Genetic fuzzy control for time-varying delayed uncertain systems with a robust stability safeguard
A linear uncertain system with state-varying delay described in the form \[ d{\mathbf x}/dt= (A_0+\Delta A_0) {\mathbf x}(t)+ (A_1+\Delta A_1) {\mathbf x}\bigl(t- h(t)\bigr)+ (B+\Delta B){\mathbf u}(t) \] where \({\mathbf x} (t) \in{\mathbf R}^n\) is a state vector, \({\mathbf u}\in {\mathbf R}^m\) denotes the control, \({\mathbf y}(t)\in {\mathbf R}^q\) is the vector of outputs and \(h(t)\) stands for a time-varying delay. \(A_0\), \(A_1\), \(B\) are known nominal matrices while \(\Delta A_0\), \(\Delta A_1\), and \(\Delta B\) are known perturbation matrices contributing to the uncertain nature of the system under consideration. The proposed control law is realized by the feedback controller combined additively with a fuzzy controller (FC), \({\mathbf u}(t)=K{\mathbf x}(t)+\)FC. The design objectives are two-fold: (a) constructing a robust control gain \((K)\) based upon some stability criterion and aimed at the stabilization with perturbed matrices \((\Delta A_0\), \(\Delta A_1\), and \(\Delta B)\) and (b) constructing the fuzzy controller so that the required performance is satisfied. The realization of the fuzzy controller is completed via genetic optimization (genetic algorithm).
scientific article; zbMATH DE number 1861150