Adaptive MPC with Chance Constraints for FIR Systems

TL;DR

This paper introduces an adaptive stochastic MPC approach for FIR systems with bounded disturbances, leveraging distributionally robust optimization to handle constraints and ensure persistent feasibility, validated through numerical experiments.

Contribution

It presents a novel adaptive stochastic MPC method for FIR systems that incorporates distributionally robust optimization for constraint handling and feasibility guarantees.

Findings

Successfully handles hard input and probabilistic output constraints.

Ensures persistent feasibility of the control algorithm.

Demonstrates effectiveness through numerical comparison with existing methods.

Abstract

This paper proposes an adaptive stochastic Model Predictive Control (MPC) strategy for stable linear time invariant systems in the presence of bounded disturbances. We consider multi-input multi-output systems that can be expressed by a finite impulse response model, whose parameters we estimate using a linear Recursive Least Squares algorithm. Building on the work of [1],[2], our approach is able to handle hard input constraints and probabilistic output constraints. By using tools from distributionally robust optimization, we formulate our MPC design task as a convex optimization problem that can be solved using existing tools. Furthermore, we show that our adaptive stochastic MPC algorithm is persistently feasible. The efficacy of the developed algorithm is demonstrated in a numerical example and the results are compared with the adaptive robust MPC algorithm of [2].