Neighboring-Extremal Control for Singular Dynamic Optimization Problems. II- Multiple-Input Systems

Dynamic optimization provides a unified framework for improving process operations while taking operational constraints into account. In the presence of uncertainty, measurements can be incorporated into the optimization framework for tracking the optimum. For nonsingular control problems, neighboring-extremal (NE) control can be used to force the first-order variation of the necessary conditions of optimality (NCO) to zero along interior arcs. An extension of NE control to singular control problems has been proposed in the companion paper for single-input problems. In this paper, a generalization to multiple-input systems is presented. In order for these controllers to be tractable from a real-time optimization perspective, an approximate NE feedback law is proposed, whose application guarantees, under mild assumptions, that the first-order variation of the NCO converge to zero exponentially. The performance of multi-input NE control is illustrated by the case study of a steered car.