Combination of RFPT-based adaptive control and classical model identification

Abstract

The traditional approach in the design of adaptive controllers for nonlinear dynamic systems normally applies Lyapunov's “direct” method that has the main characteristic features as follows: a) it yields satisfactory conditions for the stability, b) instead focusing on the primary design intent (e.g. the precise prescription of the trajectory tracking error relaxation) it concentrates on proving “global stability” that often is “too much” for common practical applications, c) in the identification of the model parameters of the controlled system it provides a tuning algorithm that contains certain components of the Lyapunov functions therefore it works with a large number of arbitrary adaptive control parameters; d) the parameter identification process in certain cases is vulnerable if unknown external perturbations can disturb the system under control. In order to replace this technique by a simpler approach concentrating on the primary design intent the “Robust Fixed Point Transformation (RFPT)”-based technique was suggested that - at the cost of sacrificing the need for global stability - applied iteratively deformed control signal sequences that on the basis of Banach Fixed Point Theorem converged to the appropriate control signal only within a bounded basin of attraction. This method was found to be applicable for a wide class of systems to be controlled, it was robust against the unknown external disturbances, used only three adaptive control parameters and later was completed by fine tuning of only one of these control parameters to keep the system in the region of convergence. In the present paper theoretical and simulations based considerations are presented revealing that the two methods can be combined in the control of certain physical systems.