Data-Driven Analysis and Predictive Control of Descriptor Systems with Application to Power and Water Networks

TL;DR

This paper presents a novel data-driven framework for analyzing and controlling descriptor systems, particularly in power and water networks, without explicit models, addressing non-causality and controllability challenges.

Contribution

It extends Willems' fundamental lemma to descriptor systems and develops data-based conditions for controllability and observability, enabling effective data-driven control in complex systems.

Findings

DeePC achieved frequency regulation in power systems despite controllability violations.

Successful output tracking in water networks under algebraic constraints.

Framework enables control without explicit state-space models.

Abstract

Despite growing interest in data-driven analysis and control of linear systems, descriptor systems--which are essential for modeling complex engineered systems with algebraic constraints like power and water networks--have received comparatively little attention. This paper develops a comprehensive data-driven framework for analyzing and controlling discrete-time descriptor systems without relying on explicit state-space models. We address fundamental challenges posed by non-causality through the construction of forward and backward data matrices, establishing data-based sufficient conditions for controllability and observability in terms of input-output data, where both R-controllability and C-controllability (R-observability and C-observability) have been considered. We then extend Willems' fundamental lemma to incompletely controllable systems. These methodological advances enable Data-Enabled Predictive Control (DeePC) to achieve output tracking in descriptor systems and to maintain performance under incomplete controllability conditions, as demonstrated in two case studies: i) Frequency regulation in an IEEE 9-bus power system with 3 generators, where DeePC maintained the frequency stability of the power system despite deliberate violations of R-controllability; and ii) Pressure head control in an EPANET water network with 3 tanks, 2 reservoirs, and 117 pipes, where output tracking was successfully enforced under algebraic constraints.