Lyapunov-function-based design of fuzzy logic controllers and its application on combining controllers

Abstract

Abstract-This paper presents the design of fuzzy logic controllers (FLC's) for nonlinear systems with guaranteed closedloop stability and its application on combining controllers. The design is based on heuristic fuzzy rules. Although each rule in the FLC refers to a stable closed-loop subsystem, the overall system stability cannot be guaranteed when all these rules are applied together. In this paper, it is proved that if each subsystem is stable in the sense of Lyapunov (ISL) under a common Lyapunov function, the overall system is also stable ISL. Since no fuzzy plant model is involved, the number of subsystems generated is relatively small, and the common Lyapunov function can be found more easily. To probe further, an application of this design approach to an inverted pendulum system that combines a sliding-mode controller (SMC) and a state feedback controller (SFC) is to be reported. Each rule in this FLC has an SMC or an SFC in the consequent part. The role of the FLC is to schedule the final control under different antecedents. The stability of the whole system is guaranteed by the proposed design approach. More importantly, the controller thus designed can keep the advantages and remove the disadvantages of the two conventional controllers.

A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models

“…However, a possible limitation of their approach is the use of the Lyapunov method, which is conservative. Hence, the stability analysis of fuzzy control systems was discussed in the bulk of literature, e.g., (Bernal and Hušek, 2005;Blanco et al, 2001;Chadli et al, 2000;Chadli et al, 2001;Chadli et al, 2005;Jadbabaie, 1999;Johansson et al, 1999;Ohtake et al, 2003;Tanaka and Sugeno, 1992;Tanaka et al, 2003;Wang et al, 1995;Wang et al, 1996;Wong et al, 1998). Especially, piecewise Lyapunov functions and multiple Lyapunov functions have attracted a lot of attention due to avoiding the conservatism of stability and stabilization problems.…”

Stable and robust fuzzy control for uncertain nonlinear systems

“…To alleviate the chattering problem and eliminate the finite steady state error, some fuzzy tuning algorithms [35], [42], and adaptive techniques [14], [34] were introduced to the fuzzy sliding mode controller. Other stability analyses can be found in [43], [62], and [91]. It can be seen that the studies of the fuzzy control system based on the mathematical model approach were mainly on the system stability and other system characteristics through combining conventional control theories with fuzzy logic.…”

Takagi-Sugeno Fuzzy System based Stable Direct Adaptive Control of Nonlinear Systems

“…The overall system stability [18] governing the control of the plants has been put together into a rule base for the FLC. Design of FLC [19] for nonlinear systems with assured closed loop stability and its application on combining controller is based on heuristic fuzzy rules. Adaptive sliding mode schemes [20] along with fuzzy approximators are used to approximate the unknown function of nonlinear systems.…”