Rule chain and dominant rule control algorithm for unknown nonlinear systems

This paper is focused on the control method based upon rule chains of a rule-base for unknown nonlinear systems. At first, the fuzzy point is employed to simplify the expression of multi-input multi-output fuzzy rules. Some relations between the fuzzy point and fuzzy number are obtained. Second, the input dominant region and output dominant region of a rule are proposed. Third, the dominant rule control algorithm is constructed by means of the extension rule, which contains not only the fuzzy couple of system state and system input, but also the information about its action time and the prospective system state after its action time. Following that, the rule chain and ε-level stability are presented. Furthermore, a sufficient and necessary condition for the ε-level stability of the rule-base control systems is obtained. A method to analyze the ε-level stability of the rule-base control systems is presented. An upper bound about the settling time and the maximum steady-error for the system are estimated. Finally, an application result is employed to show the effectivity of the method.