Closed-loop analysis of linear stochastic MPC with risk-averse constraints

TL;DR

This paper extends linear stochastic MPC with risk-averse constraints, ensuring recursive feasibility, constraint satisfaction, and near-optimal performance under certain conditions.

Contribution

It introduces a risk-averse MPC framework based on conditional value-at-risk, with theoretical guarantees for feasibility and performance.

Findings

Recursive feasibility and constraint satisfaction are established.

Near-optimality of the closed-loop performance is shown.

The approach extends existing methods from chance constraints to risk-averse constraints.

Abstract

Chance constraints are widely used in stochastic model predictive control (MPC) to enforce probabilistic state and input constraints in the presence of unbounded disturbances. However, they only restrict violation probabilities and do not account for the magnitude of rare but severe constraint violations. In this paper, we extend the indirect feedback approach for linear stochastic MPC from chance constraints to risk-averse constraints like the conditional value-at-risk. For the resulting risk-averse MPC scheme, we establish recursive feasibility and closed-loop constraint satisfaction. Furthermore, based on a stochastic dissipativity notion and suitable conditions on the terminal ingredients we show that (near)-optimality of the averaged closed-loop performance can be ensured.