Regularized economic model predictive control with barrier functions

In this article, we consider the use of barrier functions as a regularizing cost in economic model predictive control (EMPC). We focus on a specific variant, EMPC with generalized terminal constraints (G-EMPC), as it is suitable for tackling large-scale problems commonly arising in multiagent settings, which motivates our work. The benefits of using barrier functions are providing smoothing of the constrained problem, allowing the use of second-order methods and warm-starting, which reduces the iteration count significantly. Apart from these numerical benefits, recentered barrier functions can be used as a regularizing cost in the EMPC problem for enhancing closed-loop convergence properties. We show that in the case of G-EMPC, which allows the terminal state to be any equilibrium point, regularizing the problem provides (i) convergence of the predicted terminal state to a neighborhood of a globally optimal equilibrium point, (ii) asymptotic average performance guarantees for the closed-loop system, and (iii) empirical evidence of accelerated numerical solution of the optimal control problem. Specifically we use a proximal-like regularization, which penalizes the deviation from the previously predicted trajectories. We analyze system theoretic properties of the proposed scheme and provide simulation examples illustrating the numerical and system theoretical benefits of using barriers.