A STABLE CONSTRAINED OPTIMAL-MODEL FOLLOWING CONTROLLER FOR DISCRETE-TIME NONLINEAR-SYSTEMS AFFINE IN THE CONTROL

An on-line tracking algorithm is developed for a system described by n onlinear difference equations with control variables appearing linearl y. This algorithm computes the control variables at each sample time s o that the state of the controlled system is tracking the desired stat e optimally. By formulating the controller computation task as a linea r programming problem, the algorithm can be readily implemented on-lin e. The tracking error is shown to converge to zero when there are no b ounds on the control variables. In the presence of control constraints , two new sufficient conditions on the convergence oi the tracking err or are derived. For illustration, a ship steering problem of a directi onally unstable vessel, and an optimal terrain tracking problem involv ing an aircraft are solved using the proposed algorithm.