Towards nonlinear model predictive control with integrated experiment design

Abstract

Nonlinear model predictive control (NMPC) has become an important tool in the control and optimization of nonlinear systems in a variety of engineering applications. A requirement for a well-performing NMPC implementation is obtaining and maintaining an appropriate mathematical model of the considered system. For linear dynamic systems, developments have been made to incorporate information content objectives in closed loop, i.e., to solve the dual control problem. However, formulations for nonlinear dynamic systems remain scarce. In this paper we extend the formulation for the integration of experiment design of linear dynamic systems to nonlinear dynamic systems resulting in a NMPC formulation with integrated experiment design (iED-NMPC). This results for nonlinear systems in the presence of a nonlinear matrix inequality. We propose to reformulate this nonlinear matrix inequality using Sylvester's criterion. The suggested approach allows us to replace the nonlinear matrix inequality by additional nonlinear constraints. The resulting formulation can subsequently be implemented in existing NMPC software packages.