Mixed fractional order adaptive control: Theory and applications

In this paper we study the adaptive control problem of integer order plants using fractional order adaptive laws in the controller. The study is based on a general methodology developed recently to establish boundeness and asymptotic behavior of solutions to multi-order systems (set of differential equations with different derivation orders) having multiple time-varying delays. Also it is based on recent results for fractional order systems under the perspective of the so called”Error Models”. The method relies on vector Lyapunov-like functions and on comparison arguments. Boundedness and convergence of the solutions are theoretically analyzed and applications to fractional adaptive schemes are presented towards the end of the paper, including numerical simulations to verify the analytical results.