Stochastic Model Predictive Control with Discounted Probabilistic Constraints

TL;DR

This paper introduces a stochastic MPC approach with discounted probabilistic constraints, ensuring recursive feasibility and stability for linear systems under disturbances without requiring bounded disturbances.

Contribution

It proposes a novel discounted chance constraint formulation and an online constraint-tightening method to guarantee feasibility and stability in stochastic MPC.

Findings

Guarantees recursive feasibility of the MPC scheme.

Ensures the closed-loop system satisfies the chance constraint.

Provides a quadratic stability condition for the system.

Abstract

This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law to minimise a quadratic cost function subject to a chance constraint. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and ignoring violation probabilities in the far future, this form of constraint enables the feasibility of the online optimisation to be guaranteed without an assumption of boundedness of the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility based on knowledge of a suboptimal solution. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition.