A framework for analysis and synthesis of fuzzy linguistic control systems
G. Langari, Masayoshi Tomizuka · 1991
Fuzzy Linguistic Control(FLC) may be viewed as a knowledge based control strategy that can be used when the dynamic characteristics of the plant or the associated control objectives are not sufficiently well posed to warrant the, at least immediate, application of conventional control techniques. Alternatively, in these situations one may opt for a heuristically designed control strategy that relies on empirically acquired knowledge regarding the operation of the process. This knowledge cast into linguistic or rule based form constitutes the core of a fuzzy linguistic control system. In other words, the control law, instead of being stated as an analytic function of the process output (or state for that matter), is composed of condition $\to$ action rules that capture, in an approximate sense, the empirical knowledge or know-how necessary to effectively control the process. This heuristic approach to control design raises important issues regarding the stability and reliability of fuzzy linguistic control systems. In this connection, the purpose of this dissertation is twofold. First, we present an approach to the analysis of stability of fuzzy linguistic control systems that is based on Lyapunov's Direct Method and as such offers sufficient conditions, which if met, guarantee global asymptotic stability of the system under consideration. Second, we will present an alternative framework for analysis, as well as synthesis, of fuzzy linguistic control systems that is intended to bridge the gap between this type of control strategy and conventional control techniques. Specifically, by parametrizing the characteristic functions of fuzzy subsets describing the linguistic terms used in the definition of the control rules, we develop an analytic formulation of the control scheme, which is then used to derive sufficient conditions for asymptotic stability of the closed loop dynamic system operating under fuzzy linguistic control. In this process, we will also establish a connection between fuzzy linguistic control and a class of nonlinear control schemes, namely those with piecewise linear characteristics. Furthermore, we present a new interpretation of fuzzy linguistic control that helps explain how certain types of nonlinearities, such as asymmetric response characteristics, can in effect be canceled by appropriate formulation of control rules. Finally, we will suggest how fuzzy linguistic control, in general, can be used to deal with other commonly occurring nonlinear behavior in industrial processes such as actuator saturation, nonlinear sensor behavior, and/or operating regime dependent variations in the response characteristics of the process.