Adaptive Control by Using Time-Sharing and Fixed Point Transformation

In this paper a novel combination of the "adaptive" and "optimal" control is suggested in which the main sources of the mathematical complexities, i.e. The application of cost functional in optimal control, and the use of Lyapunov´s "Direct Method" in adaptive control are replaced by simple time-sharing and a Fixed Point Transformation based adaptive solution. To exemplify the efficiency of the suggested method the adaptive synchronization of two under actuated chaotic systems is shown via simulation. Each of these systems corresponds to a 3 degree of freedom Chua - Matsumoto circuit that has one smoothly and two rather "abruptly" propagating variables. Even little changes in the model parameters drastically influence the timing of these abrupt variations therefore this control task is especially challenging. The control solution applied is based on a novel fixed point technique that was not published up to the present paper.