applied to the stabilization of a class of biochemical reactors exhibiting partially known highly nonlinear dynamic behavior. An uncertain environment with the presence of unknown inputs is considered. Based on some structural and operational conditions, this regulation law is shown to exponentially stabilize the aforementioned bioreactors around a desired set-point. This approach is experimentally applied and validated on a pilot-scale (1 m3) anaerobic digestion process for the treatment of raw industrial wine distillery wastewater where the objective is the regulation of the chemical oxygen demand (COD) by using the dilution rate as the manipulated variable. Despite large disturbances on the input COD and state and parametric uncertainties, this regulation law gave excellent performances leading the output COD towards its set-point and keeping it inside a pre-specified interval.
Guo, Zhenyuan; Yang, Shaofu; Wang, Jun
2015-06-01
This paper presents theoretical results on the global exponential synchronization of multiple memristive neural networks with time delays. A novel coupling scheme is introduced, in a general topological structure described by a directed or undirected graph, with a linear diffusive term and discontinuous sign term. Several criteria are derived based on the Lyapunov stability theory to ascertain the global exponential stability of synchronization manifold in the coupling scheme. Simulation results for several examples are given to substantiate the effectiveness of the theoretical results.
Robust reliable sampled-data control for switched systems with application to flight control
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Joby, Maya; Shi, P.; Mathiyalagan, K.
2016-11-01
This paper addresses the robust reliable stabilisation problem for a class of uncertain switched systems with random delays and norm bounded uncertainties. The main aim of this paper is to obtain the reliable robust sampled-data control design which involves random time delay with an appropriate gain control matrix for achieving the robust exponential stabilisation for uncertain switched system against actuator failures. In particular, the involved delays are assumed to be randomly time-varying which obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and employing an average-dwell time approach, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched system. More precisely, the Schur complement and Jensen's integral inequality are used in derivation of stabilisation criteria. By considering the relationship among the random time-varying delay and its lower and upper bounds, a new set of sufficient condition is established for the existence of reliable robust sampled-data control in terms of solution to linear matrix inequalities (LMIs). Finally, an illustrative example based on the F-18 aircraft model is provided to show the effectiveness of the proposed design procedures.
Structurally robust biological networks
2011-01-01
Background The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation. Results In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature. Conclusions The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters. PMID:21586168
A Spectral Lyapunov Function for Exponentially Stable LTV Systems
NASA Technical Reports Server (NTRS)
Zhu, J. Jim; Liu, Yong; Hang, Rui
2010-01-01
This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.
Predicting Escherichia coli's chemotactic drift under exponential gradient
NASA Astrophysics Data System (ADS)
Samanta, Sibendu; Layek, Ritwik; Kar, Shantimoy; Raj, M. Kiran; Mukhopadhyay, Sudipta; Chakraborty, Suman
2017-09-01
Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.
Simple robust control laws for robot manipulators. Part 1: Non-adaptive case
NASA Technical Reports Server (NTRS)
Wen, J. T.; Bayard, D. S.
1987-01-01
A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.
EXPONENTIAL GALAXY DISKS FROM STELLAR SCATTERING
Elmegreen, Bruce G.; Struck, Curtis E-mail: curt@iastate.edu
2013-10-01
Stellar scattering off of orbiting or transient clumps is shown to lead to the formation of exponential profiles in both surface density and velocity dispersion in a two-dimensional non-self gravitating stellar disk with a fixed halo potential. The exponential forms for both nearly flat rotation curves and near-solid-body rotation curves. The exponential does not depend on initial conditions, spiral arms, bars, viscosity, star formation, or strong shear. After a rapid initial development, the exponential saturates to an approximately fixed scale length. The inner exponential in a two-component profile has a break radius comparable to the initial disk radius; the outer exponential is primarily scattered stars.
Designing and engineering evolutionary robust genetic circuits
2010-01-01
Background One problem with engineered genetic circuits in synthetic microbes is their stability over evolutionary time in the absence of selective pressure. Since design of a selective environment for maintaining function of a circuit will be unique to every circuit, general design principles are needed for engineering evolutionary robust circuits that permit the long-term study or applied use of synthetic circuits. Results We first measured the stability of two BioBrick-assembled genetic circuits propagated in Escherichia coli over multiple generations and the mutations that caused their loss-of-function. The first circuit, T9002, loses function in less than 20 generations and the mutation that repeatedly causes its loss-of-function is a deletion between two homologous transcriptional terminators. To measure the effect between transcriptional terminator homology levels and evolutionary stability, we re-engineered six versions of T9002 with a different transcriptional terminator at the end of the circuit. When there is no homology between terminators, the evolutionary half-life of this circuit is significantly improved over 2-fold and is independent of the expression level. Removing homology between terminators and decreasing expression level 4-fold increases the evolutionary half-life over 17-fold. The second circuit, I7101, loses function in less than 50 generations due to a deletion between repeated operator sequences in the promoter. This circuit was re-engineered with different promoters from a promoter library and using a kanamycin resistance gene (kanR) within the circuit to put a selective pressure on the promoter. The evolutionary stability dynamics and loss-of-function mutations in all these circuits are described. We also found that on average, evolutionary half-life exponentially decreases with increasing expression levels. Conclusions A wide variety of loss-of-function mutations are observed in BioBrick-assembled genetic circuits including point
Equivalences between nonuniform exponential dichotomy and admissibility
NASA Astrophysics Data System (ADS)
Zhou, Linfeng; Lu, Kening; Zhang, Weinian
2017-01-01
Relationship between exponential dichotomies and admissibility of function classes is a significant problem for hyperbolic dynamical systems. It was proved that a nonuniform exponential dichotomy implies several admissible pairs of function classes and conversely some admissible pairs were found to imply a nonuniform exponential dichotomy. In this paper we find an appropriate admissible pair of classes of Lyapunov bounded functions which is equivalent to the existence of nonuniform exponential dichotomy on half-lines R± separately, on both half-lines R± simultaneously, and on the whole line R. Additionally, the maximal admissibility is proved in the case on both half-lines R± simultaneously.
Giving Exponential Functions a Fair Shake
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2005-01-01
This article details an exploration of exponential decay and growth relationships using M&M's and dice. Students collect data for mathematical models and use graphing calculators to make sense of the general form of the exponential functions. (Contains 10 figures and 2 tables.)
The matrix exponential in transient structural analysis
NASA Technical Reports Server (NTRS)
Minnetyan, Levon
1987-01-01
The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.
NASA Astrophysics Data System (ADS)
Sun, Gongchen; Pan, Zehao; Senapati, Satyajyoti; Chang, Hsueh-Chia
2017-06-01
We study the spatiotemporal dynamics of a microfluidic system with a nonselective microfluidic channel gated by an ion-selective membrane which separates the ion flux paths of cations and anions. To preserve electroneutrality, the ionic concentration in the system is shown to converge to a specific inhomogeneous distribution with robust constant current fluxes. A circuit scaling theory that collapses measured asymptotic currents verifies that this is a generic and robust mechanism insensitive to channel geometry, ion selectivity, and electrolyte ionic strength. This first temporally stationary but spatially inhomogeneous depletion front can be used for modulating ionic current and for isotachophoretic isolation of low-mobility molecules and exosomes on small diagnostic chips for various medical applications that require robust high-throughput and integrated platforms.
Exponential fitted Gauss, Radau and Lobatto methods of low order
NASA Astrophysics Data System (ADS)
Martín-Vaquero, J.; Vigo-Aguiar, J.
2008-08-01
Several exponential fitting Runge-Kutta methods of collocation type are derived as a generalization of the Gauss, Radau and Lobatto traditional methods of two steps. The new methods are capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential and ordinary polynomials. Theorems of the truncation error reveal the good behavior of the new methods for stiff problems. Plots of their absolute stability regions that include the whole of the negative real axis are provided. A different procedure to find the parameter of the method is proposed. The variable step Radau method of two stages is derived. Finally, numerical examples underscore the efficiency of the proposed codes, especially when they are integrating stiff problems.
Comparing exponential and exponentiated models of drug demand in cocaine users.
Strickland, Justin C; Lile, Joshua A; Rush, Craig R; Stoops, William W
2016-12-01
Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, or 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use) whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values affects demand parameters and their association with drug-use outcomes when using the exponential model but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency and demonstrating construct validity and generalizability. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays.
Zheng, Song
2015-09-01
In this paper, the robust exponential stabilization of uncertain impulsive complex-variable chaotic delayed systems is considered with parameters perturbation and delayed impulses. It is assumed that the considered complex-variable chaotic systems have bounded parametric uncertainties together with the state variables on the impulses related to the time-varying delays. Based on the theories of adaptive control and impulsive control, some less conservative and easily verified stability criteria are established for a class of complex-variable chaotic delayed systems with delayed impulses. Some numerical simulations are given to validate the effectiveness of the proposed criteria of impulsive stabilization for uncertain complex-variable chaotic delayed systems.
Exponential wave-packet spreading via self-interaction time modulation
NASA Astrophysics Data System (ADS)
Zhao, Wen-Lei; Gong, Jiangbin; Wang, Wen-Ge; Casati, Giulio; Liu, Jie; Fu, Li-Bin
2016-11-01
The time-periodic modulation of the self-interaction of a Bose-Einstein condensate or a nonlinear optics system has been recognized as an exciting tool to explore interesting physics that was previously unavailable. This tool is exploited here to examine the exotic dynamics of a nonlinear system described by the Gross-Pitaevskii equation. We observe three remarkable and closely related dynamical phenomena, exponentially localized profile of wave functions in momentum space with localization length exponentially increasing in time, exponential wave-packet spreading, and exponential sensitivity to initial conditions. A hybrid quantum-classical theory is developed to partly explain these findings. Time-periodic self-interaction modulation is seen to be a robust method to achieve superfast spreading and induce genuine chaos even in the absence of any external potential.
A Simulation To Model Exponential Growth.
ERIC Educational Resources Information Center
Appelbaum, Elizabeth Berman
2000-01-01
Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)
A Simulation To Model Exponential Growth.
ERIC Educational Resources Information Center
Appelbaum, Elizabeth Berman
2000-01-01
Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental
2015-01-21
advanced the chemis1:Iy of ftmctional nanopruiicles and used these patiicles in advanced materials assembly for the fabrication of nanopatiicle...polymer ligands, and the robustness resulting fi:om ligand cross-linking post- assembly . The project developed a facile evaporative assembly method...used these particles in advanced materials assembly for the fabrication of nanoparticle-based mesostructures. These hybrid materials possess extremely
ADAPTIVE ROBUST VARIABLE SELECTION
Fan, Jianqing; Fan, Yingying; Barut, Emre
2014-01-01
Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted L1-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the L1-penalty. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, we investigate the model selection oracle property and establish the asymptotic normality of the WR-Lasso. We show that only mild conditions on the model error distribution are needed. Our theoretical results also reveal that adaptive choice of the weight vector is essential for the WR-Lasso to enjoy these nice asymptotic properties. To make the WR-Lasso practically feasible, we propose a two-step procedure, called adaptive robust Lasso (AR-Lasso), in which the weight vector in the second step is constructed based on the L1-penalized quantile regression estimate from the first step. This two-step procedure is justified theoretically to possess the oracle property and the asymptotic normality. Numerical studies demonstrate the favorable finite-sample performance of the AR-Lasso. PMID:25580039
Jana, Sunit Kumar; Guo, Xiurong; Mei, Hui; Seela, Frank
2015-12-18
A new unprecedented metal-mediated base pair was designed that stabilizes reverse Watson-Crick DNA (parallel strand orientation, ps) as well as canonical Watson-Crick DNA (antiparallel strand orientation, aps). This base pair contains two imidazolo-dC units decorated with furan residues. Tm measurements and spectroscopic studies reveal that each silver-mediated furano-imidazolo-dC forms exceptionally stable duplexes with ps and aps chain orientation. This stability increase by a silver-mediated base pair is the highest reported so far for ps and aps DNA helices.
Zhu, Zonglong; Bai, Yang; Liu, Xiao; ...
2016-05-11
Here highly crystalline SnO2 is demonstrated to serve as a stable and robust electron-transporting layer for high-performance perovskite solar cells. Benefiting from its high crystallinity, the relatively thick SnO2 electron-transporting layer (≈120 nm) provides a respectable electron-transporting property to yield a promising power conversion efficiency (PCE)(18.8%) Over 90% of the initial PCE can be retained after 30 d storage in ambient with ≈70% relative humidity.
Zhu, Zonglong; Bai, Yang; Liu, Xiao; Chueh, Chu -Chen; Yang, Shihe; Jen, Alex K. -Y.
2016-05-11
Here highly crystalline SnO_{2} is demonstrated to serve as a stable and robust electron-transporting layer for high-performance perovskite solar cells. Benefiting from its high crystallinity, the relatively thick SnO_{2} electron-transporting layer (≈120 nm) provides a respectable electron-transporting property to yield a promising power conversion efficiency (PCE)(18.8%) Over 90% of the initial PCE can be retained after 30 d storage in ambient with ≈70% relative humidity.
Zhu, Zonglong; Bai, Yang; Liu, Xiao; Chueh, Chu -Chen; Yang, Shihe; Jen, Alex K. -Y.
2016-05-11
Here highly crystalline SnO_{2} is demonstrated to serve as a stable and robust electron-transporting layer for high-performance perovskite solar cells. Benefiting from its high crystallinity, the relatively thick SnO_{2} electron-transporting layer (≈120 nm) provides a respectable electron-transporting property to yield a promising power conversion efficiency (PCE)(18.8%) Over 90% of the initial PCE can be retained after 30 d storage in ambient with ≈70% relative humidity.
