Guaranteeing Input Tracking For Constrained Systems: Theory and Application to Demand Response

TL;DR

This paper introduces a linear programming-based method to certify exact input trackability for constrained linear systems, with applications in demand response for power consumption, ensuring systems can follow specified reference signals within constraints.

Contribution

The paper develops a novel approach inspired by robust model predictive control to certify input trackability over finite horizons and identifies convex parameterizations for largest trackable signal sets.

Findings

Method certifies exact input tracking within constraints.

Convex programs identify largest sets of trackable signals.

Application demonstrated on building heating system.

Abstract

A method for certifying exact input trackability for constrained discrete time linear systems is introduced in this paper. A signal is assumed to be drawn from a reference set and the system must track this signal with a linear combination of its inputs. Using methods inspired from robust model predictive control, the proposed approach certifies the ability of a system to track any reference drawn from a polytopic set on a finite time horizon by solving a linear program. Optimization over a parameterization of the set of reference signals is discussed, and particular instances of parameterization of this set that result in a convex program are identified, allowing one to find the largest set of trackable signals of some class. Infinite horizon feasibility of the methods proposed is obtained through use of invariant sets, and an implicit description of such an invariant set is proposed. These results are tailored for the application of power consumption tracking for loads, where the operator of the load needs to certify in advance his ability to fulfill some requirement set by the network operator. An example of a building heating system illustrates the results.