Region-free explicit model predictive control for linear systems on Hilbert spaces

TL;DR

This paper develops a region-free explicit model predictive control method for linear distributed parameter systems, demonstrating its effectiveness on a constrained Timoshenko beam modeled by a hyperbolic PDE.

Contribution

It extends explicit MPC to infinite-dimensional systems on Hilbert spaces and introduces a fast dual active set method for real-time control.

Findings

Successfully controls a Timoshenko beam with constraints

Demonstrates real-time applicability of the proposed MPC method

Validates the approach on a hyperbolic PDE system

Abstract

We extend discrete-time explicit model predictive control (MPC) rigorously to linear distributed parameter systems. After formulating an MPC framework and giving a relevant KKT theorem, we realize fast regionless explicit MPC by using the dual active set method QPKWIK. A Timoshenko beam with input and state constraints is used to demonstrate the efficacy of the design at controlling a continuous-time hyperbolic PDE with constraints, using a discrete-time explicit MPC controller.