NASA Astrophysics Data System (ADS)
van de Vyver, Hans
2006-04-01
This paper provides an investigation of the stability properties of a family of exponentially fitted Runge-Kutta-Nystrom (EFRKN) methods. P-stability is a very important property usually demanded for the numerical solution of stiff oscillatory second-order initial value problems. P-stable EFRKN methods with arbitrary high order are presented in this work. We have proved our results based on a symmetry argument.
Phylogenetic Stochastic Mapping Without Matrix Exponentiation
Irvahn, Jan; Minin, Vladimir N.
2014-01-01
Abstract Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices—an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, which does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods. PMID:24918812
Stochastic Satbility and Performance Robustness of Linear Multivariable Systems
NASA Technical Reports Server (NTRS)
Ryan, Laurie E.; Stengel, Robert F.
1990-01-01
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
Decoherence and Exponential Law: A Solvable Model
NASA Technical Reports Server (NTRS)
Pascazio, Saverio; Namiki, Mikio
1996-01-01
We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.
Exponential energy growth in a Fermi accelerator.
Shah, Kushal; Turaev, Dmitry; Rom-Kedar, Vered
2010-05-01
An unbounded energy growth of particles bouncing off two-dimensional (2D) smoothly oscillating polygons is observed. Notably, such billiards have zero Lyapunov exponents in the static case. For a special 2D polygon geometry--a rectangle with a vertically oscillating horizontal bar--we show that this energy growth is not only unbounded but also exponential in time. For the energy averaged over an ensemble of initial conditions, we derive an a priori expression for the rate of the exponential growth as a function of the geometry and the ensemble type. We demonstrate numerically that the ensemble averaged energy indeed grows exponentially, at a close to the analytically predicted rate-namely, the process is controllable.
Modeling aftershocks as a stretched exponential relaxation
NASA Astrophysics Data System (ADS)
Mignan, A.
2015-11-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.
Method for exponentiating in cryptographic systems
Brickell, Ernest F.; Gordon, Daniel M.; McCurley, Kevin S.
1994-01-01
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view.
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view. PMID:23515240
Designing efficient exponential integrators with EPIRK framework
NASA Astrophysics Data System (ADS)
Rainwater, Greg; Tokman, Mayya
2017-07-01
Exponential propagation iterative methods of Runge-Kutta type (EPIRK) provide a flexible framework to derive efficient exponential integrators for different types of ODE systems. Different classes of EPIRK methods can be constructed depending on the properties of the equations to be solved. Both classically and stiffly accurate EPIRK schemes can be derived. Flexibility of the order conditions allows to optimize coefficients to construct more efficient schemes. Particularly well-performing fourth-order stiffly accurate methods have been derived and applied to a number of problems. A new efficient three-stage fourth order method is presented and tested here using numerical examples.
A method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
ERIC Educational Resources Information Center
Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
2016-01-01
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
ERIC Educational Resources Information Center
Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
2016-01-01
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
Exponentially Fragile PT Symmetry in Lattices with Localized Eigenmodes
Bendix, Oliver; Fleischmann, Ragnar; Kottos, Tsampikos; Shapiro, Boris
2009-07-17
We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting deltaapproxexp{sup -N/x}i where xi is their localization length. The level 'evolution' with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gamma{sub PT}approxmin(delta), thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gamma{sub PT}approx1/N{sup 2} and the distribution P(gamma{sub PT}) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.
Hayes, Roger; LeLacheur, Richard; Dumont, Isabelle; Couerbe, Philippe; Safavi, Afshin; Islam, Rafiq; Pattison, Colin; Cape, Stephanie; Rocci, Mario; Briscoe, Chad; Cojocaru, Laura; Groeber, Elizabeth; Silvestro, Luigi; Bravo, Jennifer; Shoup, Ron; Verville, Manon; Zimmer, Jennifer; Caturla, Maria Cruz; Khadang, Ardeshir; Bourdage, James; Hughes, Nicola; Fatmi, Saadya; Di Donato, Lorella; Sheldon, Curtis; Keyhani, Anahita; Satterwhite, Christina; Yu, Mathilde; Fiscella, Michele; Hulse, James; Lin, Zhongping John; Garofolo, Wei; Savoie, Natasha; Xiao, Yi Qun; Kurylak, Kai; Harris, Sarah; Saxena, Manju; Buonarati, Mike; Lévesque, Ann; Boudreau, Nadine; Lin, Jenny; Khan, Masood U; Ray, Gene; Liu, Yansheng; Xu, Allan; Soni, Gunjan; Ward, Ian; Kingsley, Clare; Ritzén, Hanna; Tabler, Edward; Nicholson, Bob; Bennett, Patrick; van de Merbel, Nico; Karnik, Shane; Bouhajib, Mohammed; Wieling, Jaap; Mulvana, Daniel; Ingelse, Benno; Allen, Mike; Malone, Michele; Fang, Xinping
2016-03-01
The 9th GCCClosed Forum was held just prior to the 2015 Workshop on Recent Issues in Bioanalysis (WRIB) in Miami, FL, USA on 13 April 2015. In attendance were 58 senior-level participants, from eight countries, representing 38 CRO companies offering bioanalytical services. The objective of this meeting was for CRO bioanalytical representatives to meet and discuss scientific and regulatory issues specific to bioanalysis. The issues selected at this year's closed forum include CAPA, biosimilars, preclinical method validation, endogenous biomarkers, whole blood stability, and ELNs. A summary of the industry's best practices and the conclusions from the discussion of these topics is included in this meeting report.
Exponential lifetime improvement in topological quantum memories
NASA Astrophysics Data System (ADS)
Bardyn, Charles-Edouard; Karzig, Torsten
2016-09-01
We propose a simple yet efficient mechanism for passive error correction in topological quantum memories. Our scheme relies on driven-dissipative ancilla systems which couple to local excitations (anyons) and make them "sink" in energy, with no required interaction among ancillae or anyons. Through this process, anyons created by some thermal environment end up trapped in potential "trenches" that they themselves generate, which can be interpreted as a "memory foam" for anyons. This self-trapping mechanism provides an energy barrier for anyon propagation and removes entropy from the memory by favoring anyon recombination over anyon separation (responsible for memory errors). We demonstrate that our scheme leads to an exponential increase of the memory-coherence time with system size L , up to an upper bound Lmax, which can increase exponentially with Δ /T , where T is the temperature and Δ is some energy scale defined by potential trenches. This results in a double exponential increase of the memory time with Δ /T , which greatly improves over the Arrhenius (single-exponential) scaling found in typical quantum memories.
Sparse Exponential Family Principal Component Analysis.
Lu, Meng; Huang, Jianhua Z; Qian, Xiaoning
2016-12-01
We propose a Sparse exponential family Principal Component Analysis (SePCA) method suitable for any type of data following exponential family distributions, to achieve simultaneous dimension reduction and variable selection for better interpretation of the results. Because of the generality of exponential family distributions, the method can be applied to a wide range of applications, in particular when analyzing high dimensional next-generation sequencing data and genetic mutation data in genomics. The use of sparsity-inducing penalty helps produce sparse principal component loading vectors such that the principal components can focus on informative variables. By using an equivalent dual form of the formulated optimization problem for SePCA, we derive optimal solutions with efficient iterative closed-form updating rules. The results from both simulation experiments and real-world applications have demonstrated the superiority of our SePCA in reconstruction accuracy and computational efficiency over traditional exponential family PCA (ePCA), the existing Sparse PCA (SPCA) and Sparse Logistic PCA (SLPCA) algorithms.
A Simple Mechanical Experiment on Exponential Growth
ERIC Educational Resources Information Center
McGrew, Ralph
2015-01-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
A note on the Jackson exponentiality test
NASA Astrophysics Data System (ADS)
Caeiro, Frederico; Marques, Filipe J.; Mateus, Ayana; Atal, Serra
2016-12-01
In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.
Graphical Models via Univariate Exponential Family Distributions
Yang, Eunho; Ravikumar, Pradeep; Allen, Genevera I.; Liu, Zhandong
2016-01-01
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions. PMID:27570498
A Simple Mechanical Experiment on Exponential Growth
ERIC Educational Resources Information Center
McGrew, Ralph
2015-01-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
Non-uniform exponential tension splines
NASA Astrophysics Data System (ADS)
Bosner, Tina; Rogina, Mladen
2007-11-01
We describe explicitly each stage of a numerically stable algorithm for calculating with exponential tension B-splines with non-uniform choice of tension parameters. These splines are piecewisely in the kernel of D 2(D 2?p 2), where D stands for ordinary derivative, defined on arbitrary meshes, with a different choice of the tension parameter p on each interval. The algorithm provides values of the associated B-splines and their generalized and ordinary derivatives by performing positive linear combinations of positive quantities, described as lower-order exponential tension splines. We show that nothing else but the knot insertion algorithm and good approximation of a few elementary functions is needed to achieve machine accuracy. The underlying theory is that of splines based on Chebyshev canonical systems which are not smooth enough to be ECC-systems. First, by de Boor algorithm we construct exponential tension spline of class C 1, and then we use quasi-Oslo type algorithms to evaluate classical non-uniform C 2 tension exponential splines.
Intersection of the Exponential and Logarithmic Curves
ERIC Educational Resources Information Center
Boukas, Andreas; Valahas, Theodoros
2009-01-01
The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…
Exponential examples of solving parity games
NASA Astrophysics Data System (ADS)
Lebedev, V. N.
2016-04-01
This paper is devoted to solving certain problems on the computational complexity of deciding the winner in cyclic games. The main result is the proof of the fact that the nondeterministic potential transformation algorithm designed for solving parity games is exponential in terms of computation time.
Robust control of a spin-stabilized spacecraft via a 1DoF gimbaled-thruster and two reaction wheels.
Kouhi, Hamed; Kabganian, Mansour; Saberi, Farhad Fani; Shahravi, Morteza
2017-01-01
In impulsive orbital maneuvers, thrust vector misalignment from the center of mass (C.M) results in a large disturbance torque. In this paper a thrusting maneuver system is proposed and studied which is based on the combination of a one degree of freedom (1DoF) gimbaled-thruster, two reaction wheels (RWs) and spin-stabilization. The main goals are disturbance rejection and thrust vector stabilization without using reaction control systems (RCS). The nonlinear two-body dynamics of the proposed system is formulated. The controller design is formulated as a multi-objective optimization problem where the peak-value of the control input and H∞ performance are the cost functions. Based on the peak-to-peak gain minimization, the accuracy of the linearized model can be guaranteed. The optimization results give many optimal controllers which are acceptable for a thrusting maneuver. The simulation results illustrate the applicability of the proposed method in presence of the sampling effects of the control inputs. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Zhang, Xuming; Peng, Xiang; Li, Wan; Li, Limin; Gao, Biao; Wu, Guosong; Huo, Kaifu; Chu, Paul K
2015-04-17
A coaxial electrode structure composed of manganese oxide-decorated TiC/C core/shell nanofiber arrays is produced hydrothermally in a KMnO4 solution. The pristine TiC/C core/shell structure prepared on the Ti alloy substrate provides the self-sacrificing carbon shell and highly conductive TiC core, thus greatly simplifying the fabrication process without requiring an additional reduction source and conductive additive. The as-prepared electrode exhibits a high specific capacitance of 645 F g(-1) at a discharging current density of 1 A g(-1) attributable to the highly conductive TiC/C and amorphous MnO2 shell with fast ion diffusion. In the charging/discharging cycling test, the as-prepared electrode shows high stability and 99% capacity retention after 5000 cycles. Although the thermal treatment conducted on the as-prepared electrode decreases the initial capacitance, the electrode undergoes capacitance recovery through structural transformation from the crystalline cluster to layered birnessite type MnO2 nanosheets as a result of dissolution and further electrodeposition in the cycling. 96.5% of the initial capacitance is retained after 1000 cycles at high charging/discharging current density of 25 A g(-1). This study demonstrates a novel scaffold to construct MnO2 based SCs with high specific capacitance as well as excellent mechanical and cycling stability boding well for future design of high-performance MnO2-based SCs.
Global ?-exponential stabilisation of a class of nonlinear networked control systems
NASA Astrophysics Data System (ADS)
Shen, Yan-Jun; Zhang, Daoyuan; Huang, Yuehua; Liu, Yungang
2016-11-01
In this paper, we investigate global ?-exponential stabilisation of a class of nonlinear networked control systems. The network-induced delays are assumed to be random and significantly smaller than the sampling period. First, sufficient conditions are presented to ensure global ?-exponential stability for a class of hybrid systems with time delay. Then, the networked control systems are modelled as the hybrid systems with time delay. By the techniques of adding a power integrator and a recursive argument, a sampled-data state feedback control law is presented. Sufficient conditions are given to ensure global ?-exponential stability of the closed-loop system by constructing a Lyapunov-Krasovskii function. Finally, a numerical example is presented to show the validity of the new methods.
NASA Technical Reports Server (NTRS)
Wen, John T.; Kreutz-Delgado, Kenneth; Bayard, David S.
1992-01-01
A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to a recently proposed energy-like Liapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates (i.e., certainty equivalence adaptation).
NASA Astrophysics Data System (ADS)
Tollaksen, Jeff; Aharonov, Yakir
2006-03-01
We introduce a new type of weak measurement which yields a quantum average of weak values that is robust, outside the range of eigenvalues, extends the valid regime for weak measurements, and for which the probability of obtaining the pre- and post-selected ensemble is not exponentially rare. This result extends the applicability of weak values, shifts the statistical interpretation previously attributed to weak values and suggests that the weak value is a property of every pre- and post-selected ensemble. We then apply this new weak measurement to Hardy's paradox. Usually the paradox is dismissed on grounds of counterfactuality, i.e., because the paradoxical effects appear only when one considers results of experiments which do not actually take place. We suggest a new set of measurements in connection with Hardy's scheme, and show that when they are actually performed, they yield strange and surprising outcomes. More generally, we claim that counterfactual paradoxes point to a deeper structure inherent to quantum mechanics characterized by weak values (Aharonov Y, Botero A, Popescu S, Reznik B, Tollaksen J, Physics Letters A, 301 (3-4): 130-138, 2002).
An exponential ESS model and its application to frequency-dependent selection.
Li, J; Liu, L
1989-10-01
A nonlinear ESS model is put forward, that is, a nonnegative exponential ESS model. For a simple case, we discuss the existence, uniqueness, and stability of an ESS. As an application of the model, we give a quantitative analysis of frequency-dependent selection in population genetics when the rare type has an advantage.
Robust impedance shaping telemanipulation
Colgate, J.E.
1993-08-01
When a human operator performs a task via a bilateral manipulator, the feel of the task is embodied in the mechanical impedance of the manipulator. Traditionally, a bilateral manipulator is designed for transparency; i.e., so that the impedance reflected through the manipulator closely approximates that of the task. Impedance shaping bilateral control, introduced here, differs in that it treats the bilateral manipulator as a means of constructively altering the impedance of a task. This concept is particularly valuable if the characteristic dimensions (e.g., force, length, time) of the task impedance are very different from those of the human limb. It is shown that a general form of impedance shaping control consists of a conventional power-scaling bilateral controller augmented with a real-time interactive task simulation (i.e., a virtual environment). An approach to impedance shaping based on kinematic similarity between tasks of different scale is introduced and illustrated with an example. It is shown that an important consideration in impedance shaping controller design is robustness; i.e., guaranteeing the stability of the operator/manipulator/task system. A general condition for the robustness of a bilateral manipulator is derived. This condition is based on the structured singular value ({mu}). An example of robust impedance shaping bilateral control is presented and discussed.
Moradi, Hojjatullah; Majd, Vahid Johari
2016-05-01
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.
Perturbing Misiurewicz Parameters in the Exponential Family
NASA Astrophysics Data System (ADS)
Dobbs, Neil
2015-04-01
In one-dimensional real and complex dynamics, a map whose post-singular (or post-critical) set is bounded and uniformly repelling is often called a Misiurewicz map. In results hitherto, perturbing a Misiurewicz map is likely to give a non-hyperbolic map, as per Jakobson's Theorem for unimodal interval maps. This is despite genericity of hyperbolic parameters (at least in the interval setting). We show the contrary holds in the complex exponential family Misiurewicz maps are Lebesgue density points for hyperbolic parameters. As a by-product, we also show that Lyapunov exponents almost never exist for exponential Misiurewicz maps. The lower Lyapunov exponent is -∞ almost everywhere. The upper Lyapunov exponent is non-negative and depends on the choice of metric.
NASA Astrophysics Data System (ADS)
Joly, Damien; Pellejà, Laia; Narbey, Stéphanie; Oswald, Frédéric; Chiron, Julien; Clifford, John N.; Palomares, Emilio; Demadrille, Renaud
2014-02-01
Among the new photovoltaic technologies, the Dye-Sensitized Solar Cell (DSC) is becoming a realistic approach towards energy markets such as BIPV (Building Integrated PhotoVoltaics). In order to improve the performances of DSCs and to increase their commercial attractiveness, cheap, colourful, stable and highly efficient ruthenium-free dyes must be developed. Here we report the synthesis and complete characterization of a new purely organic sensitizer (RK1) that can be prepared and synthetically upscaled rapidly. Solar cells containing this orange dye show a power conversion efficiency of 10.2% under standard conditions (AM 1.5G, 1000 Wm-2) using iodine/iodide as the electrolyte redox shuttle in the electrolyte, which is among the few examples of DSC using an organic dyes and iodine/iodide red/ox pair to overcome the 10% efficiency barrier. We demonstrate that the combination of this dye with an ionic liquid electrolyte allows the fabrication of solar cells that show power conversion efficiencies of up to 7.36% that are highly stable with no measurable degradation of initial performances after 2200 h of light soaking at 65°C under standard irradiation conditions. RK1 achieves one of the best output power conversion efficiencies for a solar cell based on the iodine/iodide electrolyte, combining high efficiency and outstanding stability.
Joly, Damien; Pellejà, Laia; Narbey, Stéphanie; Oswald, Frédéric; Chiron, Julien; Clifford, John N.; Palomares, Emilio; Demadrille, Renaud
2014-01-01
Among the new photovoltaic technologies, the Dye-Sensitized Solar Cell (DSC) is becoming a realistic approach towards energy markets such as BIPV (Building Integrated PhotoVoltaics). In order to improve the performances of DSCs and to increase their commercial attractiveness, cheap, colourful, stable and highly efficient ruthenium-free dyes must be developed. Here we report the synthesis and complete characterization of a new purely organic sensitizer (RK1) that can be prepared and synthetically upscaled rapidly. Solar cells containing this orange dye show a power conversion efficiency of 10.2% under standard conditions (AM 1.5G, 1000 Wm−2) using iodine/iodide as the electrolyte redox shuttle in the electrolyte, which is among the few examples of DSC using an organic dyes and iodine/iodide red/ox pair to overcome the 10% efficiency barrier. We demonstrate that the combination of this dye with an ionic liquid electrolyte allows the fabrication of solar cells that show power conversion efficiencies of up to 7.36% that are highly stable with no measurable degradation of initial performances after 2200 h of light soaking at 65°C under standard irradiation conditions. RK1 achieves one of the best output power conversion efficiencies for a solar cell based on the iodine/iodide electrolyte, combining high efficiency and outstanding stability. PMID:24504344
NASA Astrophysics Data System (ADS)
Chandrasekaran, Rajeswari; Bi, Wu; Fuller, Thomas F.
With increasing interest in energy storage and conversion devices for automobile applications, the necessity to understand and predict life behavior of rechargeable batteries, PEM fuel cells and super capacitors is paramount. These electrochemical devices are most beneficial when used in hybrid configurations rather than as individual components. A system model helps us to understand the interactions between components and enables us to determine the response of the system as a whole. However, system models that are available predict just the performance and neglect degradation. The objective of this research is to provide a framework to account for the durability phenomena that are prevalent in fuel cells and batteries in a hybrid system. Toward this end, the methodology for development of surrogate models is provided, and Pt catalyst dissolution in proton exchange membrane fuel cells (PEMFCs) is used as an example to demonstrate the approach. Surrogate models are more easily integrated into higher level system models than the detailed physics-based models. As an illustration, the effects of changes in control strategies and power management approaches in mitigating platinum instability in fuel cells are reported. A system model that includes a fuel cell stack, a storage battery, power-sharing algorithm, and dc/dc converter has been developed; and preliminary results have been presented. These results show that platinum stability can be improved with only a small impact on system efficiency. Thus, this research will elucidate the importance of degradation issues in system design and optimization as opposed to just initial performance metrics.
Joly, Damien; Pellejà, Laia; Narbey, Stéphanie; Oswald, Frédéric; Chiron, Julien; Clifford, John N; Palomares, Emilio; Demadrille, Renaud
2014-02-07
Among the new photovoltaic technologies, the Dye-Sensitized Solar Cell (DSC) is becoming a realistic approach towards energy markets such as BIPV (Building Integrated PhotoVoltaics). In order to improve the performances of DSCs and to increase their commercial attractiveness, cheap, colourful, stable and highly efficient ruthenium-free dyes must be developed. Here we report the synthesis and complete characterization of a new purely organic sensitizer (RK1) that can be prepared and synthetically upscaled rapidly. Solar cells containing this orange dye show a power conversion efficiency of 10.2% under standard conditions (AM 1.5G, 1000 Wm(-2)) using iodine/iodide as the electrolyte redox shuttle in the electrolyte, which is among the few examples of DSC using an organic dyes and iodine/iodide red/ox pair to overcome the 10% efficiency barrier. We demonstrate that the combination of this dye with an ionic liquid electrolyte allows the fabrication of solar cells that show power conversion efficiencies of up to 7.36% that are highly stable with no measurable degradation of initial performances after 2200 h of light soaking at 65°C under standard irradiation conditions. RK1 achieves one of the best output power conversion efficiencies for a solar cell based on the iodine/iodide electrolyte, combining high efficiency and outstanding stability.
Likelihood Estimation for Generalized Mixed Exponential Distributions.
1984-07-01
specified beforehand. 23 S. . ... .- ~T§777 ~"~~ 7’.7 . -- ." F0 * 0 REFERENCES L. Armijo, "Minimization of Functions Having Lipschitz Continuous...and F. W. Fairman, Exponential Approximation via a Closed Form Gauss-Newton Method, IEEE Trans. Circuit Theory, CT-20 (1973), pp. 361-369. A. R...engineering disciplines of Chemical, Civil, Electrical , and Mechanical and Aerospace to newer, more specialized fields of Biomedical Engineering
Exponential integration algorithms applied to viscoplasticity
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Walker, Kevin P.
1991-01-01
Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.
A Simple Mechanical Experiment on Exponential Growth
NASA Astrophysics Data System (ADS)
McGrew, Ralph
2015-04-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the activity are accessible to students in physical science and environmental science courses.
Exponential DNA Replication by Laminar Convection
NASA Astrophysics Data System (ADS)
Braun, Dieter; Goddard, Noel L.; Libchaber, Albert
2003-10-01
It is shown that laminar thermal convection can drive a chain reaction of DNA replication. The convection is triggered by a constant horizontal temperature gradient, moving molecules along stationary paths between hot and cold regions. This implements the temperature cycling for the classical polymerase chain reaction (PCR). The amplification is shown to be exponential and reaches 100 000-fold gains within 25min. Besides direct applications, the mechanism might have implications for the molecular evolution of life.
Method for exponentiating in cryptographic systems
Brickell, E.F.; Gordon, D.M.; McCurley, K.S.
1992-12-31
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a pre-approved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g{sup e}; transmitting the value g{sup e} to a remote facility by a communications network; receiving the value g{sup e} at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g{sup xi}, computing a{sub i} representations for a integer base b, where a{sub i} represents the weighing factor of the ith digit of the integer e; computing the individual values of c{sub d} according to the rule: c{sub d}={product}a{sub i}=d g{sup x {sub i}}; and computing the product of {product}{sup h}/{sub d=1} c{sub d}{sup d} from the stored values of from the plurality of memory locations so as to determine a value for g{sup e}.
Dynamo theory, vorticity generation, and exponential stretching.
Friedlander, Susan; Vishik, Misha M.
1991-08-01
A discussion is given of the analogy between the dynamo equation for the generation of a magnetic field by the motion of an electrically conducting fluid and the equation for the evolution of vorticity of a viscous fluid. In both cases exponential stretching is an important feature of the underlying instability problem. For the "fast" dynamo problem, the existence of exponential stretching (i.e., the positivity of the Lyapunov exponent) somewhere in the flow is a necessary condition when the flow is smooth. An example is presented of a flow with exponential stretching (an Anosov flow) that supports fast dynamo action. A parallel treatment is described for the linearized Navier-Stokes equations for the motion of a viscous fluid. In this problem the analogous necessary condition for "fast vorticity generation" is the existence of some instability in the corresponding Euler (i.e., inviscid) equation. Dynamo theory methods give a second related result, namely a universal geometric estimate from below on the growth rate of a small perturbation in an inviscid fluid. This bound gives an effective sufficient condition for local instability for Eulers equations. In particular, it is proved that a steady flow with a hyperbolic stagnation point is unstable. The growth rate of an infinitesimal perturbation in a metric with derivatives depends on this metric. This dependence is completely described.
Black hole as a magnetic monopole within exponential nonlinear electrodynamics
NASA Astrophysics Data System (ADS)
Kruglov, S. I.
2017-03-01
We perform the gauge covariant quantization of the exponential model of nonlinear electrodynamics. Magnetically charged black holes, in the framework of our model are considered, and the regular black hole solution is obtained in general relativity. The asymptotic black hole solution at r → ∞ is found. We calculate the magnetic mass of the black hole and the metric function which are expressed via the parameter β of the model and the magnetic charge. The thermodynamic properties and thermal stability of regular black holes are analysed. We calculate the Hawking temperature of black holes and their heat capacity at the constant magnetic charge. We find a point where the temperature changes the sign that corresponds to the first-order phase transition. It is shown that at critical point, where the heat capacity diverges, there is a phase transition of the second-order. We obtain the parameters of the model when the black hole is stable.
On Using Exponential Parameter Estimators with an Adaptive Controller
NASA Technical Reports Server (NTRS)
Patre, Parag; Joshi, Suresh M.
2011-01-01
Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators.
Exponential synchronization of a class of neural networks with time-varying delays.
Cheng, Chao-Jung; Liao, Teh-Lu; Yan, Jun-Juh; Hwang, Chi-Chuan
2006-02-01
This paper aims to present a synchronization scheme for a class of delayed neural networks, which covers the Hopfield neural networks and cellular neural networks with time-varying delays. A feedback control gain matrix is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory, and its exponential synchronization condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. This condition can avoid solving an algebraic Riccati equation. Both the cellular neural networks and Hopfield neural networks with time-varying delays are given as examples for illustration.
NASA Astrophysics Data System (ADS)
Sun, Xifang; Chen, Weisheng; Wu, Jian
2016-12-01
In this paper, we address the global generalised exponential stabilisation problem for a class of lower-triangular systems with multiple unknown directions. Instead of the well-known Nussbaum-gain adaptive rule, a Lyapunov-based adaptive logic switching rule is proposed to seek the correct control directions for such systems. The main advantage of the proposed controller is that it can guarantee the global generalised exponential stability of closed-loop systems. Simulation examples are given to verify the effectiveness of the developed control approach.
