Data-Driven Output Prediction and Control of Stochastic Systems: An Innovation-Based Approach

TL;DR

This paper introduces an innovation-based data-driven output predictor for stochastic LTI systems that improves prediction reliability and control performance without explicit system identification, validated through simulations.

Contribution

It presents a novel innovation-based approach for data-driven output prediction and control of stochastic systems, bypassing explicit system identification.

Findings

Outperforms existing methods in output prediction accuracy

Ensures bounded second moment of prediction errors

Enhances control performance through data-driven design

Abstract

Recent years have witnessed a booming interest in data-driven control of dynamical systems. However, the implicit data-driven output predictors are vulnerable to uncertainty such as process disturbance and measurement noise, causing unreliable predictions and unexpected control actions. In this brief, we put forward a new data-driven approach to output prediction of stochastic linear time-invariant (LTI) systems. By utilizing the innovation form, the uncertainty in stochastic LTI systems is recast as innovations that can be readily estimated from input-output data without knowing system matrices. In this way, by applying the fundamental lemma to the innovation form, we propose a new innovation-based data-driven output predictor (OP) of stochastic LTI systems, which bypasses the need for identifying state-space matrices explicitly and building a state estimator. The boundedness of the second moment of prediction errors in closed-loop is established under mild conditions. The proposed data-driven OP can be integrated into optimal control design for better performance. Numerical simulations demonstrate the outperformance of the proposed innovation-based methods in output prediction and control design over existing formulations.