Recursive Feasibility of Stochastic Model Predictive Control with Mission-Wide Probabilistic Constraints

TL;DR

This paper addresses the challenge of ensuring recursive feasibility in stochastic model predictive control by focusing on mission-wide safety probabilities, proposing a novel approach that conserves overall safety in expectation.

Contribution

It introduces a new concept of recursive feasibility based on remaining mission-wide safety probabilities, differing from traditional methods that enforce constraints at each step independently.

Findings

Proposes a scenario-based algorithm for linear SMPC.

Demonstrates the effectiveness of mission-wide SMPC in simulations.

Ensures mission-wide safety with probabilistic guarantees.

Abstract

This paper is concerned with solving chance-constrained finite-horizon optimal control problems, with a particular focus on the recursive feasibility issue of stochastic model predictive control (SMPC) in terms of mission-wide probability of safety (MWPS). MWPS assesses the probability that the entire state trajectory lies within the constraint set, and the objective of the SMPC controller is to ensure that it is no less than a threshold value. This differs from classic SMPC where the probability that the state lies in the constraint set is enforced independently at each time instant. Unlike robust MPC, where strict recursive feasibility is satisfied by assuming that the uncertainty is supported by a compact set, the proposed concept of recursive feasibility for MWPS is based on the notion of remaining MWPSs, which is conserved in the expected value sense. We demonstrate the idea of mission-wide SMPC in the linear SMPC case by deploying a scenario-based algorithm.