Optimal plug-and-control of unknown nonlinear systems

Abstract

Modeling and control design are typically subsequent but independent activities. Optimal control is traditionally developed on the basis of explicit models. While this usually yields good results for linear systems, the same is not as true for nonlinear ones, for which explicit solutions can be found only for few cases. In practice, in most cases receding horizon controls based on linear approximations are used. In this paper, we propose a procedure which delivers in one step both a model and an optimal receding horizon control algorithm, without requiring a linearization. Our procedure relies essentially on a system identification by a suitable class of functions which offers universal approximation properties that can be directly incorporated in the control algorithm. Using directional forgetting we show that an adaptive extension can be realized. Measurements and simulations based on a standard automotive control problem are presented to confirm the validity of our proposal.