Learning composite adaptive control for a class of nonlinear systems

An adaptive composite control technique was suggested before for nonlinear adaptive control with statistical learning methods. While this original work was restricted to a simple class of nonlinear SISO systems that were linear in the inputs, in this paper we present a more general treatment of learning a composite controller for the class of nonlinear systems characterized by the form x˙ = f(x) + g(x)u. We would first examine such systems in the first order SISO framework, and present a stability proof including a parameter projection method that is needed to avoid potential singularities during adaptation. Second, we generalize our adaptive controller to higher order SISO systems, and discuss the application to MIMO problems. We evaluate our theoretical control framework in numerical simulations to illustrate the effectiveness of the proposed learning adaptive controller for rapid convergence and high accuracy of control.