H∞ tracking control for nonlinear multivariable systems using wavelet-type TSK fuzzy brain emotional learning with particle swarm optimization

This paper studies the ${\mathit{H}}_{\infty }$ tracking control for uncertain nonlinear multivariable systems. We propose a control strategy, which combines the adaptive wavelet-type Takagi-Sugeno-Kang (TSK) fuzzy brain emotional learning controller (WTFBELC) and the $H_{\infty }$ robust tracking compensator. As for the adaptive WTFBELC, it is a main controller designed to mimic the ideal controller. The proposed WTFBELC is to obtain much better ability of handling nonlinearities and uncertainties, but the proposed $H_{\infty }$ robust tracking compensator is to compensate the residual error between the adaptive WTFBELC and the ideal controller. Furthermore, the optimal learning rates of the adaptive WTFBELC are searched quickly by using the particle swarm optimization (PSO) algorithm, and the parameter updated laws are derived based on the steepest descent gradient method. The robust tracking performance of this novel control scheme is guaranteed based on Lyapunov stability theory. The mass-spring-damper mechanical system and the three-link robot manipulator, are used to verify the effectiveness of the proposed adaptive PSO-WTFBELC $H_{\infty }$ control scheme.     

Event-triggered H∞ control for network-based uncertain Markov jump systems under DoS attacks

This paper investigates the event-triggered $H_{\infty }$ control problem for network-based Markov jump systems subject to denial-of-service (DoS) attacks. In order to reduce the amount of signal transmission, the event-triggering scheme (ETS) is adopted between sensor and controller. Due to DoS attacks invalidating data over networks, a new switched time-delay Markov jump model with unstable subsystems is developed based on state feedback controller. Then with the help of piecewise Lyapunov-Krasovskii functional method, a set of sufficient conditions incorporating constraints of DoS attacks are provided, which guarantees that the resulting switched time-delay Markov jump system is stochastically stable with a certain $H_{\infty }$ performance. Subsequently, we present criterions to obtain the parameters of state feedback gain and ETS. Finally, an example is provided to show the effectiveness of the proposed method.     

Mean square consensus of double-integrator multi-agent systems under intermittent control: A stochastic time scale approach

We consider the leader–follower consensus problem for a multi-agent system where information is exchanged only on a non-uniform discrete stochastic time domain. For a second-order multi-agent system subject to intermittent information exchange, we model the tracking error dynamics as a $\mu ?$varying linear system on a discrete stochastic time scale, where μ is the graininess operator. Based on a Lyapunov operator and a positive perturbation operator on the space of symmetric matrices, we derive necessary and sufficient conditions to design a decentralized consensus protocol. This protocol allows us to cast the mean-square exponential consensus problem within the framework of dynamic equations on stochastic time scales. We establish some theoretical results which allow for the computation of the control gain matrix which guarantees the mean-square exponential stability with a given decay rate for the error dynamics. To show the effectiveness of the theoretical results, some simulation and experimental results on multi-robot systems have been performed.     

Feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon

This paper deals with the feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon. The optimal control problem of the follower is first studied. Employing the discrete-time linear quadratic (LQ) mean-field stochastic optimal control theory, the sufficient conditions for the solvability of the optimization of the follower are presented and the optimal control is obtained based on the stabilizing solutions of two coupled generalized algebraic Riccati equations (GAREs). Then, the optimization of the leader is transformed into a constrained optimal control problem. Applying the Karush-Kuhn-Tucker (KKT) conditions, the necessary conditions for the existence and uniqueness of the Stackelberg strategies are derived and the Stackelberg strategies are expressed as linear feedback forms involving the state and its mean based on the solutions $(K_i,{\widehat{K}}_i),$ $i=1,2$ of a set of cross-coupled stochastic algebraic equations (CSAEs). An iterative algorithm is put forward to calculate efficiently the solutions of the CSAEs. Finally, an example is solved to show the effectiveness of the proposed algorithm.