Model predictive control for singular differential-algebraic equations

TL;DR

This paper develops a novel approach to applying model predictive control to singular differential-algebraic equations of higher index by using regularization techniques to transform the problem into a standard ODE setting.

Contribution

It introduces a new method for controlling higher-index singular differential-algebraic equations using regularization to enable existing MPC techniques.

Findings

Successfully transforms singular DAE control problems into ODE control problems.

Ensures asymptotic stability of the closed-loop system.

Extends MPC applicability to a broader class of systems.

Abstract

We study model predictive control for singular differential-algebraic equations with higher index. This is a novelty when compared to the literature where only regular differential-algebraic equations with additional assumptions on the index and/or controllability are considered. By regularization techniques, we are able to derive an equivalent optimal control problem for an ordinary differential equation to which well-known model predictive control techniques can be applied. This allows the construction of terminal constraints and costs such that the origin is asymptotically stable w.r.t. the resulting closed-loop system.