Contribution à la commande adaptative optimale d’ordre fractionnaire.

Abstract

This work focuses on the introduction of optimization techniques in fractional adaptive control systems and on optimized approximation of fractional systems with reduced order models for identification and control purpose. Indeed, a new technique of approximation has been proposed in this direction, using the DE (differential evolution) technique while showing its advantage compared to other famous techniques such as those developed by Charef or Oustaloup. Fractional adaptive control laws with optimized parameters are developed in order to improve the control system behavior: In the case of fractional order linear systems, a model reference PID control based on a new optimization algorithm (Moth-Flame) has been proposed. In the case of fractional order chaotic nonlinear systems, the following approaches are considered: a first control with adaptive sliding mode to improve performance and robustness. Since fuzzy systems are universal approximators, this property is exploited to strengthen the previous control law by an adaptive fuzzy controller. For an optimal control, the parameters of the sliding controller are calculated by PSO optimization technique. In all the previous cases, the analysis of stability and robustness are justified by the Lyapunov approach. The theoretical results are validated by simulation examples.