Direct adaptive neural control for affine nonlinear systems

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)f(x) and g(x)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)f(x) and g(x)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.