H∞ filtering of discrete-time switched singular systems with time-varying delays

In this article, the analysis and design problems of H_∞ filtering for a class of discrete-time switched singular systems with time-varying delay under an arbitrary switching signal are investigated. The main attention is focused on the design of a linear mode-dependent filter guaranteeing the regularity, causality, and asymptotic stability of the resulting filtering error system with a prescribed H_∞ performance bound. By using a multiple Lyapunov-Krasovskii functional, and utilizing the linearization technique, novel sufficient conditions for the solvability of H_∞ problem are derived in terms of linear matrix inequalities. Solving that, the desired filter gains can be determined. Any model transformation of system, which often leads the large computational burden is involved. The free weighting matrix technique is introduced to provide additional degree of freedom, which improves the conservativeness of the developed method. Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed approach and to compare the obtained results with some previous works in the literature.     

Suboptimal control for nonlinear slow-fast coupled systems using reinforcement learning and Takagi–Sugeno fuzzy methods

In this article, by using singular perturbation theory, reinforcement learning (RL), and Takagi–Sugeno (T-S) fuzzy methods, a RL-fuzzy-based composite suboptimal control method is proposed for nonlinear slow-fast coupled systems (SFCSs) with unknown slow dynamics. First, the SFCSs is decomposed into slow and fast subsystems and the original optimal control problem is reduced to two subproblems. Then, for the slow subsystem, a nonlinear coordinate transformation is introduced to transform the nonquadratic slow utility function into the quadratic form. Unmeasurable virtual slow subsystem state is reconstructed by the state measurements of original system and slow controller design algorithm is proposed in the framework of RL by utilizing the actor-critic neural networks to approximate the controller and cost function. For the fast subsystem, T-S fuzzy model is established and state measurements of the original system are exploited to reconstruct the unmeasurable fast subsystem state. Fast controller is designed with the approach of parallel distributed compensation. The obtained slow and fast controllers form the composite suboptimal controller for the original SFCSs. Considering the state reconstruction error, convergence of the slow controller design algorithm, suboptimality of the composite controller, and stability of the closed-loop SFCSs are analyzed. Finally, the effectiveness of our proposed method is illustrated by examples.     

Robust fault estimation and fault-tolerant tracking control for uncertain Takagi–Sugeno fuzzy systems: Application to single link manipulator

This article concerns the estimation and tracking control problems for Takagi–Sugeno systems with disturbances and norm bounded uncertainties in presence of sensor and actuator faults (SAF). First, we propose a robust fuzzy observer (RFO) design method to estimate both state and SAF for the considered class of the nonlinear systems. Then, this RFO-based fault tolerant tracking control is developed not only to compensate the SAF effects but also to ensure the state convergence to desired trajectories in spite of their presence. To reduce the conservatism of design conditions, observer and controller gains are calculated in a single step by solving a set of linear matrix inequality constraints. H_∞ criterion is used to attenuate disturbance effects and to reduce the tracking error. Finally, simulation results by considering two types of actuator fault and comparative study on a single link flexible joint manipulator are provided to underline the performances of the mentioned process.     

H∞ filtering of discrete-time interconnected systems with failed interconnections

The H_∞ filtering problem for interconnected systems is addressed in this paper. In order to facilitate the stability analysis of interconnected systems under the conditions of failed interconnections, a strategy related to switched systems is introduced. Assume that the interconnections among these subsystems disconnect based on the mode-dependent average dwell time (MDADT), a switching signal is implemented to denote the failed interconnections cases. In the aid of the MDADT method, a filter is designed such that the fault detection (FD) system is asymptotically stable and satisfies the weighted H_∞ performance. Finally, a numerical simulation is provided to show the effectiveness of the proposed filter.     

Robust l2−l∞ dynamic output feedback control design for uncertain discrete-time switched systems with random time-varying delay

This article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time-varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed-loop switching system with an l₂−l_∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay-dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l₂−l_∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique.