Résumé:
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.
