Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets

TL;DR

This paper introduces a stochastic MPC method for linear systems with unbounded disturbances, using probabilistic reachable sets to ensure chance constraint satisfaction and proposing a backup control scheme for infeasibility cases.

Contribution

It develops a novel stochastic MPC framework utilizing probabilistic reachable sets for constraint tightening, ensuring chance constraints are met under certain disturbance assumptions.

Findings

Closed-loop chance constraints are satisfied in simulations.

The proposed controller improves robustness against unmodeled disturbances.

A backup scheme guarantees feasibility and stability.

Abstract

In this paper we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in analogy to robust MPC using a constraint tightening based on the concept of probabilistic reachable sets, which is shown to provide closed-loop fulfillment of chance constraints under a unimodality assumption on the disturbance distribution. A control scheme reverting to a backup solution from a previous time step in case of infeasibility is proposed, for which an asymptotic average performance bound is derived. Two examples illustrate the approach, highlighting closed-loop chance constraint satisfaction and the benefits of the proposed controller in the presence of unmodeled disturbances.