Guaranteeing input tracking for constrained systems: Theory and application to demand response

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.

Robust optimal control with adjustable uncertainty sets

“…In particular, we extend the results of [10,12] in two ways: First, we show that any convex set can be used as a primitive set, allowing us to target a much larger class of uncertainty sets. Second, by allowing the primitive sets to be defined on higher dimensional spaces than those of the uncertainty sets, we are able to design more flexible uncertainty sets.…”

“…Reserve provision problems of this kind were first formulated and studied in [10] where it was shown that for uncertainty sets described by norm balls, the problems can be reformulated as tractable convex optimization problems. Another problem that admits the interpretation as a robust control problem with adjustable uncertainty set is robust input tracking [11,12], where the aim is to determine the largest set of inputs that can be tracked by a system without violating its constraints. Reserve provision and input tracking problems have recently received increased attention in demand response applications of control reserves for electrical power grids [13,14,15].…”

Trajectory Tracking With an Aggregation of Domestic Hot Water Heaters: Combining Model-Based and Model-Free Control in a Commercial Deployment

“…This allows to model dispatch heuristics in the central optimization problem and accounts for the heterogeneous nature of the cluster of TCLs. In [21] an approach is presented that generates a trackable reduced order tank model from a set of individual models using techniques from robust optimization.…”

Experimental demonstration of buildings providing frequency regulation services in the Swiss market

“…Several theoretical works have then proposed frameworks for computing the tracking capabil-ity of such systems. Several model-based methods using robust programming concepts have been proposed including [14], [15], [16], [17]. Other works have proposed analytical methods to analyze the aggregate flexibility of populations of loads in order to characterize it as an equivalent 'virtual battery' [4], [18], [19], [20].…”