Output Feedback Stochastic MPC with Hard Input Constraints

TL;DR

This paper introduces a stochastic model predictive control method that guarantees constraint satisfaction under Gaussian disturbances using output feedback and a tube-based approach.

Contribution

It develops a novel SMPC framework with hard input constraints and invariant tightened constraints, ensuring feasibility and robustness.

Findings

Guarantees an infeasibility rate below a user-defined threshold.

Demonstrates improved constraint satisfaction over classical methods.

Shows effectiveness through numerical simulations.

Abstract

We present an output feedback stochastic model predictive controller (SMPC) for constrained linear time-invariant systems. The system is perturbed by additive Gaussian disturbances on state and additive Gaussian measurement noise on output. A Kalman filter is used for state estimation and an SMPC is designed to satisfy chance constraints on states and hard constraints on actuator inputs. The proposed SMPC constructs bounded sets for the state evolution and a tube-based constraint tightening strategy where the tightened constraints are time-invariant. We prove that the proposed SMPC can guarantee an infeasibility rate below a user-specified tolerance. We numerically compare our method with a classical output feedback SMPC with simulation results which highlight the efficacy of the proposed algorithm.