Control For Discrete-time Fuzzy Systems Research Articles

Constrained Output-Feedback Control for Discrete-Time Fuzzy Systems With Local Nonlinear Models Subject to State and Input Constraints.

This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.

Integrated event-triggered fault estimation and fault-tolerant control for discrete-time fuzzy systems with input quantization and incomplete measurements

This paper addresses the problem of robust integrated fault estimation (FE) and fault-tolerant control (FTC) for a class of discrete-time networked Takagi–Sugeno (T–S) fuzzy systems with two-channel event-triggered schemes, input quantization and incomplete measurements. The incomplete information under consideration includes randomly occurring sensor saturation and randomly occurring quantization. In order to save the limited networked resources, this paper firstly proposed a novel dynamic event-triggered scheme on the sensor side and a static one on the controller side. Secondly, an event-triggered FE observer for the T–S fuzzy model is designed to estimate actuator faults and system states, simultaneously. Then, a specified discrete sliding surface in the state-estimation space is constructed. By using time-delay analysis technique and considering the effects of event-triggered scheme, quantization, networked conditions, actuator fault and external disturbance, the sliding mode dynamics and error dynamics are unified into a new networked time-delay model. Based on this model, sufficient conditions are established such that the resulting augmented fuzzy system is stochastically stable with a prescribed H∞ performance level with a single-step linear matrix inequality (LMI) formulation. Furthermore, an observer-based sliding mode controller for reaching motion is synthesized to guarantee the reachability of the sliding surface. Finally, a single-link flexible manipulator example is present to illustrate the effectiveness of the proposed method.

Improved results on observer-based control for discrete-time fuzzy systems

ABSTRACTThis paper is concerned with the design problem of observer-based H∞ control for discrete-time Takagi−Sugeno (T−S) fuzzy systems. New sufficient conditions guaranteeing the H∞ performance of the T−S fuzzy systems are derived. With the aid of some special derivations, bilinear matrix inequalities are converted into a set of linear matrix inequalities which can be solved using a single-step resolution procedure. In comparison with the existing literature results, the proposed approach may provide more relaxed conditions while ensuring better H∞ performance. Finally, both numerical and practical examples are given to verify the effectiveness of the proposed approach.

Reliable observer-based H∞ control for discrete-time fuzzy systems with time-varying delays and stochastic actuator faults via scaled small gain theorem

Abstract This paper is concerned with the reliable observer-based H ∞ control problem for discrete-time Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and stochastic actuator faults based on input–output approach. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. First, the discrete-time T–S fuzzy system is transformed into the form of interconnection of two subsystems by employing a new model transformation for the delayed state variables. Furthermore, a sufficient condition on discrete-time T–S fuzzy systems with time-varying delay and actuator faults, which guarantees the corresponding closed-loop system to be stochastically stable and preserves a guaranteed H ∞ performance, is derived by employing the scaled small gain theorem. Meanwhile, the solvability condition for the reliable observer-based H ∞ control is also established, by which the reliable H ∞ fuzzy controller can be solved as linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.

Robust H ∞ networked control for discrete-time fuzzy systems with state quantisation

The problem of robust H ∞ control for uncertain discrete-time Takagi and Sugeno (T-S) fuzzy networked control systems (NCSs) with state quantisation is investigated. A new model of network-based control with simultaneous consideration of network-induced delays and packet dropouts is proposed. By using a fuzzy Lyapunov–Krasovskii functional (LKF), we derive a less conservative delay-dependent stability condition for the closed-loop NCSs. Robust H ∞ fuzzy controller is developed for the asymptotical stabilisation of the NCSs. Since it is not expressed as strict LMI conditions, the cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. A numerical example shows the feasibility applications of the proposed technique.

A new approach to non-fragile H ∞ observer-based control for discrete-time fuzzy systems

In this article, a new approach regarding H ∞ and non-fragile stability analysis and observer-based controller synthesis problem for a class of discrete-time fuzzy systems is investigated. The multiplicative gain variations under consideration are contained in both the controller gain and observer gain. By defining a basis-dependent Lyapunov function and introducing some additional matrix variables, new sufficient conditions are derived to guarantee the stability of the non-fragile H ∞ observer-based control system. Seeking computational convenience, the developed results are cast in the format of linear matrix inequalities and two numerical examples are presented to illustrate the feasibility of theoretical developments.

Stabilization for discrete-time fuzzy systems with Takagi-Sugeno’s models: reduce the complexity

The problem of sate feedback control for discrete-time fuzzy systems with Takagi-Sugeno’s models is investigated to reduce the computational burden. A stabilization condition is obtained by applying a new Lyapunov function. It is shown that our new theorem is equivalent to an existing result in guaranteeing the stability of the fuzzy system but consumes less computational time than the latter. The effectiveness and the superiority of the proposed design approach are demonstrated by an example borrowed from the literature.

H/sub /spl infin// output feedback control of discrete-time fuzzy systems with application to chaos control

This paper presents an observer based H/sub /spl infin// output feedback synthesis method for discrete time fuzzy dynamic systems based on a piecewise Lyapunov function. The basic idea of the approach is to design an observer based piecewise linear output feedback control law to guarantee the global stability with H/sub /spl infin// performance of the resulting closed-loop fuzzy control systems. It is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible with commercially available software. Application to control chaotic systems is given to illustrate the effectiveness and advantages of the proposed method.

Improved [formula omitted] control of discrete-time fuzzy systems: a cone complementarity linearization approach

In this paper, new results are presented for H ∞ analysis and synthesis problems of discrete-time Takagi–Sugeno (TS) fuzzy systems. By defining a multiple Lyapunov function, a new sufficient condition guaranteeing the H ∞ performance of the TS fuzzy systems is first derived, which is expressed by a set of linear matrix inequalities (LMIs). Both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework. Based on this new condition for H ∞ performance, the corresponding H ∞ controller design problem is then investigated. Different from the traditional quadratic framework, the synthesis problem is solved by exploiting the cone complementarity linearization (CCL) method, together with a sequential minimization problem subject to LMI constraints obtained for the existence of admissible controllers, which can be readily solved by using standard numerical software.

Robust H∞ control for discrete-time fuzzy systems via basis-dependent Lyapunov functions

This paper deals with the robust H ∞ control problem for a class of discrete-time fuzzy systems with uncertainty. The uncertainty is assumed to be of structured linear fractional form. By using basis-dependent Lyapunov function, an H ∞ control design approach is developed. The control design approach is facilitated by introducing some additional instrumental matrix variables. These additional matrix variables decouple the Lyapunov and the system matrices, which makes the control design feasible. The proposed approach leads to some sufficient results in the form of strict linear matrix inequalities (LMIs). It is expected that the basis-dependent results are less conservative than the basis-independent ones due to the introduction of basis-dependent Lyapunov function. Finally, numerical examples including the discrete chaotic Lorenz system are also given to demonstrate the applicability of the proposed approach.

H∞ control for discrete-time Takagi-Sugeno fuzzy systems

We consider the design problem of H X controllers for discrete-time fuzzy systems. We introduce two Riccati inequalities from the standard H X theory, one for the state feedback controller, the other for the filter gain. We rewrite the second inequality and obtain an equivalent inequality for the inverse. We then rewrite this using LMI to obtain the final form of the inequality and show that the proposed output feedback controller is n -suboptimal. We give two examples and construct n -suboptimal controllers for them.