Robustness enhancement of neurocontroller and state estimator
NASA Technical Reports Server (NTRS)
Troudet, Terry
1993-01-01
The feasibility of enhancing neurocontrol robustness, through training of the neurocontroller and state estimator in the presence of system uncertainties, is investigated on the example of a multivariable aircraft control problem. The performance and robustness of the newly trained neurocontroller are compared to those for an existing neurocontrol design scheme. The newly designed dynamic neurocontroller exhibits a better trade-off between phase and gain stability margins, and it is significantly more robust to degradations of the plant dynamics.
Applications of an exponential finite difference technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.; Keith, Theo G., Jr.
1988-01-01
An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.
Exponential expansion: galactic destiny or technological hubris?
NASA Astrophysics Data System (ADS)
Finney, B. R.
Is it our destiny to expand exponentially to populate the galaxy, or is such a vision but an extreme example of technological hubris? The overall record of human evolution and dispersion over the Earth can be cited to support the view that we are a uniquely expansionary and technological animal bound for the stars, yet an examination of the fate of individual migrations and exploratory initiatives raises doubts. Although it may be in keeping with our hubristic nature to predict ultimate galactic expansion, there is no way to specify how far expansionary urges may drive our spacefaring descendants.
Mixtures of multivariate power exponential distributions.
Dang, Utkarsh J; Browne, Ryan P; McNicholas, Paul D
2015-12-01
An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness have received much attention in the model-based clustering literature recently, we investigate the use of a distribution that can deal with both varying tail-weight and peakedness of data. A family of parsimonious models is proposed using an eigen-decomposition of the scale matrix. A generalized expectation-maximization algorithm is presented that combines convex optimization via a minorization-maximization approach and optimization based on accelerated line search algorithms on the Stiefel manifold. Lastly, the utility of this family of models is illustrated using both toy and benchmark data.
Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons.
Ladenbauer, Josef; Augustin, Moritz; Shiau, LieJune; Obermayer, Klaus
2012-01-01
The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in
Global exponential almost periodicity of a delayed memristor-based neural networks.
Chen, Jiejie; Zeng, Zhigang; Jiang, Ping
2014-12-01
In this paper, the existence, uniqueness and stability of almost periodic solution for a class of delayed memristor-based neural networks are studied. By using a new Lyapunov function method, the neural network that has a unique almost periodic solution, which is globally exponentially stable is proved. Moreover, the obtained conclusion on the almost periodic solution is applied to prove the existence and stability of periodic solution (or equilibrium point) for delayed memristor-based neural networks with periodic coefficients (or constant coefficients). The obtained results are helpful to design the global exponential stability of almost periodic oscillatory memristor-based neural networks. Three numerical examples and simulations are also given to show the feasibility of our results. Copyright © 2014 Elsevier Ltd. All rights reserved.
Chen, Boshan; Wang, Jun
2005-11-01
In this paper, we present the analytical results on the global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays. Sufficient conditions are derived for ascertaining the existence, uniqueness and global exponential periodicity of the oscillatory solution of such recurrent neural networks by using the comparison principle and mixed monotone operator method. The periodicity results extend or improve existing stability results for the class of recurrent neural networks with and without time delays.
Preconditioned implicit-exponential integrators (IMEXP) for stiff PDEs
NASA Astrophysics Data System (ADS)
Luan, Vu Thai; Tokman, Mayya; Rainwater, Greg
2017-04-01
We propose two new classes of time integrators for stiff DEs: the implicit exponential (IMEXP) and the hybrid exponential methods. In contrast to the existing exponential schemes, the new methods offer significant computational advantages when used with preconditioners. Any preconditioner can be used with any of these new schemes. This leads to a broader applicability of exponential methods. The proof of convergence of these integrators and numerical demonstration of their efficiency are presented.
The LEM exponential integrator for advection-diffusion-reaction equations
NASA Astrophysics Data System (ADS)
Caliari, Marco; Vianello, Marco; Bergamaschi, Luca
2007-12-01
We implement a second-order exponential integrator for semidiscretized advection-diffusion-reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja-Euler-Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.
Exponential Size Distribution of von Willebrand Factor
Lippok, Svenja; Obser, Tobias; Müller, Jochen P.; Stierle, Valentin K.; Benoit, Martin; Budde, Ulrich; Schneppenheim, Reinhard; Rädler, Joachim O.
2013-01-01
Von Willebrand Factor (VWF) is a multimeric protein crucial for hemostasis. Under shear flow, it acts as a mechanosensor responding with a size-dependent globule-stretch transition to increasing shear rates. Here, we quantify for the first time, to our knowledge, the size distribution of recombinant VWF and VWF-eGFP using a multilateral approach that involves quantitative gel analysis, fluorescence correlation spectroscopy, and total internal reflection fluorescence microscopy. We find an exponentially decaying size distribution of multimers for recombinant VWF as well as for VWF derived from blood samples in accordance with the notion of a step-growth polymerization process during VWF biosynthesis. The distribution is solely described by the extent of polymerization, which was found to be reduced in the case of the pathologically relevant mutant VWF-IIC. The VWF-specific protease ADAMTS13 systematically shifts the VWF size distribution toward smaller sizes. This dynamic evolution is monitored using fluorescence correlation spectroscopy and compared to a computer simulation of a random cleavage process relating ADAMTS13 concentration to the degree of VWF breakdown. Quantitative assessment of VWF size distribution in terms of an exponential might prove to be useful both as a valuable biophysical characterization and as a possible disease indicator for clinical applications. PMID:24010664
Are Urban-Canopy Velocity Profiles Exponential?
NASA Astrophysics Data System (ADS)
Castro, Ian P.
2017-09-01
Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer's logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.
Prion disease: exponential growth requires membrane binding.
Cox, Daniel L; Sing, Rajiv R P; Yang, Sichun
2006-06-01
A hallmark feature of prions, whether in mammals or yeast and fungi, is exponential growth associated with fission or autocatalysis of protein aggregates. We have employed a rigorous kinetic analysis to recent data from transgenic mice lacking a glycosylphosphatidylinositol membrane anchor to the normal cellular PrP(C) protein, which show that toxicity requires the membrane binding. We find as well that the membrane is necessary for exponential growth of prion aggregates; without it, the kinetics is simply the quadratic-in-time growth characteristic of linear elongation as observed frequently in in vitro amyloid growth experiments with other proteins. This requires both: i), a substantial intercellular concentration of anchorless PrP(C), and ii), a concentration of small scrapies seeding aggregates from the inoculum, which remains relatively constant with time and exceeds the concentration of large polymeric aggregates. We also can explain via this analysis why mice heterozygous for the anchor-full/anchor-free PrP(C) proteins have more rapid incubation than mice heterozygous for anchor-full/null PrP(C), and contrast the mammalian membrane associated fission or autocatalysis with the membrane free fission of yeast and fungal prions.
Measuring Entanglement Spectrum via Density Matrix Exponentiation
NASA Astrophysics Data System (ADS)
Zhu, Guanyu; Seif, Alireza; Pichler, Hannes; Zoller, Peter; Hafezi, Mohammad
Entanglement spectrum (ES), the eigenvalues of the reduced density matrix of a subsystem, serves as a powerful theoretical tool to study many-body systems. For example, the gap and degeneracies of the entanglement spectrum have been used to identify various topological phases. However, the usefulness of such a concept in real experiments has been debated, since it is believed that obtaining the ES requires full state tomography, at a cost which exponentially grows with the systems size. Inspired by a recent density matrix exponentiation technique, we propose a scheme to measure ES by evolving the system with a Hamiltonian that is the subsystem's own reduced density matrix. Such a time evolution can be induced by an ancilla photon that is coupled to multiple qubits at the same time. The phase associated with the time evolution can be detected and converted into ES through either a digital or an analogue scheme. The digital scheme involves a modified quantum phase estimation algorithm based on random time evolution, while the analogue scheme is in the spirit of Ramsey interferometry. Both schemes are not limited by the size of the system, and are especially sensitive to the gap and degeneracies. We also discuss the implementation in cavity/circuit-QED and ion trap systems.
Are Urban-Canopy Velocity Profiles Exponential?
NASA Astrophysics Data System (ADS)
Castro, Ian P.
2017-06-01
Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer's logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.
Robust control with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1988-01-01
Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.
Human-chimpanzee alignment: ortholog exponentials and paralog power laws.
Gao, Kun; Miller, Jonathan
2014-12-01
Genomic subsequences conserved between closely related species such as human and chimpanzee exhibit an exponential length distribution, in contrast to the algebraic length distribution observed for sequences shared between distantly related genomes. We find that the former exponential can be further decomposed into an exponential component primarily composed of orthologous sequences, and a truncated algebraic component primarily composed of paralogous sequences.
Aston, Elizabeth; Channon, Alastair; Day, Charles; Knight, Christopher G
2013-01-01
Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has
A Robustly Stabilizing Model Predictive Control Algorithm
NASA Technical Reports Server (NTRS)
Ackmece, A. Behcet; Carson, John M., III
2007-01-01
A model predictive control (MPC) algorithm that differs from prior MPC algorithms has been developed for controlling an uncertain nonlinear system. This algorithm guarantees the resolvability of an associated finite-horizon optimal-control problem in a receding-horizon implementation.
Exponential-Krylov methods for ordinary differential equations
NASA Astrophysics Data System (ADS)
Tranquilli, Paul; Sandu, Adrian
2014-12-01
This paper develops a new family of exponential time discretization methods called exponential-Krylov (EXPK). The new schemes treat the time discretization and the Krylov-based approximation of exponential matrix-vector products as a single computational process. The classical order conditions theory developed herein accounts for both the temporal and the Krylov approximation errors. Unlike traditional exponential schemes, EXPK methods require the construction of only a single Krylov space at each timestep. The number of basis vectors that guarantee the temporal order of accuracy does not depend on the application at hand. Numerical results show favorable properties of EXPK methods when compared to current exponential schemes.
NASA Astrophysics Data System (ADS)
Bég, O. Anwar; Khan, M. S.; Karim, Ifsana; Alam, Md. M.; Ferdows, M.
2013-10-01
A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (G r ), species Grashof number (G m ), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (E c ), Lewis number (L e ), Brownian motion parameter (N b) and thermophoresis parameter (N t). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.
Poissonian renormalizations, exponentials, and power laws.
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
An exponentiation method for XML element retrieval.
Wichaiwong, Tanakorn
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP.
Exponential networks and representations of quivers
NASA Astrophysics Data System (ADS)
Eager, Richard; Selmani, Sam Alexandre; Walcher, Johannes
2017-08-01
We study the geometric description of BPS states in supersymmetric theories with eight supercharges in terms of geodesic networks on suitable spectral curves. We lift and extend several constructions of Gaiotto-Moore-Neitzke from gauge theory to local Calabi-Yau threefolds and related models. The differential is multi-valued on the covering curve and features a new type of logarithmic singularity in order to account for D0-branes and non-compact D4-branes, respectively. We describe local rules for the three-way junctions of BPS trajectories relative to a particular framing of the curve. We reproduce BPS quivers of local geometries and illustrate the wall-crossing of finite-mass bound states in several new examples. We describe first steps toward understanding the spectrum of framed BPS states in terms of such "exponential networks".
An exponential multireference wave-function Ansatz
Hanrath, Michael
2005-08-22
An exponential multireference wave-function Ansatz is formulated. In accordance with the state universal coupled-cluster Ansatz of Jeziorski and Monkhorst [Phys. Rev. A 24, 1668 (1981)] the approach uses a reference specific cluster operator. In order to achieve state selectiveness the excitation- and reference-related amplitude indexing of the state universal Ansatz is replaced by an indexing which is based on excited determinants. There is no reference determinant playing a particular role. The approach is size consistent, coincides with traditional single-reference coupled cluster if applied to a single-reference, and converges to full configuration interaction with an increasing cluster operator excitation level. Initial applications on BeH{sub 2}, CH{sub 2}, Li{sub 2}, and nH{sub 2} are reported.
Fluctuation Bounds in the Exponential Bricklayers Process
NASA Astrophysics Data System (ADS)
Balázs, Márton; Komjáthy, Júlia; Seppäläinen, Timo
2012-04-01
This paper is the continuation of our earlier paper (Balázs et al. in Ann. Inst. Henri Poincaré Probab. Stat. 48(1):151-187, 2012), where we proved t 1/3-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity. We also claimed two models with concave hydrodynamic flux which satisfied the assumptions which made our proof work. In the present note we show that the totally asymmetric exponential bricklayers process also satisfies these assumptions. Hence this is the first example with convex hydrodynamics of a model with t 1/3-order current fluctuations across the characteristics. As such, it further supports the idea of universality regarding this scaling.
Arsenic for the fool: an exponential connection.
Dani, Sergio U
2010-03-15
Anthropogenic arsenic is insidiously building up together with natural arsenic to a level unprecedented in the history of mankind. Arsenopyrite (FeAsS) is the principal ore of arsenic and gold in hard rock mines; it is formed by a coupled substitution of sulphur by arsenic in the structure of pyrite (FeS(2)) - nicknamed "fool's gold". Other important sources of anthropogenic arsenic are fossil fuels such as coal and oil. Here I report on the first indication that the environmental concentration of total arsenic in topsoils - in the 7-18ppm range - is exponentially related to the prevalence and mortality of Alzheimer's disease and other dementias in European countries. This evidence defies the imputed absence of verified cases of human morbidity or mortality resulting from exposure to low-level arsenic in topsoils.
Application of stochastic robustness to aircraft control systems
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Ryan, Laura E.
1989-01-01
Stochastic robustness, a simple numerical procedure for estimating the stability robustness of linear, time-invariant systems, is applied to a forward-swept-wing aircraft control system. Based on Monte Carlo evaluation of the system's closed-loop eignevalues, this analysis approach introduces the probability of instability as a scalar stability robustness measure. The related stochastic root locus provides insight into robustness characteristics of the closed-loop system. Three Linear Quadratic controllers of decreasing robustness are chosen to demonstrate the use of stochastic robustness to analyze and compare control designs. Examples are presented illustrating the use of stochastic robustness analysis to address the effects of actuator dynamics and unmodeled dynamics on the stability robustness of the forward-swept-wing aircraft.
