Identification-based Adaptive Control for Systems with Time-varying Parameters

This paper proposes an identification-based adaptive control scheme for nonlinear systems with time-varying parameters designed on the basis of the so-called congelation of variables method. First a scalar example to demonstrate the design methodology, which relies on re-arranging the identifier subsystems from a cascaded topology to a cyclic topology, is discussed. A small-gain-like control synthesis exploiting the cyclic topology is then presented to replace the classical control synthesis based on the swapping lemma, which exploits the cascaded topology. Then a state feedback design for a class of lower triangular nonlinear systems is presented: this combines the same design methodology with the backstepping techniques. Boundedness of all closed-loop signals and convergence of the system state are proved. Finally, simulation results showing that the proposed controller achieves superior performance than the classical design are presented.