Yuanqing Xia

Robust Adaptive Sliding-Mode Control for Fuzzy Systems With Mismatched Uncertainties

This paper is devoted to design adaptive sliding-mode controllers for the Takagi-Sugeno (T--S) fuzzy system with mismatched uncertainties and exogenous disturbances. The uncertainties in state matrices are mismatched and norm-bounded, while the exogenous disturbances are assumed to be bounded with an unknown bound, which is estimated by a simple and effective adaptive approach. Both state- and static-output-feedback sliding-mode-control problems are considered. In terms of linear-matrix inequalities (LMIs), both sliding surfaces and sliding-mode controllers can be easily obtained via a convex optimization technique. Finally, two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper.

Brief paper: Control for discrete singular hybrid systems

The problems of stability, state feedback control and static output feedback control for a class of discrete-time singular hybrid systems are investigated in this paper. A new sufficient and necessary condition for a class of discrete-time singular hybrid systems to be regular, causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict LMIs, respectively. Finally, two illustrative examples are provided to demonstrate the applicability of the proposed approach.

Technical communique: New bounded real lemma for discrete-time singular systems

In this paper, the problem of bounded real lemma for discrete-time singular system with strict matrix inequalities is investigated. It is proved that the bounded real lemma for discrete singular system can be described by a strict matrix inequality. The results lead to more tractable and reliable computation when applying them to design control systems.

Observer-based sliding mode control for a class of discrete systems via delta operator approach

In this paper, an observer-based sliding mode control (SMC) problem is investigated for a class of uncertain delta operator systems with nonlinear exogenous disturbance. A novel robust stability condition is obtained for a sliding mode dynamics by using Lyapunov theory in delta domain. Based on a designed sliding mode observer, a sliding mode controller is synthesized by employing SMC theory combined with reaching law technique. The robust asymptotical stability problem is also discussed for the closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the developed method.

Sliding mode attitude tracking of rigid spacecraft with disturbances

Abstract The attitude tracking control problem of a spacecraft nonlinear model with external disturbances and inertia uncertainties is addressed in this paper. First, a new sliding mode controller is designed to ensure the asymptotic convergence of the attitude and angular velocity tracking errors against external disturbances and inertia uncertainties by using a modified differentiator to estimate the total disturbances. Second, an adaptive algorithm is applied to compensating the disturbances, by which another sliding mode controller is successfully designed to achieve a high performance on the attitude tracking in the presence of the inertia uncertainties, external disturbances and actuator saturations. Finally, simulation results are presented to illustrate effectiveness of the control strategies.

Design of Static Output Feedback Sliding Mode Control for Uncertain Linear Systems

This paper considers the problem of designing a sliding mode controller via static output feedback for a class of uncertain systems with mismatched uncertainty in the state matrix. First, we derive a new existence condition of linear sliding surface in terms of strict linear matrix inequalities (LMIs) and propose an adaptive reaching control law such that the motion of the closed-loop system satisfies the reaching condition. Second, we further consider the delay-type switching function, and a new robust stability condition is given in terms of LMIs for the reduced-order sliding mode dynamics. Then, a synthesis procedure is established to design the sliding surface parameters. Finally, three examples, including an aircraft model, are utilized to illustrate the design procedures proposed in this paper.

Robust Sliding-Mode Control for Uncertain Time-Delay Systems Based on Delta Operator

This paper is devoted to robust sliding-mode control for time-delay systems with mismatched parametric uncertainties. Based on a delta-operator approach, a delay-dependent sufficient condition for the existence of linear sliding surfaces is given, and a reaching motion controller is also developed. The results obtained in this paper can unify some previous related results of the continuous and discrete systems into the delta-operator systems framework. The feasibility and effectiveness of the developed method are illustrated by an example.

Adaptive Fuzzy Control for Multilateral Cooperative Teleoperation of Multiple Robotic Manipulators Under Random Network-Induced Delays

In this paper, an adaptive fuzzy control is investigated for multilateral teleoperation of two cooperating robotic manipulators that manipulate an object with constrained trajectory/force in the presence of dynamics uncertainties and random network-induced delays. First, the interconnected dynamics that consist of two master robots and cooperating slave robots are formulated. To consider multiple stochastic delays in communication channels, Markov processes are used to model these random network-induced delays. The interconnected dynamics of the teleoperation are divided into a local master/slave position/force subsystem and a stochastic-delayed motion synchronization subsystem. Then, an adaptive fuzzy control strategy, which is based on linear matrix inequalities (LMIs) that combine adaptive update techniques, is proposed to suppress the dynamics uncertainties, the external disturbances, and the multiple stochastic delays in communication channels. The control approach ensures that the defined synchronization errors converge to zero. The stochastic stability in mean square of the closed-loop system is proved using LMIs based on Lyapunov-Krasovskii functional synthesis. The proposed controls are validated using extensive simulation studies.

New stability and stabilization conditions for systems with time-delay

In this article, the problems of stability and stabilization for systems with both constant and time-varying delays have been considered. By the so-called lifting method, time-delay systems are transformed into delay-free systems such that simple necessary and sufficient conditions have been developed for the stability analysis of systems with constant delays. For systems with time-varying delays, they have been converted to a switched system so that the existing results can be applied to analyze the problems of stability and stabilization. Linear matrix inequality (LMI) approach has been employed to the state feedback control design. Numerical examples are given to show the effectiveness of the proposed technique.

New Results on

This paper is concerned with the H infin fuzzy filtering problem for a class of continuous-time fuzzy systems with time-varying delays. The objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed H infin performance of the filtering error system. Motivated by the parallel distributed compensation technique, we design a new filter model in this paper. Filter parameter matrices can be obtained from the solution of a convex optimization problem in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H infin fuzzy filter is given. Two numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed design approach.