Measured-state conditioned recursive feasibility for stochastic model predictive control

TL;DR

This paper introduces a new approach for stochastic MPC that ensures recursive feasibility by conditioning on measured states, using probabilistic reachable sets, and demonstrates improved performance over traditional methods.

Contribution

It proposes the concept of measured-state conditioned recursive feasibility and develops a stochastic MPC scheme utilizing ellipsoidal probabilistic reachable sets for better initialization.

Findings

The new scheme guarantees recursive feasibility under unbounded disturbances.

Numerical examples show improved performance over open-loop initialization.

The approach effectively incorporates current measurements into the control scheme.

Abstract

In this paper, we address the problem of designing stochastic model predictive control (MPC) schemes for linear systems affected by unbounded disturbances. The contribution of the paper is twofold. First, motivated by the difficulty of guaranteeing recursive feasibility in this framework, due to the nonzero probability of violating chance-constraints in the case of unbounded noise, we introduce the novel definition of measured-state conditioned recursive feasibility in expectation. Second, we construct a stochastic MPC scheme, based on the introduction of ellipsoidal probabilistic reachable sets, which implements a closed-loop initialization strategy, i.e., the current measured-state is employed for initializing the optimization problem. This new scheme is proven to satisfy the novel definition of recursive feasibility, and its superiority with respect to open-loop initialization schemes, arising from the fact that one never neglects the information brought by the current measurement, is shown through numerical examples.