Stochastic Model Predictive Control using Initial State Optimization

TL;DR

This paper introduces a stochastic MPC approach that optimizes the initial state to improve trajectory planning under unbounded stochastic disturbances, ensuring constraint satisfaction and better transient behavior.

Contribution

It presents a novel stochastic MPC scheme that incorporates initial state optimization to handle unbounded disturbances and guarantee stability and constraints.

Findings

Guarantees constraint satisfaction under unimodal disturbances.

Avoids infeasibility issues with unbounded disturbances.

Improves transient behavior through initial state optimization.

Abstract

We propose a stochastic MPC scheme using an optimization over the initial state for the predicted trajectory. Considering linear discrete-time systems under unbounded additive stochastic disturbances subject to chance constraints, we use constraint tightening based on probabilistic reachable sets to design the MPC. The scheme avoids the infeasibility issues arising from unbounded disturbances by including the initial state as a decision variable. We show that the stabilizing control scheme can guarantee constraint satisfaction in closed loop, assuming unimodal disturbances. In addition to illustrating these guarantees, the numerical example indicates further advantages of optimizing over the initial state for the transient behavior.