Learning Surrogate LPV State-Space Models with Uncertainty Quantification

TL;DR

This paper introduces a Bayesian method for LPV state-space modeling that quantifies uncertainty, improving model reliability assessment and enabling better control design for complex systems.

Contribution

It presents a novel Bayesian approach that jointly estimates LPV models and their uncertainties, addressing a key gap in data-driven LPV modeling.

Findings

The method provides confidence bounds on model responses.

It accounts for both measurement noise and limited data.

Demonstrated on a nonlinear mass-spring-damper system.

Abstract

The Linear Parameter-Varying (LPV) framework enables the construction of surrogate models of complex nonlinear and high-dimensional systems, facilitating efficient stability and performance analysis together with controller design. Despite significant advances in data-driven LPV modelling, existing approaches do not quantify the uncertainty of the obtained LPV models. Consequently, assessing model reliability for analysis and control or detecting operation outside the training regime requires extensive validation and user expertise. This paper proposes a Bayesian approach for the joint estimation of LPV state-space models together with their scheduling, providing a characterization of model uncertainty and confidence bounds on the predicted model response directly from input-output data. Both aleatoric uncertainty due to measurement noise and epistemic uncertainty arising from limited training data and structural bias are considered. The resulting model preserves the LPV structure required for controller synthesis while enabling computationally efficient simulation and uncertainty propagation. The approach is demonstrated on the surrogate modelling of a two-dimensional nonlinear interconnection of mass-spring-damper systems.