Lyapunov Function Technique Research Articles

Exponential synchronization of Cohen-Grossberg neural networks with stochastic perturbation and reaction-diffusion terms via periodically intermittent control

In this paper, a class of Cohen-Grossberg neural networks with mixed time-varying delays, stochastic perturbation and reaction-diffusion terms is investigated. The exponential synchronization criteria in terms of p-norm are obtained based on periodically intermittent control by means of Lyapunov functional theory, mathematical induction and inequality technique. The influences of stochastic perturbation, spacial diffusion, the control rate and the control strength on the exponential synchronization are discussed according to the obtained synchronization criteria. The proposed criteria improve the previous known results in the literature and remove the restrictions on the mixed time-varying delays. Numerical simulations are carried out to illustrate the feasibility of the results. https://doi.org/10.28919/cmbn/2853

H∞ Control for T-S Fuzzy Singularly Perturbed Switched Systems

This paper is concerned with the design of fuzzy controller with guaranteed H∞ performance for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. First, by using the average dwell time approach together with the piecewise Lyapunov function technique, a state feedback controller that depends on the singular perturbation parameter ε is developed. This controller is shown to work well for all ε∈(0,ε0]. Then, for sufficiently small ε, an ε-independent controller design method is proposed. Furthermore, under the ε-independent controller, the ε-bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to evaluate the feasibility and effectiveness of the obtained results.

CLFs-based optimization control for a class of constrained visual servoing systems

In this paper, we use the control Lyapunov function (CLF) technique to present an optimized visual servo control method for constrained eye-in-hand robot visual servoing systems. With the knowledge of camera intrinsic parameters and depth of target changes, visual servo control laws (i.e. translation speed) with adjustable parameters are derived by image point features and some known CLF of the visual servoing system. The Fibonacci method is employed to online compute the optimal value of those adjustable parameters, which yields an optimized control law to satisfy constraints of the visual servoing system. The Lyapunov's theorem and the properties of CLF are used to establish stability of the constrained visual servoing system in the closed-loop with the optimized control law. One merit of the presented method is that there is no requirement of online calculating the pseudo-inverse of the image Jacobian's matrix and the homography matrix. Simulation and experimental results illustrated the effectiveness of the method proposed here.

Pseudo almost periodic solutions for neutral type SICNNs with D operator

In this paper, neutral type shunting inhibitory cellular neural networks with D operator are considered. Based on Lyapunov functional method and differential inequality technique, some new criteria are derived to guarantee the existence and global exponential stability of pseudo almost periodic solutions of considered systems. In addition, an example and its numerical simulations are provided to show the validity and the advantages of the obtained results.

Global convergence of discrete-time inhomogeneous Markov processes from dynamical systems perspective

Given the continuous real-valued objective function f and the discrete time inhomogeneous Markov process Xt defined by the recursive equation of the form Xt+1=Tt(Xt,Yt), where Yt is an independent sequence, we target the problem of finding conditions under which the Xt converges towards the set of global minimums of f. Our methodology is based on the Lyapunov function technique and extends the previous results to cover the case in which the sequence f(Xt) is not assumed to be a supermartingale. We provide a general convergence theorem. An application example is presented: the general result is applied to the Simulated Annealing algorithm.

Pseudo Almost Periodic Solutions for High-Order Hopfield Neural Networks with Time-Varying Leakage Delays

In this paper, high-order Hopfield neural networks with time-varying leakage delays are investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. Some simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies.

Mean-square global exponential stability in Lagrange sense for delayed recurrent neural networks with Markovian switching

The paper discusses the mean-square global exponential stability in Lagrange sense for delayed recurrent neural networks (DRNNs) with Markovian switching. Two different types of activation functions are considered, which include both bounded and unbounded activation functions. By using the vector Lyapunov function and stochastic analysis technique, we establish two L-operator differential inequalities. By employing the two L-operator differential inequalities and vector Lyapunov functions methods, we provide easily verifiable criteria for Lagrange stability in mean-square sense of DRNNs with Markovian switching. Finally, two numerical examples are given to illustrate the efficiency of the derived results.

