Non‐Fragile Extended Dissipativity Control Design for Generalized Neural Networks with Interval Time‐Delay Signals

The problem of non‐fragile extended dissipative control design for a class of generalized neural networks (GNNs) with interval time‐delay signals is investigated in this paper. By constructing a suitable Lyapunov‐Krasovskii functional (LKF) with double and triple integral terms, and estimating their derivative by using the Wirtinger single integral inequality (WSII) and Wirtinger double integral inequality (WDII) technique respectively, and that is mixed with the reciprocally convex combination (RCC) approach. A new delay‐dependent non‐fragile extended dissipative control design for GNNs are expressed in terms of the linear matrix inequalities (LMIs). Then, the desired non‐fragile extended dissipative controller can be obtained by solving the linear matrix inequalities (LMIs). Furthermore, a non‐fragile state feedback controller is designed for GNNs such that the closed‐loop system is extended dissiptive. Thus, the non‐fragile extended dissipative controller can be adopted to deal with the non‐fragile performance, non‐fragile performance, non‐fragile passive performance, non‐fragile mixed and passivity performance, and non‐fragile dissipative performance for GNNs by selecting the weighting matrices. Finally, simulation studies are demonstrated for showing the feasibility of the proposed method. Among them, one example was supported by the real‐life application of the quadruple tank process system.     

异构多智能体系统耗散性异步控制器设计

为应对因复杂网络攻击、物理限制等因素导致异构多智能体系统的系统模态与控制器模态异步问题,保证多智能体系统的一致性,提高系统运行安全性,提出了一种基于耗散性能的输出反馈控制器设计方法。针对实际工程中状态不可测得的情况,采用了更具实际意义的输出反馈控制,并设计了一个分布式动态补偿器,结合输出调节技术将异构多智能体系统构建为一个闭环误差系统。采用隐马尔可夫模型,对多智能体系统与控制器的异步现象进行刻画,形成一个双链马尔可夫跳变模型。利用Lyapunov稳定性分析方法给出闭环误差系统的随机稳定与严格(D,E,F)-α耗散性条件,实现了异构多智能体系统的输出一致性。进一步,通过将具有耗散性能的异步控制器增益设计转化为一组线性矩阵不等式的可行解问题,得到了增益设计方法。最后通过一个仿真实例验证了本研究所提出控制算法的有效性。结果表明：与现有结果相比,本研究所设计的基于输出反馈的耗散性异步控制器对各类多智能体系统具有良好的兼容性;同时,还有许多技术难题亟需解决,而随着科技的发展,更加通畅的网络通信方式与灵敏的传感器网络可以作为以后多智能体协同控制领域关键问题突破的参考。     

Exponential quasi‐(Q,S,R)‐dissipativity and practical stability for switched nonlinear systems

In this paper, the problems of exponential quasi‐(Q,S,R)‐dissipativity and practical stability analysis for a switched nonlinear system are addressed. First, the concept of exponential quasi‐(Q,S,R)‐dissipativity for switched nonlinear systems without requiring the exponential quasi‐(Q,S,R)‐dissipativity property of each subsystem is proposed. Then, we show that an exponentially quasi‐(Q,S,R)‐dissipative switched nonlinear system is practically stable. Second, this exponential quasi‐(Q,S,R)‐ dissipativity property for a switched nonlinear system is obtained by the design of a state‐dependent switching law. Third, a composite state‐dependent switching law is designed to render the feedback interconnection of switched nonlinear systems exponentially quasi‐(Q,S,R)‐dissipative. This switching law allows interconnected switched nonlinear systems to switch asynchronously. Finally, the effectiveness of the results is verified by a numerical example.     

Robust dissipativity of discrete systems and its investigation with the help of a sequence of sets of Lyapunov functions

A generalized concept of robust dissipativity is introduced and theorems on the analysis of this property are formulated and proved with the help of the Lyapunov functions method. It is proposed to use a specially constructed sequence of sets of Lyapunov functions that can allow one to improve the initial estimate of the boundary set of a dissipative system up to the establishment of the asymptotic robust stability property in the limiting case. An example of investigating the dissipativity of a linear discrete system with unknown parameters under additive perturbation is given. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 13–23, March–April 2008.     

经济性预测控制的切换控制策略优化算法设计

针对经济性预测控制优化问题,设计了切换控制策略的优化算法。首先,离线计算具有耗散性的Hessian矩阵指标;其次,在线优化阶段,根据系统状态所处的不同可行域,分别在经济指标优化和Hessian矩阵对应的动态指标优化之间进行切换,从而驱动系统状态收敛到稳态工作点,取得了较优的经济性能;最后,仿真结果验证了方法的有效性。     

切换非线性系统全局优化运行的经济预测控制

切换非线性系统在不同模式间平稳切换和经济切换是全局优化运行的主要需求.针对不同模式有限时域下控制算法可行域未必存在交集的系统,提出了对应的经济预测控制算法（Economic model predictive control,EMPC）及切换策略.切换发生时,该方法在实时优化层求解和更新可行中间点,并构造基于耗散的局部EMPC辅助性能指标,在考虑中间点稳定性问题上使其尽可能逼近原经济性能.在先进控制层,利用局部EMPC将状态逐次稳定至中间点,同时利用中间点问题得到的最优轨迹保证模式间的经济切换.最后,分析了切换过程的暂态经济性.该方法实际可操作性强,仿真结果说明了方法的有效性.     

区间线性脉冲系统的鲁棒耗散性及其反馈镇定

主要讨论了区间线性脉冲系统相对于二次供给率的鲁棒耗散性问题, 得到了该系统是鲁棒耗散的充分条件, 而且还给出了这样的鲁棒耗散系统能被一个状态反馈控制律所镇定的条件, 最后, 给出了一个例子.     

Stochastic stability and extended dissipativity analysis for uncertain neutral systems with semi‐Markovian jumping parameters via novel free matrix–based integral inequality

This paper investigates the issues of stochastic stability and extended dissipativity analysis for uncertain neutral systems with semi‐Markovian jumping parameters. A new criterion about the stochastic stability and extended dissipativity of uncertain neutral systems with semi‐Markovian jumping parameters is obtained based on the new Lyapunov‐Krasovskii functionals together with the introduced novel free matrix–based integral inequality. The major contribution of this study is that the stochastic stability and extended dissipativity concept for uncertain neutral systems with semi‐Markovian jumping parameters can be developed to simultaneously analyze the solutions of the L₂ ? L_∞ performance, H_∞ action, passivity behavior, and dissipativity by selecting different weighting matrices. Finally, several interesting numerical examples are provided to show the effectiveness and less conservatism of the proposed method.     

A dissipative dynamical systems approach to stability analysis of time delay systems

In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite‐dimensional linear dynamical system and an infinite‐dimensional time delay operator, we show that the time delay operator is dissipative with respect to a quadratic supply rate and with a storage functional involving an integral term identical to the integral term appearing in standard Lyapunov–Krasovskii functionals. Finally, using stability of feedback interconnection results for dissipative systems, we develop sufficient conditions for asymptotic stability of time delay dynamical systems. The overall approach provides a dissipativity theoretic interpretation of Lyapunov–Krasovskii functionals for asymptotically stable dynamical systems with arbitrary time delay. Copyright © 2004 John Wiley & Sons, Ltd.     

Dissipativity analysis of neural networks with time-varying delays

A new definition of dissipativity for neural networks is presented in this paper. By constructing proper Lyapunov functionals and using some analytic techniques, sufficient conditions are given to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties and the integro-differential neural networks in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the obtained results.