Stochastic MPC with Realization-Adaptive Constraint Tightening

TL;DR

This paper introduces a stochastic model predictive control method that adaptively tightens constraints based on realized disturbances, reducing conservatism while maintaining feasibility in systems with unknown disturbance distributions.

Contribution

It proposes a novel realization-adaptive constraint tightening strategy for SMPC that improves performance and reduces conservatism compared to existing methods.

Findings

Recursive feasibility is guaranteed.

Reduces conservatism in constraint handling.

Effective in numerical simulations.

Abstract

This paper presents a stochastic model predictive controller (SMPC) for linear time-invariant systems in the presence of additive disturbances. The distribution of the disturbance is unknown and is assumed to have a bounded support. A sample-based strategy is used to compute sets of disturbance sequences necessary for robustifying the state chance constraints. These sets are constructed offline using samples of the disturbance extracted from its support. For online MPC implementation, we propose a novel reformulation strategy of the chance constraints, where the constraint tightening is computed by adjusting the offline computed sets based on the previously realized disturbances along the trajectory. The proposed MPC is recursive feasible and can lower conservatism over existing SMPC approaches at the cost of higher offline computational time. Numerical simulations demonstrate the effectiveness of the proposed approach.