A Distributionally Robust Optimization Based Method for Stochastic Model Predictive Control

Two stochastic model predictive control algorithms, which are referred to as distributionally robust model predictive control algorithms, are proposed in this article for a class of discrete linear systems with unbounded noise. Participially, chance constraints are imposed on both of the state and the control, which makes the problem more challenging. Inspired by the ideas from distributionally robust optimization (DRO), two deterministic convex reformulations are proposed for tackling the chance constraints. Rigorous computational complexity analysis is carried out to compare the two proposed algorithms with the existing methods. Recursive feasibility and convergence are proven. Simulation results are provided to show the effectiveness of the proposed algorithms.

Automated summary

This article proposes two distributionally robust model predictive control algorithms for handling discrete linear systems with unbounded noise. The algorithms consider chance constraints on both state and control, and employ deterministic convex reformulations inspired by distributionally robust optimization. Computational complexity analysis demonstrates the effectiveness of the proposed algorithms, and proofs of recursive feasibility and convergence are provided. Simulation results are presented to show their effectiveness.