Real-Time Minmax Dynamic Optimization of Nonlinear Systems over a Finite-time Horizon

In this paper, we present a real-time dynamic minmax optimization technique for a class of nonlinear systems operating over finite-time horizon. The technique is suitable for peak minimization and other types of minmax problems that arise in robust control problems. As in MPC, the optimization algorithm is based on the minimization of a cost function whose minimization provides stability to the closed-loop system. An interior point method with penalty function is used to incorporate constraints into a modified cost functional, and a Lyapunov based extremum seeking approach is used to compute the trajectory parameters. A precise statement of the numerical implementation of the optimization routine is provided. It is shown how one can take into account the effect of sampling and discretization of the parameter update law.