Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Finite-time passivity for neutral-type neural networks with time-varying delays – via auxiliary function-based integral inequalities

In this paper, we investigated the problem of the finite-time boundedness and finitetime passivity for neural networks with time-varying delays. A triple, quadrable and five integral terms with the delay information are introduced in the new Lyapunov–Krasovskii functional (LKF). Based on the auxiliary integral inequality, Writinger integral inequality and Jensen’s inequality, several sufficient conditions are derived. Finally, numerical examples are provided to verify the effectiveness of the proposed criterion. There results are compared with the existing results.&nbsp

Finite-Time Boundedness of Markov Jump System with Piecewise-Constant Transition Probabilities via Dynamic Output Feedback Control

This paper first investigates the problem of finite-time boundedness of Markovian jump system with piecewise-constant transition probabilities via dynamic output feedback control, which leads to both stochastic jumps and deterministic switches. Based on stochastic Lyapunov functional, the concept of finite-time boundedness, average dwell time, and the coupling relationship among time delays, several sufficient conditions are established for finite-time boundedness and H∞ filtering finite-time boundedness. The system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method

Finite-Time Stability Analysis of Switched Genetic Regulatory Networks

This paper investigates the finite-time stability problem of switching genetic regulatory networks (GRNs) with interval time-varying delays and unbounded continuous distributed delays. Based on the piecewise Lyapunov-Krasovskii functional and the average dwell time method, some new finite-time stability criteria are obtained in the form of linear matrix inequalities (LMIs), which are easy to be confirmed by the Matlab toolbox. The finite-time stability is taken into account in switching genetic regulatory networks for the first time and the average dwell time of the switching signal is obtained. Two numerical examples are presented to illustrate the effectiveness of our results

Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results

Optimal adaptive control of time-delay dynamical systems with known and uncertain dynamics

Delays are found in many industrial pneumatic and hydraulic systems, and as a result, the performance of the overall closed-loop system deteriorates unless they are explicitly accounted. It is also possible that the dynamics of such systems are uncertain. On the other hand, optimal control of time-delay systems in the presence of known and uncertain dynamics by using state and output feedback is of paramount importance. Therefore, in this research, a suite of novel optimal adaptive control (OAC) techniques are undertaken for linear and nonlinear continuous time-delay systems in the presence of uncertain system dynamics using state and/or output feedback. First, the optimal regulation of linear continuous-time systems with state and input delays by utilizing a quadratic cost function over infinite horizon is addressed using state and output feedback. Next, the optimal adaptive regulation is extended to uncertain linear continuous-time systems under a mild assumption that the bounds on system matrices are known. Subsequently, the event-triggered optimal adaptive regulation of partially unknown linear continuous time systems with state-delay is addressed by using integral reinforcement learning (IRL). It is demonstrated that the optimal control policy renders asymptotic stability of the closed-loop system provided the linear time-delayed system is controllable and observable. The proposed event-triggered approach relaxed the need for continuous availability of state vector and proven to be zeno-free. Finally, the OAC using IRL neural network based control of uncertain nonlinear time-delay systems with input and state delays is investigated. An identifier is proposed for nonlinear time-delay systems to approximate the system dynamics and relax the need for the control coefficient matrix in generating the control policy. Lyapunov analysis is utilized to design the optimal adaptive controller, derive parameter/weight tuning law and verify stability of the closed-loop system”--Abstract, page iv

Stabilization of switched neural networks with time-varying delay via bumpless transfer control

This paper investigates the stabilization of switched neural networks with time-varying delay. In order to overcome the drawback that the classical switching state feedback controller may generate the bumps at switching time, a new switching feedback controller which can smooth effectively the bumps is proposed. According to mode-dependent average dwell time, new exponential stabilization results are deduced for switched neural networks under the proposed feedback controller. Based on a simple corollary, the procedures which are used to calculate the feedback control gain matrices are also obtained. Two simple numerical examples are employed to demonstrate the effectiveness of the proposed results.Peer reviewe