Robust nonlinear control of vectored thrust aircraft
NASA Technical Reports Server (NTRS)
Doyle, John C.; Murray, Richard; Morris, John
1993-01-01
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.
Aggarwal, Ankush
2017-03-01
Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress-strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.
Parameter Estimation for Superimposed Weighted Exponentials
1996-07-01
interval of uncertainty, is reduced. The goal of an efficient search plan is to reduce the interval of uncertainty with the minimum number of function...and the eliminated function evaluation at the next iteration make this search plan close to optimal (17:182). The plan is known as the golden section...search plan . However, the performance of IGLS is quite good when recalling that, unlike the one dimensional golden section search, IGLS has robust
NASA Technical Reports Server (NTRS)
Wen, John T.; Kreutz, Kenneth; Bayard, David S.
1988-01-01
A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.
Surface properties and exponential stress relaxations of mammalian meibum films.
Eftimov, Petar; Yokoi, Norihiko; Tonchev, Vesselin; Nencheva, Yana; Georgiev, Georgi As
2017-03-01
The surface properties of meibomian secretion (MGS), the major constituent of the tear film (TF) lipid layer, are of key importance for TF stability. The interfacial properties of canine, cMGS, and feline, fMGS, meibum films were studied using a Langmuir surface balance. These species were selected because they have blinking frequency and TF stability similar to those of humans. The sample's performance during dynamic area changes was evaluated by surface pressure (π)-area (A) isocycles and the layer structure was monitored with Brewster angle microscopy. The films' dilatational rheology was probed via the stress-relaxation technique. The animal MGS showed similar behavior both between each other and with human MGS (studied previously). They form reversible, non-collapsible, multilayer thick films. The relaxations of canine, feline, and human MGS films were well described by double exponential decay reflecting the presence of two processes: (1) fast elastic process, with characteristic time τ < 10 s and (2) slow viscous process, with τ > 100 s-emphasizing the meibum layers viscoelasticity. The temperature decrease from 35 to 25 °C resulted in decreased thickness and lateral expansion of all MGS layers accompanied with increase of the π/A hysteresis and of the elastic process contribution to π relaxation transients. Thus, MGS films of mammals with similar blinking frequency and TF stability have similar surface properties and stress relaxations unaltered by the interspecies MGS compositional variations. Such knowledge may impact the selection of animal mimics of human MGS and on a better understanding of lipid classes' impact on meibum functionality.
NASA Astrophysics Data System (ADS)
Carmele, Alexander; Heyl, Markus; Kraus, Christina; Dalmonte, Marcello
2015-11-01
We investigate the resilience of symmetry-protected topological edge states at the boundaries of Kitaev chains in the presence of a bath which explicitly introduces symmetry-breaking terms. Specifically, we focus on single-particle losses and gains, violating the protecting parity symmetry, which could generically occur in realistic scenarios. For homogeneous systems we show that the Majorana mode decays exponentially fast. By the inclusion of strong disorder, where the closed system enters a many-body localized phase, we find that the Majorana mode can be stabilized substantially. The decay of the Majorana converts into a stretched exponential form for particle losses or gains occurring in the bulk. In particular, for pure loss dynamics we find a universal exponent α ≃2 /3 . We show that this holds both in the Anderson and many-body localized regimes. Our results thus provide a first step to stabilize edge states even in the presence of symmetry-breaking environments.
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth.
Yan, Wanfeng; van Tuyll van Serooskerken, Edgar
2015-01-01
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator.
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth
Yan, Wanfeng; van Tuyll van Serooskerken, Edgar
2015-01-01
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator. PMID:26339793
Easton, D M
1978-01-01
The conductance changes, gK(t) and gNa(t), of squid giant axon under voltage clamp (Hodgkin and Huxley, 1952) may be modeled by exponentiated exponential functions (Gompertz kinetics) from any holding potential VO to any membrane clamp potential V. The equation constants are set by the membrane potential V, and include, for any voltage step in the case of gK, the initial conductance, gO, the asymptote conductance g, and rate constant k: gK = g exp(-be-kt) where b = 1n g/gO. Equations of similar form relate g and k to the voltage V, and govern the corresponding parameters of the gNa system. For the gNa, the fast phase y = y exp (-be-kt) is cut down in proportion to a slow process p = (1 - p)e-k't + p, and thus gNa = py. The expo-exponential functions involve fewer constants than the Hodgkin-Huxley model. In particular, the role of the n, m, h parameters appears to be filled largely by 1n (g/gO) in the case of gK and by 1n (y/yO) in the case of gNa. Membrane action potentials during current clamp may be computed from the conductances generated by use of the appropriate differential forms of the equations; diverse other membrane behaviors may be predicted. PMID:638223
Robust Inflation from fibrous strings
NASA Astrophysics Data System (ADS)
Burgess, C. P.; Cicoli, M.; de Alwis, S.; Quevedo, F.
2016-05-01
Successful inflationary models should (i) describe the data well; (ii) arise generically from sensible UV completions; (iii) be insensitive to detailed fine-tunings of parameters and (iv) make interesting new predictions. We argue that a class of models with these properties is characterized by relatively simple potentials with a constant term and negative exponentials. We here continue earlier work exploring UV completions for these models—including the key (though often ignored) issue of modulus stabilisation—to assess the robustness of their predictions. We show that string models where the inflaton is a fibration modulus seem to be robust due to an effective rescaling symmetry, and fairly generic since most known Calabi-Yau manifolds are fibrations. This class of models is characterized by a generic relation between the tensor-to-scalar ratio r and the spectral index ns of the form r propto (ns-1)2 where the proportionality constant depends on the nature of the effects used to develop the inflationary potential and the topology of the internal space. In particular we find that the largest values of the tensor-to-scalar ratio that can be obtained by generalizing the original set-up are of order r lesssim 0.01. We contrast this general picture with specific popular models, such as the Starobinsky scenario and α-attractors. Finally, we argue the self consistency of large-field inflationary models can strongly constrain non-supersymmetric inflationary mechanisms.
Robust Inflation from fibrous strings
Burgess, C.P.; Cicoli, M.; Alwis, S. de; Quevedo, F.
2016-05-13
Successful inflationary models should (i) describe the data well; (ii) arise generically from sensible UV completions; (iii) be insensitive to detailed fine-tunings of parameters and (iv) make interesting new predictions. We argue that a class of models with these properties is characterized by relatively simple potentials with a constant term and negative exponentials. We here continue earlier work exploring UV completions for these models — including the key (though often ignored) issue of modulus stabilisation — to assess the robustness of their predictions. We show that string models where the inflaton is a fibration modulus seem to be robust due to an effective rescaling symmetry, and fairly generic since most known Calabi-Yau manifolds are fibrations. This class of models is characterized by a generic relation between the tensor-to-scalar ratio r and the spectral index n{sub s} of the form r∝(n{sub s}−1){sup 2} where the proportionality constant depends on the nature of the effects used to develop the inflationary potential and the topology of the internal space. In particular we find that the largest values of the tensor-to-scalar ratio that can be obtained by generalizing the original set-up are of order r≲0.01. We contrast this general picture with specific popular models, such as the Starobinsky scenario and α-attractors. Finally, we argue the self consistency of large-field inflationary models can strongly constrain non-supersymmetric inflationary mechanisms.
NASA Astrophysics Data System (ADS)
Li, Danqin; Zhou, Weiqiang; Zhou, Qianjie; Ye, Guo; Wang, Tongzhou; Wu, Jing; Chang, Yanan; Xu, Jingkun
2017-09-01
Two-dimensional MoS2 materials have attracted more and more interest and been applied to the field of energy storage because of its unique physical, optical, electronic and electrochemical properties. However, there are no reports on high-stable transparent MoS2 nanofilms as supercapacitors electrode. Here, we describe a transparent 1T-MoS2 nanofilm electrode with super-long stability anchored on the indium tin oxide (ITO) glass by a simple alternate layer-by-layer (LBL) self-assembly of a highly charged cationic poly(diallyldimethylammonium chloride) (PDDA) and negative single-/few-layer 1T MoS2 nanosheets. The ITO/(PDDA/MoS2)20 electrode shows a transmittance of 51.6% at 550 nm and obviously exhibits excellent transparency by naked eye observation. Ultrasonic damage test validates that the (PDDA/MoS2)20 film with the average thickness about 50 nm is robustly anchored on ITO substrate. Additionally, the electrochemical results indicate that the ITO/(PDDA/MoS2)20 film shows areal capacitance of 1.1 mF cm‑2 and volumetric capacitance of 220 F cm‑3 at 0.04 mA cm‑2, 130.6% retention of the original capacitance value after 5000 cycles. Further experiments indicate that the formation of transparent (PDDA/MoS2) x nanofilm by LBL self-assembly can be extended to other substrates, e.g., slide glass and flexible polyethylene terephthalate (PET). Thus, the easily available (PDDA/MoS2) x nanofilm electrode has great potential for application in transparent and/or flexible optoelectronic and electronics devices.
Stretched Exponential relaxation in pure Se glass
NASA Astrophysics Data System (ADS)
Dash, S.; Ravindren, S.; Boolchand, P.
A universal feature of glasses is the stretched exponential relaxation, f (t) = exp[ - t / τ ] β . The model of diffusion of excitations to randomly distributed traps in a glass by Phillips1 yields the stretched exponent β = d[d +2] where d, the effective dimensionality. We have measured the enthalpy of relaxation ΔHnr (tw) at Tg of Se glass in modulated DSC experiments as glasses age at 300K and find β = 0.43(2) for tw in the 0
An exponential decay model for mediation.
Fritz, Matthew S
2014-10-01
Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.
An Exponential Decay Model for Mediation
Fritz, Matthew S.
2013-01-01
Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557
Density Estimation of Simulation Output Using Exponential EPI-Splines
2013-12-01
ak+1,1, k = 1, 2, ..., N − 1. Pointwise Fisher information. We define the pointwise Fisher information of an exponential epi-spline density h at x to...are required to obtain meaningful results. All exponential epi-splines are computed under the assumptions of continuity, smoothness, pointwise Fisher...Kernel 0.4310 0.3536 In the exponential epi-spline estimates, we include continuity, differentiability, and pointwise Fisher information constraints with
Exponential convergence rates for weighted sums in noncommutative probability space
NASA Astrophysics Data System (ADS)
Choi, Byoung Jin; Ji, Un Cig
2016-11-01
We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. Then we prove a noncommutative extension of the result for the exponential convergence rate by Baum, Katz and Read. As applications, we first study a large deviation type inequality for weighted sums in a noncommutative probability space, and secondly we study exponential convergence rates for weighted free additive convolution sums of probability measures.
Using Differentials to Differentiate Trigonometric and Exponential Functions
ERIC Educational Resources Information Center
Dray, Tevian
2013-01-01
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
Using Differentials to Differentiate Trigonometric and Exponential Functions
ERIC Educational Resources Information Center
Dray, Tevian
2013-01-01
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
An exponential filter model predicts lightness illusions
Zeman, Astrid; Brooks, Kevin R.; Ghebreab, Sennay
2015-01-01
Lightness, or perceived reflectance of a surface, is influenced by surrounding context. This is demonstrated by the Simultaneous Contrast Illusion (SCI), where a gray patch is perceived lighter against a black background and vice versa. Conversely, assimilation is where the lightness of the target patch moves toward that of the bounding areas and can be demonstrated in White's effect. Blakeslee and McCourt (1999) introduced an oriented difference-of-Gaussian (ODOG) model that is able to account for both contrast and assimilation in a number of lightness illusions and that has been subsequently improved using localized normalization techniques. We introduce a model inspired by image statistics that is based on a family of exponential filters, with kernels spanning across multiple sizes and shapes. We include an optional second stage of normalization based on contrast gain control. Our model was tested on a well-known set of lightness illusions that have previously been used to evaluate ODOG and its variants, and model lightness values were compared with typical human data. We investigate whether predictive success depends on filters of a particular size or shape and whether pooling information across filters can improve performance. The best single filter correctly predicted the direction of lightness effects for 21 out of 27 illusions. Combining two filters together increased the best performance to 23, with asymptotic performance at 24 for an arbitrarily large combination of filter outputs. While normalization improved prediction magnitudes, it only slightly improved overall scores in direction predictions. The prediction performance of 24 out of 27 illusions equals that of the best performing ODOG variant, with greater parsimony. Our model shows that V1-style orientation-selectivity is not necessary to account for lightness illusions and that a low-level model based on image statistics is able to account for a wide range of both contrast and assimilation effects
Exponentially Long Orbits in Hopfield Neural Networks.
Muscinelli, Samuel P; Gerstner, Wulfram; Brea, Johanni
2017-02-01
We show that Hopfield neural networks with synchronous dynamics and asymmetric weights admit stable orbits that form sequences of maximal length. For [Formula: see text] units, these sequences have length [Formula: see text]; that is, they cover the full state space. We present a mathematical proof that maximal-length orbits exist for all [Formula: see text], and we provide a method to construct both the sequence and the weight matrix that allow its production. The orbit is relatively robust to dynamical noise, and perturbations of the optimal weights reveal other periodic orbits that are not maximal but typically still very long. We discuss how the resulting dynamics on slow time-scales can be used to generate desired output sequences.
Robust lateral control of highway vehicles
Byrne, R.H.; Abdallah, C.
