Recursively feasible stochastic predictive control using an interpolating initial state constraint -- extended version

TL;DR

This paper introduces a flexible stochastic model predictive control framework that optimizes the initial state interpolation, ensuring chance constraint satisfaction and performance bounds for linear systems with disturbances.

Contribution

It proposes a novel SMPC scheme with an interpolating initial state constraint, improving flexibility and maintaining theoretical guarantees.

Findings

Ensures closed-loop chance constraint satisfaction.

Can be implemented as a standard quadratic program.

Provides performance bounds for the control scheme.

Abstract

We present a stochastic model predictive control (SMPC) framework for linear systems subject to possibly unbounded disturbances. State of the art SMPC approaches with closed-loop chance constraint satisfaction recursively initialize the nominal state based on the previously predicted nominal state or possibly the measured state under some case distinction. We improve these initialization strategies by allowing for a continuous optimization over the nominal initial state in an interpolation of these two extremes. The resulting SMPC scheme can be implemented as one standard quadratic program and is more flexible compared to state-of-the-art initialization strategies. As the main technical contribution, we show that the proposed SMPC framework also ensures closed-loop satisfaction of chance constraints and suitable performance bounds.