An Improved Constraint-Tightening Approach for Stochastic MPC

TL;DR

This paper introduces a less conservative stochastic MPC method that separates stability from feasibility, using explicit constraints and offline sampling to reduce computational complexity while maintaining recursive feasibility and stability.

Contribution

It proposes a novel constraint-tightening scheme with explicit first step constraints and offline sampling, improving efficiency and less conservativeness in stochastic MPC.

Findings

Guarantees recursive feasibility with explicit constraints.

Reduces online computational complexity to nominal MPC levels.

Demonstrates improved performance over classical stochastic and robust MPC in numerical tests.

Abstract

The problem of achieving a good trade-off in Stochastic Model Predictive Control between the competing goals of improving the average performance and reducing conservativeness, while still guaranteeing recursive feasibility and low computational complexity, is addressed. We propose a novel, less restrictive scheme which is based on considering stability and recursive feasibility separately. Through an explicit first step constraint we guarantee recursive feasibility. In particular we guarantee the existence of a feasible input trajectory at each time instant, but we only require that the input sequence computed at time $k$ remains feasible at time $k+1$ for most disturbances but not necessarily for all, which suffices for stability. To overcome the computational complexity of probabilistic constraints, we propose an offline constraint-tightening procedure, which can be efficiently solved via a sampling approach to the desired accuracy. The online computational complexity of the resulting Model Predictive Control (MPC) algorithm is similar to that of a nominal MPC with terminal region. A numerical example, which provides a comparison with classical, recursively feasible Stochastic MPC and Robust MPC, shows the efficacy of the proposed approach.