1994-08-01
Vehicle lateral dynamics are affected by vehicle mass, longitudinal velocity, vehicle inertia, and the cornering stiffness of the tires. All of these parameters are subject to variation, even over the course of a single trip. Therefore, a practical lateral control system must guarantee stability, and hopefully ride comfort, over a wide range of parameter changes. This paper describes a robust controller which theoretically guarantees stability over a wide range of parameter changes. The robust controller is designed using a frequency domain transfer function approach. An uncertainty band in the frequency domain is determined using simulations over the range of expected parameter variations. Based on this bound, a robust controller is designed by solving the Nevanlinna-Pick interpolation problem. The performance of the robust controller is then evaluated over the range of parameter variations through simulations.
Exponential and power-law contact distributions represent different atmospheric conditions.
Reynolds, A M
2011-12-01
It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution?the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a -3/2 inverse power law for convective boundary-layers with wind shear; and by a -2/3 inverse power law for stably stratified conditions.
Synthesis of robust controllers
NASA Technical Reports Server (NTRS)
Marrison, Chris
1993-01-01
At the 1990 American Controls Conference a benchmark problem was issued as a challenge for designing robust compensators. Many compensators were presented in response to the problem. In previous work Stochastic Robustness Analysis (SRA) was used to compare these compensators. In this work SRA metrics are used as guides to synthesize robust compensators, using the benchmark problem as an example.
Taller, Daniel; Go, David B; Chang, Hsueh-Chia
2013-05-01
The exponentially decaying acoustic pressure of scattered surface acoustic waves (SAWs) at the contact line of a liquid film pinned to filter paper is shown to sustain a high curvature conic tip with micron-sized modulations whose dimension grows exponentially from the tip. The large negative capillary pressure in the film, necessary for offsetting the large positive acoustic pressure at the contact line, also creates significant negative hydrodynamic pressure and robust wicking action through the paper. An asymptotic analysis of this intricate pressure matching between the quasistatic conic film and bulk drop shows that the necessary SAW power to pump liquid from the filter paper and aerosolize, expressed in terms of the acoustic pressure scaled by the drop capillary pressure, grows exponentially with respect to twice the acoustic decay constant multiplied by the drop length, with a universal preexponential coefficient. Global rapid aerosolization occurs at a SAW power twice as high, beyond which the wicking rate saturates.
NASA Astrophysics Data System (ADS)
Taller, Daniel; Go, David B.; Chang, Hsueh-Chia
2013-05-01
The exponentially decaying acoustic pressure of scattered surface acoustic waves (SAWs) at the contact line of a liquid film pinned to filter paper is shown to sustain a high curvature conic tip with micron-sized modulations whose dimension grows exponentially from the tip. The large negative capillary pressure in the film, necessary for offsetting the large positive acoustic pressure at the contact line, also creates significant negative hydrodynamic pressure and robust wicking action through the paper. An asymptotic analysis of this intricate pressure matching between the quasistatic conic film and bulk drop shows that the necessary SAW power to pump liquid from the filter paper and aerosolize, expressed in terms of the acoustic pressure scaled by the drop capillary pressure, grows exponentially with respect to twice the acoustic decay constant multiplied by the drop length, with a universal preexponential coefficient. Global rapid aerosolization occurs at a SAW power twice as high, beyond which the wicking rate saturates.
Operating ITER Robustly Without Disruptions
NASA Astrophysics Data System (ADS)
Humphreys, D. A.; Eidietis, N. W.; Hyatt, A. W.; Leuer, J. A.; Luce, T. C.; Strait, E. J.; Walker, M. L.; Welander, A. S.; Wesley, J. C.; Lodestro, L.; Pearlstein, L. D.
2011-10-01
Disruptivity in ITER must be minimized to limit downtime and maximize use of the limited number of discharges. Minimizing disruptivity requires sufficient control capability, including robustness to disturbances and disruption avoidance through prediction of controllability limits. Robust control implies a balance of passively stable nominal scenarios, robust operation near or beyond open loop stability limits, and responses to off-normal events to avoid disruptive termination. Such a solution is possible because disruptions result from deterministic loss of controllability due to many proximal causes (e.g. loss of hardware resources, human error, or uncontrollable disturbances), most of which can be addressed with good physics models and known control methods. We illustrate the required approach with DIII-D experiments to assess ITER controllability and pre-qualify ITER scenarios, and with design and analysis ensuring sufficiently robust vertical control for ITER. Supported by the US DOE under DE-FC02-04ER54698 and DE-AC52-07NA27344.
Computer-aided-analysis of linear control system robustness
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Ray, Laura R.
1990-01-01
Stochastic robustness is a simple technique used to estimate the stability and performance robustness of linear, time-invariant systems. The use of high-speed graphics workstations and control system design software in stochastic robustness analysis is discussed and demonstrated. It is shown that stochastic robustness makes good use of modern computational and graphic tools, and it is easily implemented using commercial control system design and analysis software.
A Learning Cycle on Exponential Growth and the Energy Crises.
ERIC Educational Resources Information Center
Dykstra, D. I., Jr.
1982-01-01
Describes nature and logistics of a learning cycle approach to teaching exponential growth and the energy crisis. Used with both science and nonscience majors, the cycle uses no algebra, never mentions the terms exponential or logarithmic, and requires a calculator. Instructions for obtaining student and instructor materials are provided.…
Exponential Correlation of IQ and the Wealth of Nations
ERIC Educational Resources Information Center
Dickerson, Richard E.
2006-01-01
Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…
Modeling of magnitude distributions by the generalized truncated exponential distribution
NASA Astrophysics Data System (ADS)
Raschke, Mathias
2015-01-01
The probability distribution of the magnitude can be modeled by an exponential distribution according to the Gutenberg-Richter relation. Two alternatives are the truncated exponential distribution (TED) and the cutoff exponential distribution (CED). The TED is frequently used in seismic hazard analysis although it has a weak point: when two TEDs with equal parameters except the upper bound magnitude are mixed, then the resulting distribution is not a TED. Inversely, it is also not possible to split a TED of a seismic region into TEDs of subregions with equal parameters except the upper bound magnitude. This weakness is a principal problem as seismic regions are constructed scientific objects and not natural units. We overcome it by the generalization of the abovementioned exponential distributions: the generalized truncated exponential distribution (GTED). Therein, identical exponential distributions are mixed by the probability distribution of the correct cutoff points. This distribution model is flexible in the vicinity of the upper bound magnitude and is equal to the exponential distribution for smaller magnitudes. Additionally, the exponential distributions TED and CED are special cases of the GTED. We discuss the possible ways of estimating its parameters and introduce the normalized spacing for this purpose. Furthermore, we present methods for geographic aggregation and differentiation of the GTED and demonstrate the potential and universality of our simple approach by applying it to empirical data. The considerable improvement by the GTED in contrast to the TED is indicated by a large difference between the corresponding values of the Akaike information criterion.
Exponential Correlation of IQ and the Wealth of Nations
ERIC Educational Resources Information Center
Dickerson, Richard E.
2006-01-01
Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…
Review of "Going Exponential: Growing the Charter School Sector's Best"
ERIC Educational Resources Information Center
Garcia, David
2011-01-01
This Progressive Policy Institute report argues that charter schools should be expanded rapidly and exponentially. Citing exponential growth organizations, such as Starbucks and Apple, as well as the rapid growth of molds, viruses and cancers, the report advocates for similar growth models for charter schools. However, there is no explanation of…
Flows induced by exponential stretching and shearing plate motions
NASA Astrophysics Data System (ADS)
Weidman, Patrick
2016-11-01
Boundary-layer solutions for the flow induced by an exponentially stretching surface also sheared in its own plane are given. Prior to this study no similarity solutions have been reported for flows generated by exponentially sheared surfaces concomitant with surface stretching in any form. The method of solution is self-similarity. The results found here are intimately related to those of Magyari and Keller ["Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface," J. Phys. D: Appl. Phys. 32, 577-585 (1999)] who studied the motion and heat transfer induced by an exponentially stretching plate. In addition to two particular cases reported here, a third situation is found where an exponentially stretching surface admits a concomitant arbitrary streamwise shearing motion.
Exponentially growing bubbles around early supermassive black holes
NASA Astrophysics Data System (ADS)
Gilli, R.; Calura, F.; D'Ercole, A.; Norman, C.
2017-07-01
We address the as yet unexplored issue of outflows induced by exponentially growing power sources, focusing on early supermassive black holes (BHs). We assumed that these objects grow to 109M⊙ by z = 6 by Eddington-limited accretion and convert 5% of their bolometric output into a wind. We first considered the case of energy-driven and momentum-driven outflows expanding in a region where the gas and total mass densities are uniform and equal to the average values in the Universe at z> 6. We derived analytic solutions for the evolution of the outflow: for an exponentially growing power with e-folding time tSal, we find that the late time expansion of the outflow radius is also exponential, with e-folding time of 5tSal and 4tSal in the energy-driven and momentum-driven limit, respectively. We then considered energy-driven outflows produced by quasi-stellar objects (QSOs) at the centre of early dark matter halos of different masses and powered by BHs growing from different seeds. We followed the evolution of the source power and of the gas and dark matter density profiles in the halos from the beginning of the accretion until z = 6. The final bubble radius and velocity do not depend on the seed BH mass, but are instead smaller for larger halo masses. At z = 6, bubble radii in the range 50-180 kpc and velocities in the range 400-1000 km s-1 are expected for QSOs hosted by halos in the mass range 3 × 1011-1013M⊙. These radius and velocity scales compare well with those measured for the outflowing gas in the z = 6.4 QSO SDSS J1148+5251. By the time the QSO is observed, we found that the total thermal energy injected within the bubble in the case of an energy-driven outflow is Eth 5 × 1060 erg. This is in excellent agreement with the value of Eth = (6.2 ± 1.7) × 1060 erg measured through the detection of the thermal Sunyaev-Zeldovich effect around a large population of luminous QSOs at lower redshifts. This suggests that QSO outflows are closer to the energy
Modeling and robust control of wind turbine
NASA Astrophysics Data System (ADS)
Gilev, Bogdan
2016-12-01
In this paper a model of a wind turbine is evaluated, consisting of: wind speed model, mechanical and electrical model of generator and tower oscillation model. This model is linearized around of a nominal point. By using the linear model with uncertainties is synthesized a uncertain model. By using the uncertain model and robust control theory is developed a robust controller, which provide mode of stabilizing the rotor frequency and damping the tower oscillations. Finally is simulated work of nonlinear system and robust controller
NASA Astrophysics Data System (ADS)
Hsiao, Feng-Hsiag
2016-10-01
In this study, a novel approach via improved genetic algorithm (IGA)-based fuzzy observer is proposed to realise exponential optimal H∞ synchronisation and secure communication in multiple time-delay chaotic (MTDC) systems. First, an original message is inserted into the MTDC system. Then, a neural-network (NN) model is employed to approximate the MTDC system. Next, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion derived in terms of Lyapunov's direct method, thus ensuring that the trajectories of the slave system approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Due to GA's random global optimisation search capabilities, the lower and upper bounds of the search space can be set so that the GA will seek better fuzzy observer feedback gains, accelerating feedback gain-based synchronisation via the LMI-based approach. IGA, which exhibits better performance than traditional GA, is used to synthesise a fuzzy observer to not only realise the exponential synchronisation, but also achieve optimal H∞ performance by minimizing the disturbance attenuation level and recovering the transmitted message. Finally, a numerical example with simulations is given in order to demonstrate the effectiveness of our approach.
NASA Astrophysics Data System (ADS)
Wen, Zhang; Zhan, Hongbin; Wang, Quanrong; Liang, Xing; Ma, Teng; Chen, Chen
2017-05-01
Actual field pumping tests often involve variable pumping rates which cannot be handled by the classical constant-rate or constant-head test models, and often require a convolution process to interpret the test data. In this study, we proposed a semi-analytical model considering an exponentially decreasing pumping rate started at a certain (higher) rate and eventually stabilized at a certain (lower) rate for cases with or without wellbore storage. A striking new feature of the pumping test with an exponentially decayed rate is that the drawdowns will decrease over a certain period of time during intermediate pumping stage, which has never been seen before in constant-rate or constant-head pumping tests. It was found that the drawdown-time curve associated with an exponentially decayed pumping rate function was bounded by two asymptotic curves of the constant-rate tests with rates equaling to the starting and stabilizing rates, respectively. The wellbore storage must be considered for a pumping test without an observation well (single-well test). Based on such characteristics of the time-drawdown curve, we developed a new method to estimate the aquifer parameters by using the genetic algorithm.
Parametric Uncertainty Reduction in Robust Multivariable Control
1993-09-01
presents a method for reducing the Dumber of parametric un- certainties used in the design of a robust Ho, controller. The resulting controller is shown...determining robust stability can be de- duced from Figure 2.9. Stability in the loop containing the perturbation requires that for all frequencies det {I... det (I + MA) = 01 {minAEA(a(A) I det (J + MA) = 0)1’ otherwise 15 It can be shown that the SSV has the following properties (Doyle, 1982): 1. F(oM) =1
Correcting Partial Volume Effect in Bi-exponential T2 Estimation of Small Lesions
Huang, Chuan; Galons, Jean-Philippe; Graff, Christian G.; Clarkson, Eric W.; Bilgin, Ali; Kalb, Bobby; Martin, Diego R.; Altbach, Maria I.
2014-01-01
Purpose T2 mapping provides a quantitative approach for focal liver lesion characterization. For small lesions a bi-exponential model should be used to account for partial volume effects (PVE). However, conventional bi-exponential fitting suffers from large uncertainty of the fitted parameters when noise is present. The purpose of this work is to develop a more robust method to correct for PVE affecting small lesions. Methods We developed a ROI-based joint bi-exponential fitting (JBF) algorithm to estimate the T2 of lesions affected by PVE. JBF takes advantage of the lesion fraction variation among voxels within an ROI. JBF is compared to conventional approaches using Cramér-Rao lower bound analysis, numerical simulations, phantom and -vivo data. Results JBF provides more accurate and precise T2 estimates in the presence of PVE. Furthermore, JBF is less sensitive to ROI drawing. Phantom and in-vivo results show that JBF can be combined with a reconstruction method for highly undersampled data, enabling the characterization of small abdominal lesions from data acquired in a single breath-hold. Conclusion The JBF algorithm provides more accurate and stable T2 estimates for small structures than conventional techniques when PVE is present. It should be particularly useful for the characterization of small abdominal lesions. PMID:24753061
NASA Astrophysics Data System (ADS)
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.
