Adaptation and nonlinear parametrization: nonlinear dynamics prospective

Authors:	Tyukin Ivan, RIKEN Brain Science Institute, Japan van Leeuwen Cees, RIKEN Brain Science Institute, Japan
Topic:	1.2 Adaptive and Learning Systems
Session:	Adaptive and Learning Approaches to Controller Design
Keywords:	adaptive systems, nonlinear parameterization, finite formalgorithms, convergence, nonlinear persistent excitation

Abstract

We consider adaptive control problems in the presence of nonlinearparametrization of model uncertainties. An approach that foregoeson the need for domination in the control loop during adaptationis proposed. Our approach is based on the notions of attractivity,limit sets, equilibria, and multistability from the theory ofnonlinear dynamical systems rather than on the conventional methodof Lyapunov functions. As a result of this, our algorithms areapplicable to general smooth non-monotonic parametrization and donot require any damping or domination in control inputs.