This paper investigates the problem of adaptive H∞ sliding mode control (SMC) for a class of nonlinear systems via Takagi-Sugeno (T-S) fuzzy model approach. The input matrices and output matrices in all local linear systems are different. A novel observer is designed to estimate the unmeasured states. Based on such an observer, the control input is only appeared in the T-S fuzzy singular system and error system. A new integral sliding surface is put forward to match the characteristic of T-S fuzzy singular system with different input and output matrices. Based on the new integral sliding surface, a new adaptive SMC scheme is designed to guarantee the admissibility of the T-S fuzzy singular system with H∞ performance and the reachability of the T-S fuzzy integral sliding surface. A simulation result is presented to illustrate the effectiveness and feasibility of the developed observer-based SMC design method.

This paper is concerned with the sliding mode control of nonlinear singular systems in terms of the interval type-2 (IT2) fuzzy model. To better approximate the nonlinear systems, the modeling errors are considered in the IT2 fuzzy model. The uncertainties in membership functions are expressed based on their boundedness. Admissibility conditions are obtained via a linear matrix inequalities approach. A new reaching law-based sliding controller is presented by choosing a typical sliding surface to analyze the sliding motion, such that all of the input gains are allowed to be different and the chattering of the system can be minimized with a guaranteed H∞ performance. The feasibility of the proposed control method is verified by simulation results.

The distributed optimization problem (DOP) of Takagi–Sugeno (T–S) fuzzy cyber–physical systems is studied under the framework of weight-balanced graphs and quasistrongly connected characteristics. The objective is to drive the outputs of all agents to the optimal solution of a given global objective function regarded as the desired output, based on the partial information of the local objective functions. To this end, distributed optimal coordinators (DOCs) are used to generate optimal solutions of local objective functions that converge to the desired output, and fuzzy reference-tracking controllers are designed to ensure that all agents can track the optimal solutions. As novel technical results, two Lyapunov-based fuzzy input-to-state stability (ISS) small-gain theorems are proposed for the T–S fuzzy interconnected system. Thus, the overall closed-loop system is an interconnected system involving the modules of optimal coordinators and fuzzy tracking controllers with T–S fuzzy subsystems. The fuzzy ISS cyclic-small-gain theorem is applied to analyze the system stability. The DOP of T–S fuzzy cyber–physical systems is solved using the DOCs and fuzzy reference-tracking controllers through the fuzzy small-gain approach. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed method.

This article is focused on security analysis and control problems of cyber–physical systems (CPSs) under Denial-of-Service (DoS) attacks, which jam the controller-actuator channel. Considering the limited attack energy of malicious adversaries, DoS attacks are described by a periodic model. Different from existing results, both the security analysis and secure controller design problems are addressed based on the characteristics of DoS attack model rather than utilizing the switching system theory to solve the aforementioned problems. First, sufficient conditions are derived to ensure that the resultant closed-loop CPS under DoS attacks can preserve the exponential stability, and the critical value of the attack period is derived, below which the stability is deteriorated. Second, the relation between our proposed conditions and reinforcement learning-based control is established, based on which the security of reinforcement learning-based control can be evaluated effectively. Finally, both DoS attacks and external disturbances are considered in a unified framework, and sufficient conditions are proposed to evaluate the security of the closed-loop CPSs and design a secure controller. Finally, a mobile robot is adopted to validate the efficacy of the proposed methods.

This article investigates stochastic stability of positive singular Markovian jump systems (PSMJSs) with mode-dependent derivative-term coefficient. Different from the existing results, the condition on stochastic stability of PSMJSs associated with state jumps behavior at switching instants is given by means of linear co-positive Lyapunuov function. On the basis of it, the conditions on stochastic stability under the cases of partially known transition rates and uncertain transition rates have been presented, respectively. All obtained conditions can be solved by linear programming (LP) technique. Finally, an example is introduced to illustrate the effectiveness and the merits of the results proposed in this article.