NASA Astrophysics Data System (ADS)
Yang, Yue; Zhang, Zhimeng; Jiao, Jinlong; Tian, Chao; Cao, Lihua; Wu, Yuchi; Dong, Kegong; Zhou, Weimin; Gu, Yuqiu; Zhao, Zongqing
2017-06-01
The self-focusing of ultraintense laser in plasma lenses with exponentially increasing density profiles is studied. And the robustness of this design is proved by theoretical estimates and 3D particle-in-cell simulations. Attributed to the density compensation for the increase of laser intensity during self-focusing, a modulated exponential density plasma lens can efficiently focus the laser to higher peak intensity and smaller spot than that by using optimized uniform plasma lens. In near critical density plasmas, laser focusing experiences two stages with different dominant mechanisms: self-focusing at earlier time and magnetic constraint in the plasma channel. And more enhanced effects are achieved by exponential density plasma in both stages. The focal position and the optimal density scalelength for this kind of plasma lens are also estimated through theoretical derivation. Our findings indicate the possibility for the preplasma to experimentally serve as a novel plasma lens to obtain relativistic lasers with high contrast, ultra-high intensities and micro focal spots.
Kaneko, Kunihiko
2011-06-01
Here I present and discuss a model that, among other things, appears able to describe the dynamics of cancer cell origin from the perspective of stable and unstable gene expression profiles. In identifying such aberrant gene expression profiles as lying outside the normal stable states attracted through development and normal cell differentiation, the hypothesis explains why cancer cells accumulate mutations, to which they are not robust, and why these mutations create a new stable state far from the normal gene expression profile space. Such cells are in strong contrast with normal cell types that appeared as an attractor state in the gene expression dynamical system under cell-cell interaction and achieved robustness to noise through evolution, which in turn also conferred robustness to mutation. In complex gene regulation networks, other aberrant cellular states lacking such high robustness are expected to remain, which would correspond to cancer cells.
NASA Astrophysics Data System (ADS)
Emam, Mahmoud; Han, Qi; Yu, Liyang; Zhang, Ye; Niu, Xiamu
2015-07-01
Copy-move is one of the most common methods for image manipulation. Several methods have been proposed to detect and locate the tampered regions, while many methods failed when the copied regions are rotated before being pasted. A rotational invariant detecting method using Polar Complex Exponential Transform (PCET) is proposed in this paper. Firstly, the original image is divided into overlapping circular blocks, and PCET is employed to each block to extract the rotation-invariant robust features. Secondly, the Approximate Nearest Neighbors (ANN) of each feature vector are collected by Locality Sensitive Hashing (LSH). Experimental results show that the proposed technique is robust to rotation.
NASA Astrophysics Data System (ADS)
Mohammadi, Reza
2014-03-01
In this study, the exponential spline scheme is implemented to find a numerical solution of the nonlinear Schrödinger equations with constant and variable coefficients. The method is based on the Crank-Nicolson formulation for time integration and exponential spline functions for space integration. The error analysis, existence, stability, uniqueness and convergence properties of the method are investigated using the energy method. We show that the method is unconditionally stable and accurate of orders O(k+kh+h2) and O(k+kh+h4). This method is tested on three examples by using the cubic nonlinear Schrödinger equation with constant and variable coefficients and the Gross-Pitaevskii equation. The computed results are compared wherever possible with those already available in the literature. The results show that the derived method is easily implemented and approximate the exact solution very well.
Scalar-fluid interacting dark energy: Cosmological dynamics beyond the exponential potential
NASA Astrophysics Data System (ADS)
Dutta, Jibitesh; Khyllep, Wompherdeiki; Tamanini, Nicola
2017-01-01
We extend the dynamical systems analysis of scalar-fluid interacting dark energy models performed in C. G. Boehmer et al., Phys. Rev. D 91, 123002 (2015), 10.1103/PhysRevD.91.123002 by considering scalar field potentials beyond the exponential type. The properties and stability of critical points are examined using a combination of linear analysis, computational methods and advanced mathematical techniques, such as center manifold theory. We show that the interesting results obtained with an exponential potential can generally be recovered also for more complicated scalar field potentials. In particular, employing power law and hyperbolic potentials as examples, we find late time accelerated attractors, transitions from dark matter to dark energy domination with specific distinguishing features, and accelerated scaling solutions capable of solving the cosmic coincidence problem.
Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.
Liu, Meiqin
2009-09-01
This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.
Exponential synchronization of memristive Cohen-Grossberg neural networks with mixed delays.
Yang, Xinsong; Cao, Jinde; Yu, Wenwu
2014-06-01
This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen-Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen-Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
Caraballo, Tomas Kloeden, Peter E. Schmalfuss, Bjoern
2004-10-15
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities.
Derivation of stretched exponential tap density equations of granular powders.
Hao, Tian
2015-04-21
The tap density of granular powders was found to be better fitted with the stretched exponential law. In our previous work, the stretched exponential tap density equations were derived with the rate process theory and free volume concept, under the assumption that the particle packing rate during the tapping process obeys the stretched Arrhenius equation, which, however, has an empirical origin. In this article, the above assumption is eliminated and attempts are made to obtain the stretched exponential tap density equations from very fundamental bases. In a vertical tapping process, the probability of particles attaining certain energy states is assumed to obey the Boltzmann distribution and particles traveling from one site to another are assumed to follow a very common memoryless random exponential law. The stretched exponential tap density equations are thus derived and all parameters acquire clear physical meanings. The most important parameter, the stretched exponential, is demonstrated to correlate with the interparticle forces: a small value may indicate a strong adhesive or cohesive interaction. Therefore, the stretched exponential could be a better indicator for powder flowability correlated with particle interactions as well.
NASA Technical Reports Server (NTRS)
Narendra, K. S.; Annaswamy, A. M.
1985-01-01
Several concepts and results in robust adaptive control are are discussed and is organized in three parts. The first part surveys existing algorithms. Different formulations of the problem and theoretical solutions that have been suggested are reviewed here. The second part contains new results related to the role of persistent excitation in robust adaptive systems and the use of hybrid control to improve robustness. In the third part promising new areas for future research are suggested which combine different approaches currently known.
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.; Ernazarov, K. K.
2017-01-01
A (n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: ai ∼ exp (vit), i = 1, …, n, are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on (vi ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented.
Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent
NASA Astrophysics Data System (ADS)
Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.
2016-10-01
In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
Exponential Functions, Rates of Change, and the Multiplicative Unit.
ERIC Educational Resources Information Center
Confrey, Jere; Smith, Erick
1994-01-01
Describes a covariational, rather than correspondence, approach to functions that emphasizes rate of change. Proposes three ways of understanding rate of change in relation to exponential functions. (Contains 41 references.) (Author/MKR)
On the role of exponential splines in image interpolation.
Kirshner, Hagai; Porat, Moshe
2009-10-01
A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks.
True quantum face of the "exponential" decay law
NASA Astrophysics Data System (ADS)
Urbanowski, Krzysztof
2017-05-01
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, "exponential" (or "canonical") described by the decay law of the exponential form, and late time characterized by the decay law having inverse-power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the "exponential" regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.
Robust flight control of rotorcraft
NASA Astrophysics Data System (ADS)
Pechner, Adam Daniel
With recent design improvement in fixed wing aircraft, there has been a considerable interest in the design of robust flight control systems to compensate for the inherent instability necessary to achieve desired performance. Such systems are designed for maximum available retention of stability and performance in the presence of significant vehicle damage or system failure. The rotorcraft industry has shown similar interest in adopting these reconfigurable flight control schemes specifically because of their ability to reject disturbance inputs and provide a significant amount of robustness for all but the most catastrophic of situations. The research summarized herein focuses on the extension of the pseudo-sliding mode control design procedure interpreted in the frequency domain. Application of the technique is employed and simulated on two well known helicopters, a simplified model of a hovering Sikorsky S-61 and the military's Black Hawk UH-60A also produced by Sikorsky. The Sikorsky helicopter model details are readily available and was chosen because it can be limited to pitch and roll motion reducing the number of degrees of freedom and yet contains two degrees of freedom, which is the minimum requirement in proving the validity of the pseudo-sliding control technique. The full order model of a hovering Black Hawk system was included both as a comparison to the S-61 helicopter design system and as a means to demonstrate the scaleability and effectiveness of the control technique on sophisticated systems where design robustness is of critical concern.
Adaptive Critic Nonlinear Robust Control: A Survey.
Wang, Ding; He, Haibo; Liu, Derong
2017-10-01
Adaptive dynamic programming (ADP) and reinforcement learning are quite relevant to each other when performing intelligent optimization. They are both regarded as promising methods involving important components of evaluation and improvement, at the background of information technology, such as artificial intelligence, big data, and deep learning. Although great progresses have been achieved and surveyed when addressing nonlinear optimal control problems, the research on robustness of ADP-based control strategies under uncertain environment has not been fully summarized. Hence, this survey reviews the recent main results of adaptive-critic-based robust control design of continuous-time nonlinear systems. The ADP-based nonlinear optimal regulation is reviewed, followed by robust stabilization of nonlinear systems with matched uncertainties, guaranteed cost control design of unmatched plants, and decentralized stabilization of interconnected systems. Additionally, further comprehensive discussions are presented, including event-based robust control design, improvement of the critic learning rule, nonlinear H∞ control design, and several notes on future perspectives. By applying the ADP-based optimal and robust control methods to a practical power system and an overhead crane plant, two typical examples are provided to verify the effectiveness of theoretical results. Overall, this survey is beneficial to promote the development of adaptive critic control methods with robustness guarantee and the construction of higher level intelligent systems.
Robust H ∞ Filtering for a Class of Complex Networks with Stochastic Packet Dropouts and Time Delays
Lyu, Ming; Guo, Pengfei; Bo, Yuming
2014-01-01
The robust H ∞ filtering problem is investigated for a class of complex network systems which has stochastic packet dropouts and time delays, combined with disturbance inputs. The packet dropout phenomenon occurs in a random way and the occurrence probability for each measurement output node is governed by an individual random variable. Besides, the time delay phenomenon is assumed to occur in a nonlinear vector-valued function. We aim to design a filter such that the estimation error converges to zero exponentially in the mean square, while the disturbance rejection attenuation is constrained to a given level by means of the H ∞ performance index. By constructing the proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the state detection observer for the discrete systems, and the observer gain is also derived by solving linear matrix inequalities. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method. PMID:24987738
Can distributed delays perfectly stabilize dynamical networks?
NASA Astrophysics Data System (ADS)
Omi, Takahiro; Shinomoto, Shigeru
2008-04-01
Signal transmission delays tend to destabilize dynamical networks leading to oscillation, but their dispersion contributes oppositely toward stabilization. We analyze an integrodifferential equation that describes the collective dynamics of a neural network with distributed signal delays. With the Γ distributed delays less dispersed than exponential distribution, the system exhibits reentrant phenomena, in which the stability is once lost but then recovered as the mean delay is increased. With delays dispersed more highly than exponential, the system never destabilizes.
Fast Modular Exponentiation and Elliptic Curve Group Operation in Maple
ERIC Educational Resources Information Center
Yan, S. Y.; James, G.
2006-01-01
The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…
Confronting quasi-exponential inflation with WMAP seven
Pal, Barun Kumar; Pal, Supratik; Basu, B. E-mail: pal@th.physik.uni-bonn.de
2012-04-01
We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK.
Skewed exponential pairwise velocities from Gaussian initial conditions
Juszkiewicz, R.; Fisher, K. B.; Szapudi, I.
1998-09-01
Using an Eulerian perturbative calculation, we show that the distribution of relative pairwise velocities which arises from gravitational instability of Gaussian density fluctuations has asymmetric (skewed) exponential tails. The negative skewness is induced by the negative mean streaming velocity of pairs (the infall prevails over expansion), while the exponential tails arise because the relative pairwise velocity is a number, not volume weighted statistic. The derived probability distribution is compared with N-body simulations and shown to provide a reasonable fit.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1985-01-01
Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1986-01-01
Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Demonstration of the exponential decay law using beer froth
NASA Astrophysics Data System (ADS)
Leike, A.
2002-01-01
The volume of beer froth decays exponentially with time. This property is used to demonstrate the exponential decay law in the classroom. The decay constant depends on the type of beer and can be used to differentiate between different beers. The analysis shows in a transparent way the techniques of data analysis commonly used in science - consistency checks of theoretical models with the data, parameter estimation and determination of confidence intervals.
Fast Modular Exponentiation and Elliptic Curve Group Operation in Maple
ERIC Educational Resources Information Center
Yan, S. Y.; James, G.
2006-01-01
The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…
NASA Astrophysics Data System (ADS)
Johnson, Y.; Dasgupta, S.
2014-07-01
Multiple unmanned aerial vehicle (UAV) control in formation flight is comparatively a new research area in the field of aerospace engineering. In the proposed work, robust control techniques are implemented to maintain a fixed relative distance in horizontal and vertical direction with uniform pitch orientation in an uncertain leader-follower pattern of close formation flight platform. The forward velocity dynamics is of focal interest in this paper. H-infinity controllers are designed for leader control and its tracking. The robustness of the H-infinity controller is validated with Kharitonov related bounded phase conditions by forming interval polynomials.
1981-12-01
Controller ................... 38 Sampled-Data Performance Analysis ............. 44 Doyle and Stein Technique in Discrete-Time Systems - 1...48 Doyle and Stein Technique in Discretd-Time System.s - 2 ................................. 50 Enhancing Robustness of... Technique Extended to Sampled-Data Controllers ................ 73 G715 Robustness Enhancement by Directly D"?C TAB E
Robust Critical Point Detection
Bhatia, Harsh
2016-07-28
Robust Critical Point Detection is a software to compute critical points in a 2D or 3D vector field robustly. The software was developed as a part of the author's work at the lab as a Phd student under Livermore Scholar Program (now called Livermore Graduate Scholar Program).
Mechanisms for Robust Cognition
ERIC Educational Resources Information Center
Walsh, Matthew M.; Gluck, Kevin A.
2015-01-01
To function well in an unpredictable environment using unreliable components, a system must have a high degree of robustness. Robustness is fundamental to biological systems and is an objective in the design of engineered systems such as airplane engines and buildings. Cognitive systems, like biological and engineered systems, exist within…
Mechanisms for Robust Cognition
ERIC Educational Resources Information Center
Walsh, Matthew M.; Gluck, Kevin A.
2015-01-01
To function well in an unpredictable environment using unreliable components, a system must have a high degree of robustness. Robustness is fundamental to biological systems and is an objective in the design of engineered systems such as airplane engines and buildings. Cognitive systems, like biological and engineered systems, exist within…
Average-cost based robust structural control
NASA Technical Reports Server (NTRS)
Hagood, Nesbitt W.
1993-01-01
A method is presented for the synthesis of robust controllers for linear time invariant structural systems with parameterized uncertainty. The method involves minimizing quantities related to the quadratic cost (H2-norm) averaged over a set of systems described by real parameters such as natural frequencies and modal residues. Bounded average cost is shown to imply stability over the set of systems. Approximations for the exact average are derived and proposed as cost functionals. The properties of these approximate average cost functionals are established. The exact average and approximate average cost functionals are used to derive dynamic controllers which can provide stability robustness. The robustness properties of these controllers are demonstrated in illustrative numerical examples and tested in a simple SISO experiment on the MIT multi-point alignment testbed.
Exponential convergence analysis of uncertain genetic regulatory networks with time-varying delays.
Wang, Wenqin; Nguang, Sing Kiong; Zhong, Shouming; Liu, Feng
2014-09-01
This study is concerned with the problem of exponential convergence of uncertain genetic regulatory networks with time-varying delays in the case of the unknown equilibrium point. The system׳s uncertainties are modeled as a structured linear fractional form. Novel stability criteria are obtained by using the lower bound lemma together with Jensen inequality lemma. In order to get rid of the rigorous constraint that the derivatives of time-varying delays must be less than one, a new approach is introduced by improving Lyapunov-Krasovskii functional rather than using the traditional free-weighting matrices. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.
On long-time algebraic and exponential instabilities found in linear dispersive flows
NASA Astrophysics Data System (ADS)
Barlow, Nathaniel; King, Kristina; Zaretzky, Paula; Cromer, Michael; Weinstein, Steven
2016-11-01
A physically-motivated class of partial differential equations that describes the response of a system to disturbances is examined. Morphological differences are identified between system responses that exhibit algebraic growth and the more typical case of exponential growth. Specifically, the propagation characteristics of the response are examined in the context of spatio-temporal hydrodynamic stability theory. One key attribute of predicted algebraically growing solutions is the prevalence of transient growth in almost all of the response, with the long-time growth occurring asymptotically at precisely one wave speed.
NASA Astrophysics Data System (ADS)
Liu, Yurong; Alsaadi, Fuad E.; Yin, Xiaozhou; Wang, Yamin
2015-02-01
In this paper, we are concerned with the robust H∞ filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under consideration involves parameter uncertainties, stochastic disturbances, time-varying delays and sector nonlinearities. Both missing measurements and randomly occurring nonlinearities are described via the binary switching sequences satisfying a conditional probability distribution, and the nonlinearities are assumed to be sector bounded. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the filtering error is constrained to be robustly exponentially stable in the mean square, and a prescribed ? disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality. Finally, a numerical example is exploited to show the usefulness of the results derived.
Berthelot, Geoffroy; Len, Stéphane; Hellard, Philippe; Tafflet, Muriel; Guillaume, Marion; Vollmer, Jean-Claude; Gager, Bruno; Quinquis, Laurent; Marc, Andy; Toussaint, Jean-François
2012-08-01
The physiological parameters characterizing human capacities (the ability to move, reproduce or perform tasks) evolve with ageing: performance is limited at birth, increases to a maximum and then decreases back to zero at the day of death. Physical and intellectual skills follow such a pattern. Here, we investigate the development of sport and chess performances during the lifetime at two different scales: the individual athletes' careers and the world record by age class in 25 Olympic sports events and in grandmaster chess players. For all data sets, a biphasic development of growth and decline is described by a simple model that accounts for 91.7% of the variance at the individual level and 98.5% of the variance at the species one. The age of performance peak is computed at 26.1 years old for the events studied (26.0 years old for track and field, 21.0 years old for swimming and 31.4 years old for chess). The two processes (growth and decline) are exponential and start at age zero. Both were previously demonstrated to happen in other human and non-human biological functions that evolve with age. They occur at the individual and species levels with a similar pattern, suggesting a scale invariance property.
Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised
NASA Technical Reports Server (NTRS)
Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.
1995-01-01
The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.
Biological robustness: paradigms, mechanisms, and systems principles.
Whitacre, James Michael
2012-01-01
Robustness has been studied through the analysis of data sets, simulations, and a variety of experimental techniques that each have their own limitations but together confirm the ubiquity of biological robustness. Recent trends suggest that different types of perturbation (e.g., mutational, environmental) are commonly stabilized by similar mechanisms, and system sensitivities often display a long-tailed distribution with relatively few perturbations representing the majority of sensitivities. Conceptual paradigms from network theory, control theory, complexity science, and natural selection have been used to understand robustness, however each paradigm has a limited scope of applicability and there has been little discussion of the conditions that determine this scope or the relationships between paradigms. Systems properties such as modularity, bow-tie architectures, degeneracy, and other topological features are often positively associated with robust traits, however common underlying mechanisms are rarely mentioned. For instance, many system properties support robustness through functional redundancy or through response diversity with responses regulated by competitive exclusion and cooperative facilitation. Moreover, few studies compare and contrast alternative strategies for achieving robustness such as homeostasis, adaptive plasticity, environment shaping, and environment tracking. These strategies share similarities in their utilization of adaptive and self-organization processes that are not well appreciated yet might be suggestive of reusable building blocks for generating robust behavior.
Biological Robustness: Paradigms, Mechanisms, and Systems Principles
Whitacre, James Michael
2012-01-01
Robustness has been studied through the analysis of data sets, simulations, and a variety of experimental techniques that each have their own limitations but together confirm the ubiquity of biological robustness. Recent trends suggest that different types of perturbation (e.g., mutational, environmental) are commonly stabilized by similar mechanisms, and system sensitivities often display a long-tailed distribution with relatively few perturbations representing the majority of sensitivities. Conceptual paradigms from network theory, control theory, complexity science, and natural selection have been used to understand robustness, however each paradigm has a limited scope of applicability and there has been little discussion of the conditions that determine this scope or the relationships between paradigms. Systems properties such as modularity, bow-tie architectures, degeneracy, and other topological features are often positively associated with robust traits, however common underlying mechanisms are rarely mentioned. For instance, many system properties support robustness through functional redundancy or through response diversity with responses regulated by competitive exclusion and cooperative facilitation. Moreover, few studies compare and contrast alternative strategies for achieving robustness such as homeostasis, adaptive plasticity, environment shaping, and environment tracking. These strategies share similarities in their utilization of adaptive and self-organization processes that are not well appreciated yet might be suggestive of reusable building blocks for generating robust behavior. PMID:22593762
Application of the stretched exponential function to fluorescence lifetime imaging.
Lee, K C; Siegel, J; Webb, S E; Lévêque-Fort, S; Cole, M J; Jones, R; Dowling, K; Lever, M J; French, P M
2001-09-01
Conventional analyses of fluorescence lifetime measurements resolve the fluorescence decay profile in terms of discrete exponential components with distinct lifetimes. In complex, heterogeneous biological samples such as tissue, multi-exponential decay functions can appear to provide a better fit to fluorescence decay data than the assumption of a mono-exponential decay, but the assumption of multiple discrete components is essentially arbitrary and is often erroneous. Moreover, interactions, both between fluorophores and with their environment, can result in complex fluorescence decay profiles that represent a continuous distribution of lifetimes. Such continuous distributions have been reported for tryptophan, which is one of the main fluorophores in tissue. This situation is better represented by the stretched-exponential function (StrEF). In this work, we have applied, for the first time to our knowledge, the StrEF to time-domain whole-field fluorescence lifetime imaging (FLIM), yielding both excellent tissue contrast and goodness of fit using data from rat tissue. We note that for many biological samples for which there is no a priori knowledge of multiple discrete exponential fluorescence decay profiles, the StrEF is likely to provide a truer representation of the underlying fluorescence dynamics. Furthermore, fitting to a StrEF significantly decreases the required processing time, compared with a multi-exponential component fit and typically provides improved contrast and signal/noise in the resulting FLIM images. In addition, the stretched-exponential decay model can provide a direct measure of the heterogeneity of the sample, and the resulting heterogeneity map can reveal subtle tissue differences that other models fail to show.
NASA Technical Reports Server (NTRS)
Ryan, Robert
1993-01-01
The concept of rubustness includes design simplicity, component and path redundancy, desensitization to the parameter and environment variations, control of parameter variations, and punctual operations. These characteristics must be traded with functional concepts, materials, and fabrication approach against the criteria of performance, cost, and reliability. The paper describes the robustness design process, which includes the following seven major coherent steps: translation of vision into requirements, definition of the robustness characteristics desired, criteria formulation of required robustness, concept selection, detail design, manufacturing and verification, operations.
NASA Technical Reports Server (NTRS)
Ryan, Robert
1993-01-01
The concept of rubustness includes design simplicity, component and path redundancy, desensitization to the parameter and environment variations, control of parameter variations, and punctual operations. These characteristics must be traded with functional concepts, materials, and fabrication approach against the criteria of performance, cost, and reliability. The paper describes the robustness design process, which includes the following seven major coherent steps: translation of vision into requirements, definition of the robustness characteristics desired, criteria formulation of required robustness, concept selection, detail design, manufacturing and verification, operations.
Searching for robust quantum memories in many coupled oscillators
NASA Astrophysics Data System (ADS)
Bosco de Magalhães, A. R.
2011-11-01
The relation between microscopic symmetries in the system-environment interaction and the emergence of robust states is studied for many linearly coupled harmonic oscillators. Different types of symmetry, which are introduced into the model as terms in the coupling constants between each system's oscillator and a common reservoir, lead to distinct robust modes. Since these modes are partially or completely immune to the symmetric part of the environmental noise, they are good candidates for building quantum memories. A comparison of the model investigated here, with bilinear system-reservoir coupling, and a model where such coupling presents an exponential dependence on the variables of interest is performed.
NASA Astrophysics Data System (ADS)
Lu, Y.; Chatterjee, S.
2014-11-01
Exponential family statistical distributions, including the well-known normal, binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of the data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that result in the data. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular normal distributional assumption dependent cumulative sum (Gaussian CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, so to understand whether the nature of these tropical storms has remained stable over the last few decades.
Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles
Warshaw, S I
2001-07-15
In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resulted from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.
Non-exponential and oscillatory decays in quantum mechanics
Peshkin, Murray; Volya, Alexander; Zelevinsky, Vladimir
2014-08-07
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.
Non-exponential and oscillatory decays in quantum mechanics
NASA Astrophysics Data System (ADS)
Peshkin, Murray; Volya, Alexander; Zelevinsky, Vladimir
2014-08-01
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.
Bayesian estimation of generalized exponential distribution under noninformative priors
NASA Astrophysics Data System (ADS)
Moala, Fernando Antonio; Achcar, Jorge Alberto; Tomazella, Vera Lúcia Damasceno
2012-10-01
The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional noninformative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.
Robust Active Portfolio Management
2006-11-27
the Markowitz mean-variance model led to development of the Capital Asset Pricing Model ( CAPM ) for asset pricing [35, 29, 23] which remains one of the...active portfolio management. Our model uses historical returns and equilibrium expected returns predicted by the CAPM to identify assets that are...we construct robust models for active portfolio management in a market with transaction costs. The goal of these robust models is to control the impact
NASA Technical Reports Server (NTRS)
Pratt, D. T.
1984-01-01
Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
NASA Technical Reports Server (NTRS)
Pratt, D. T.
1984-01-01
Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
Exponential Sensitivity and its Cost in Quantum Physics.
Gilyén, András; Kiss, Tamás; Jex, Igor
2016-02-10
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed.
Design of a 9-loop quasi-exponential waveform generator.
Banerjee, Partha; Shukla, Rohit; Shyam, Anurag
2015-12-01
We know in an under-damped L-C-R series circuit, current follows a damped sinusoidal waveform. But if a number of sinusoidal waveforms of decreasing time period, generated in an L-C-R circuit, be combined in first quarter cycle of time period, then a quasi-exponential nature of output current waveform can be achieved. In an L-C-R series circuit, quasi-exponential current waveform shows a rising current derivative and thereby finds many applications in pulsed power. Here, we have described design and experiment details of a 9-loop quasi-exponential waveform generator. In that, design details of magnetic switches have also been described. In the experiment, output current of 26 kA has been achieved. It has been shown that how well the experimentally obtained output current profile matches with the numerically computed output.
Exponential rise of dynamical complexity in quantum computing through projections
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-01-01
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics. PMID:25300692