A Pontryagin-Based Game-Theoretic Approach for Robust Nonlinear Model Predictive Control

A Pontryagin-based differential game approach to solve a class of robust Nonlinear Model Predictive Control is proposed. The methodology defines an optimal control policy that takes into account non-accurate predictions of the system dynamics due to modeling errors and/or unknown exogenous disturbance, which may seriously compromise the controller performances. To this end, we propose a Pontryagin-based solution to the nonlinear min-max problem, which can be viewed as a zero-sum differential game, where the two players are the controlled input and the system's uncertainty/external disturbance. We show that, under suitable assumptions on system's dynamics, the game admits a Nash equilibrium, whose knowledge drastically decreases the high algorithmic complexity usually required for min-max optimization schemes. Finally, the theoretical results are confirmed by numerical simulations, performed on the Van der Pol nonlinear oscillator.