State and input simultaneous estimation for discrete‐time switched singular delay systems with missing measurements

SummaryThis paper presents an approach to simultaneously estimating the states and inputs of discrete‐time linear switched singular state‐delayed systems with unknown inputs, multiple missing measurements, and average dwell time (ADT) switching. In each output measurement channel of the system, the data loss incident is controlled by an individual stochastic variable obeying a certain probability distribution on the interval [01]. The proposed approach is based on the design of a switched, loss‐probability‐dependent proportional integral observer under the ℓ2 input attenuation framework. By using piecewise Lyapunov function technique, ADT scheme, stochastic analysis, and projection lemma, sufficient conditions for the existence of such an observer are established in terms of linear matrix inequalities, which guarantee that the resulting estimation error system is stochastically exponentially admissible and achieves an (non‐weighted) ℓ2 gain from the augmented unknown input to the state and unknown input estimation errors under ADT switching. Moreover, a method is provided to seek the minimum allowable ℓ2 gain level for a desired ADT of the switching signals. The effectiveness of the proposed approach is illustrated by a simulation example of direct current (DC) servomechanism control system. Copyright © 2016 John Wiley & Sons, Ltd.

H ∞ filtering for switched linear parameter‐varying systems and its application to aero‐engines

This study deals with the H ∞ filtering problem for switched linear parameter-varying (LPV) systems using the multiple parameter-dependent Lyapunov function technique. The parameter and mode-dependent switching law and the filter state-relied controllers are designed to ensure the H ∞ performance without requiring the stability of each individual subsystem. An H ∞ filtering synthesis condition is obtained by a matrix optimisation iterating algorithm. Simulation result on a switched LPV aero-engine model shows the feasibility and the validity of the H ∞ filtering scheme.

Twisting sliding mode control with adaptation: Lyapunov design, methodology and application

A novel adaptive-gain twisting controller that is robust to the bounded disturbances with the unknown boundaries is proposed. The control algorithm is derived using the Lyapunov function technique. It is shown that an ideal or real second order sliding mode is established, and the adaptation algorithm does not overestimate the control gain. The efficacy of the proposed adaptive twisting control is experimentally verified on a mass–spring–damper system.

LMI‐based criterion for the robust guaranteed cost control of uncertain switched neutral systems with time‐varying mixed delays and nonlinear perturbations by dynamic output feedback

This article reports on an investigation into robust guaranteed cost control (GCC) for uncertain switched neutral systems (USNSs) with interval time‐varying mixed delays and nonlinear perturbations via dynamic output feedback. Delay‐dependent sufficient conditions are suggested to guarantee the robust exponential stability and to obtain robust GCC for USNSs using the average dwell time approach and the piecewise Lyapunov function technique in terms of a set of linear matrix inequalities. The problem of uncertainty in the system model is solved by deploying the Yakubovich lemma. Lastly, two examples (i.e., a numerical example and the water‐quality dynamic model for the Nile River) are given to verify the efficiency of the propounded theories. © 2016 Wiley Periodicals, Inc. Complexity 21: 555–578, 2016

Ultimate boundedness theorems for impulsive stochastic differential systems with Markovian switching

This paper is concerned with ultimate boundedness analysis of impulsive stochastic differential systems (ISDSs) with Markovian switching. Using the generalized Itô formula, Lyapunov function and matrix inequality technique, several criteria for global pth moment exponential ultimate boundedness are derived. The finding shows that unbounded stochastic differential systems with Markovian switching can be made into bounded systems by impulses.

Noise-to-State Stability for a Class of Random Systems With State-Dependent Switching

This note is intended to investigate noise-to-state stability for random nonlinear systems with state-dependent switching. Under some mild and easily verified conditions, the existence of global solution to random switched systems can be proved. Based on a reasonable requirement for the random disturbance, the criteria on noise-to-state stability of random switched systems are presented by the aid of single Lyapunov function technique. The reasonability of the obtained results is illustrated by using a mechanical model in random vibration environment.

On the periodic dynamics of memristor-based neural networks with leakage and time-varying delays

In this paper, the periodic dynamics have been studied for a general kind of memristor-based neural networks with leakage and time-varying delays. Some new sufficient conditions have been derived ensuring that the existence, uniqueness and globally exponential stability of the periodic solution for the neural network by using differential inclusions theory, the topological degree theory in set-valued analysis and Lyapunov function technique and so on. As a special case, we have shown that the existence, uniqueness and global exponential stability of equilibrium point for the autonomous neural networks with leakage delays.

