LMI relaxed stability conditions for fuzzy-model-based control systems

Author name used in this publication: F. H. F. LeungCentre for Multimedia Signal Processing, Department of Electronic and Information EngineeringRefereed conference paper2006-2007 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples. © 2011 The Author(s).published_or_final_versionSpringer Open Choice, 28 May 201

Sampled-data fuzzy controller for continuous nonlinear systems

The sampled-data fuzzy control of nonlinear systems is presented. The consequents of the fuzzy controller rules are linear sampled-data sub-controllers. As a result, the fuzzy controller is a weighted sum of some linear sampled-data sub-controllers that can be implemented by a microcontroller or a digital computer to lower the implementation cost. Consequently, a hybrid fuzzy controller consisting of continuous-time grades of memberships and discrete-time sub-controller is obtained. The system stability of the fuzzy control system is investigated on the basis of Lyapunov-based approach. The sampling activity introduces discontinuity to complicate the system dynamics and make the stability analysis difficult. The proposed fuzzy controller exhibits a favourable property to alleviate the conservativeness of the stability analysis. Furthermore, linear matrix inequality-based performance conditions are derived to guarantee the system performance of the fuzzy control system. An application example is given to illustrate the merits of the proposed approac

Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Synchronization of chaotic systems using time-delayed fuzzy state-feedback controller

This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, T-S fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. A simulation example is presented to illustrate the merits of the proposed approach

Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults

The goal of this paper is to describe a novel fault tolerant tracking control (FTTC) strategy based on robust fault estimation and compensation of simultaneous actuator and sensor faults. Within the framework of fault tolerant control (FTC) the challenge is to develop an FTTC design strategy for nonlinear systems to tolerate simultaneous actuator and sensor faults that have bounded first time derivatives. The main contribution of this paper is the proposal of a new architecture based on a combination of actuator and sensor Takagi-Sugeno (T-S) proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators together with a T-S dynamic output feedback control (TSDOFC) capable of time-varying reference tracking. Within this architecture the design freedom for each of the T-S estimators and the control system are available separately with an important consequence on robust L₂ norm fault estimation and robust L₂ norm closed-loop tracking performance. The FTTC strategy is illustrated using a nonlinear inverted pendulum example with time-varying tracking of a moving linear position reference. Keyword

Robust Multi-Criteria Optimal Fuzzy Control of Discrete-Time Nonlinear Systems

This paper presents a novel fuzzy control design of discrete-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with an inherent stability property together with a dissipativity type of disturbance reduction. The Takagi–Sugeno-type fuzzy model is used in our control system design. By solving a linear matrix inequality at each time step, the optimal control solution can be found to satisfy mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system on a cart

Integrated fault estimation and accommodation design for discrete-time Takagi-Sugeno fuzzy systems with actuator faults

This paper addresses the problem of integrated robust fault estimation (FE) and accommodation for discrete-time Takagi–Sugeno (T–S) fuzzy systems. First, a multiconstrained reduced-order FE observer (RFEO) is proposed to achieve FE for discrete-time T–S fuzzy models with actuator faults. Based on the RFEO, a new fault estimator is constructed. Then, using the information of online FE, a new approach for fault accommodation based on fuzzy-dynamic output feedback is designed to compensate for the effect of faults by stabilizing the closed-loop systems. Moreover, the RFEO and the dynamic output feedback fault-tolerant controller are designed separately, such that their design parameters can be calculated readily. Simulation results are presented to illustrate our contributions