Data-Driven Predictive Control for Stochastic Descriptor Systems: An Innovation-Based Approach Handling Non-Causal Dynamics

TL;DR

This paper introduces a data-driven predictive control method for stochastic descriptor systems with algebraic constraints and non-causal dynamics, using an innovation-based approach that avoids explicit system identification.

Contribution

It extends Willems' Fundamental Lemma to stochastic descriptor systems and develops an Inno-DeePC algorithm for effective control without system identification.

Findings

Successfully handles non-causal stochastic dynamics

Demonstrates effectiveness on a DC microgrid example

Provides a practical data-driven control framework

Abstract

Descriptor systems arise naturally in applications governed by algebraic constraints, such as power networks and chemical processes. The singular system matrix in descriptor systems may introduce non-causal dynamics, where the current output depends on future inputs and, in the presence of stochastic process and measurement noise, on future noise realizations as well. This paper proposes a data-driven predictive control framework for stochastic descriptor systems that accommodates algebraic constraints and impulsive modes without explicit system identification. A causal innovation representation is constructed by augmenting the system state with a noise buffer that encapsulates the non-causal stochastic interactions, transforming the descriptor system into an equivalent proper state-space form. Willems' Fundamental Lemma is then extended to the innovation form with fully data-verifiable conditions. Building on these results, a practical Inno-DeePC algorithm is developed that integrates offline innovation estimation and online predictive control. Numerical experiments on a direct-current (DC) microgrid demonstrate the effectiveness of the proposed approach for stochastic descriptor systems.