Near-Optimal Performance of Stochastic Model Predictive Control

TL;DR

This paper provides a rigorous analysis showing that stochastic model predictive control (SMPC) can achieve near-optimal performance with exponentially small dynamic regret relative to the horizon length, under certain conditions.

Contribution

It offers the first theoretical guarantee of near-optimality for SMPC, demonstrating exponential decay of regret with horizon length under stabilizability and detectability.

Findings

SMPC's dynamic regret decreases exponentially with horizon length.

SMPC achieves near-optimal performance with reduced computational complexity.

Theoretical bounds are established under stabilizability and detectability conditions.

Abstract

This article presents a dynamic regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. While this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: Under stabilizability and detectability conditions, the dynamic regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.