Model Predictive Control for Regular Linear Systems

TL;DR

This paper develops a model predictive control approach for infinite-dimensional linear systems modeled by PDEs, using a structure-preserving discretization that avoids spatial discretization or reduction.

Contribution

It introduces a Cayley-Tustin transformation-based discretization method for PDE systems, enabling explicit constrained MPC design without spatial discretization.

Findings

The proposed MPC effectively stabilizes PDE systems with constraints.

The discretization preserves system structure and avoids spatial discretization.

Numerical examples demonstrate practical applicability.

Abstract

The present work extends known finite-dimensional constrained optimal control realizations to the realm of well-posed regular linear infinite-dimensional systems modelled by partial differential equations. The structure-preserving Cayley-Tustin transformation is utilized to approximate the continuous-time system by a discrete-time model representation without using any spatial discretization or model reduction. The discrete-time model is utilized in the design of model predictive controller accounting for optimality, stabilization, and input and output/state constraints in an explicit way. The proposed model predictive controller is dual-mode in the sense that predictive controller steers the state to a set where exponentially stabilizing unconstrained feedback can be utilized without violating the constraints. The construction of the model predictive controller leads to a finite-dimensional constrained quadratic optimization problem easily solvable by standard numerical methods. Two representative examples of partial differential equations are considered.