Relaxed stability analysis for fuzzy-model-based observer-control systems

• Main Author: Liu, Chuang
• Other Authors: Lam, Hak-Keung ; Althoefer, Kaspar Alexander
• Published: King's College London (University of London) 2016
• Subjects: 629.8
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.700815

Fuzzy-model-based (FMB) control scheme is an efficient approach to conduct stability analysis for nonlinear systems. Both Takagi-Sugeno (T-S) FMB and polynomial fuzzy-model-based (PFMB) control systems have been widely investigated. In this thesis, the stability analysis of FMB control systems is conducted via Lyapunov stability theory. The main contribution of the thesis is improving the applicability of T-S FMB and PFMB control strategies by relaxing stability conditions and designing fuzzy observer-controller, which is presented in the following three parts: 1) The stability conditions of FMB control systems are relaxed such that the FMB control strategy can be applied to a wider range of nonlinear systems. For T-S FMB control systems, higher order derivatives of Lyapunov function (HODLF) are employed, which generalizes the commonly used first order derivative. For PFMB control systems, Taylor series membership functions (TSMF) are brought into stability conditions such that the relation between membership grades and system states is expressed. 2) Two types of T-S fuzzy observer-controller are designed such that the T-S FMB control strategy can be applied to systems with unmeasurable states. For the first type, the T-S fuzzy observer with unmeasurable premise variables is designed to estimate the system states and then the estimated states are employed for state-feedback control of nonlinear systems. Convex stability conditions are obtained through matrix decoupling technique. For the second type, the T-S fuzzy functional observer is designed to directly estimate the control input instead of the system states, which can reduce the order of the observer. A new form of fuzzy functional observer is proposed to facilitate the stability analysis such that the observer gains can be numerically obtained and the stability can be guaranteed simultaneously. 3) The polynomial fuzzy observer-controller with unmeasurable premise variables is designed for systems with unmeasurable states. Although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the FMB control strategy, it leads to non-convex stability conditions. Therefore, two methods are applied to derive convex stability conditions: refined completing square approach and matrix decoupling technique. Additionally, the designed polynomial fuzzy observer-controller is extended for systems where only sampled-output measurements are available. Furthermore, the membership functions of the designed polynomial observer-controller are optimized by the improved gradient descent method. Simulation examples are provided to demonstrate and verify the theoretical analysis.