Direct adaptive neural control for affine nonlinear systems

Abstract

This paper presents a direct adaptive neural control scheme for a class of affine nonlinear systems which are exactly input–output linearizable by nonlinear state feedback. For single-input–single-output (SISO) systems of the form x ˙ = f ( x ) + g ( x ) u , the control problem is comprehensively solved when both f ( x ) and g ( x ) are unknown. In this case, the control input comprises two terms. One is an adaptive feedback linearization term and the other one is a sliding mode term. The weight update laws for two neural networks, which approximate f ( x ) and g ( x ) , have been derived to make the closed loop system Lyapunov stable. It is also shown that a similar control approach can be applied for a class of multi-input–multi-output (MIMO) systems whose structure is formulated in this paper. Simulation results for both SISO- and MIMO-type nonlinear systems have been presented to validate the theoretical formulations.