Adaptive control via embedding in reproducing kernel Hilbert spaces

Abstract

This paper derives a formulation of an adaptive tracking control problem for systems having uncertain nonlinear dynamics by embedding an original L1 adaptive control problem in a reproducing kernel Hilbert space (RKHS). This paper proves the well-posedness of the closed loop evolution laws in the RKHS and derives sufficient conditions for stability and tracking convergence. When the uncertainty in the dynamics is represented in a RKHS that satisfies certain fundamental smoothness properties, the adaptive controller yields a closed loop system whose stability and convergence properties are analogous to that obtained for conventional model reference and L1 control for systems of ordinary differential equations.