Stability analysis and state feedback control of continuous-time T–S fuzzy systems via anew switched fuzzy Lyapunov function approach

This paper deals with stability analysis and control design problems for continuous-time Takagi–Sugeno (T–S) fuzzy systems. First, a new membership-function-dependent switching law is proposed and a relaxation parameter is introduced into this switching law to guarantee a minimal dwell time between two consecutive switching. Compared to the existing methods, the most important point is that with the help of the dwell time, the discretized Lyapunov function (DLF) technique can be adopted. Then a new stability criterion of the T–S fuzzy system with less conservatism is derived based on a fuzzy discretized Lyapunov function (FDLF). Second, to estimate the domain of attraction (DA), an algorithm with less iteration steps is proposed. Based on the proposed switching method, sufficient conditions for existence of the state feedback controllers are presented via the switched non-parallel distributed compensation (non-PDC) scheme. The effectiveness of the proposed method is illustrated through three simulation examples.

Adaptive Fuzzy Output Constrained Control Design for Multi-Input Multioutput Stochastic Nonstrict-Feedback Nonlinear Systems.

In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Integrated Finite-Time Disturbance Observer and Controller Design for Reusable Launch Vehicle in Reentry Phase

AbstractAn integrated finite-time disturbance observer (FDO) and attitude controller is designed for a reusable launch vehicle (RLV) in this paper. In accordance with the multiple-timescale features, RLV attitude dynamics are divided into an outer-loop subsystem and an inner-loop subsystem. Based on the recently developed sliding mode control (SMC), a novel multivariable supertwisting sliding mode controller driven by a FDO is designed to achieve a fast and accurate reentry attitude tracking. This integrated design can generate a continuous control law which has excellent robustness to uncertainty and disturbances with known bounds while achieving an arbitrarily fast convergence. The finite-time stability of the overall system is proved by using the Lyapunov function technique and the multiple-timescale separation principle. In addition, an optimal control allocation for allocating torque commands into aerodynamic surface deflection commands with constraints is also proposed. Finally, the effectiveness an...

Dissipativity based repetitive control for switched stochastic dynamical systems

This paper addresses the issues of dissipativity analysis and repetitive control synthesis for a class of switched stochastic dynamical systems with time-varying delay. By using the lifting technique, the considered one dimensional model is converted into a continuous-discrete stochastic two dimensional delayed model to describe the control and learning actions of the repetitive controller. By employing stochastic system theory together with Lyapunov function technique, a new set of sufficient conditions in terms of linear matrix inequalities (LMIs) is established such that the switched stochastic system in two dimensional delayed model is mean square asymptotically stable and (Q,S,R)-dissipative. Then, the desired repetitive controller is designed by solving a convex optimization problem established in terms of LMIs. More precisely, repetitive controllers with H∞, passivity and mixed H∞ and passivity performances can be obtained as the special cases for the considered system. Finally, numerical examples are provided to demonstrate the effectiveness and potential of the developed design technique.

Event-triggered [formula omitted] filter design for delayed neural network with quantization

This paper is concerned with H∞ filter design for a class of neural network systems with event-triggered communication scheme and quantization. Firstly, a new event-triggered communication scheme is introduced to determine whether or not the current sampled sensor data should be broadcasted and transmitted to quantizer, which can save the limited communication resource. Secondly, a logarithmic quantizer is used to quantify the sampled data, which can reduce the data transmission rate in the network. Thirdly, considering the influence of the constrained network resource, we investigate the problem of H∞ filter design for a class of event-triggered neural network systems with quantization. By using Lyapunov functional and linear matrix inequality (LMI) techniques, some delay-dependent stability conditions for the existence of the desired filter are obtained. Furthermore, the explicit expression is given for the designed filter parameters in terms of LMIs. Finally, a numerical example is given to show the usefulness of the obtained theoretical results.

Barrier Lyapunov function-based model-free constraint position control for mechanical systems

In this article, a motion constraint control scheme is presented for mechanical systems without a modeling process by introducing a barrier Lyapunov function technique and adaptive estimation laws. The transformed error and filtered error surfaces are defined to constrain the motion tracking error in the prescribed boundary layers. Unknown parameters of mechanical systems are estimated using adaptive laws derived from the Lyapunov function. Then, robust control used the conventional sliding mode control, which give rise to excessive chattering, is changed to finite time-based control to alleviate undesirable chattering in the control action and to ensure finite-time error convergence. Finally, the constraint controller from the barrier Lyapunov function is designed and applied to the constraint of the position tracking error of the mechanical system. Two experimental examples for the XY table and articulated manipulator are shown to evaluate the proposed control scheme.