Stochastic Model Predictive Control for tracking of distributed linear systems with additive uncertainty

TL;DR

This paper introduces a stochastic model predictive control approach for distributed linear systems with uncertainties, ensuring constraint satisfaction and convergence to reference points through probabilistic and invariant set techniques.

Contribution

It presents a novel chance constrained MPC scheme with analytical reformulation, invariant set design, and recursive feasibility for distributed systems with stochastic uncertainties.

Findings

Ensures constraint satisfaction in closed-loop operation.

Demonstrates convergence to changing reference points.

Validates effectiveness through a numerical example.

Abstract

In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated analytically based on mean-variance information, where we design suitable Probabilistic Reachable Sets for constraint tightening. Furthermore, the chance constraints are proven to be satisfied in closed-loop operation. The design of an invariant set for tracking complements the controller and ensures convergence to arbitrary admissible reference points, while a conditional initialization scheme provides the fundamental property of recursive feasibility. The paper closes with a numerical example, highlighting the convergence to changing output references and empirical constraint satisfaction.