Learning Surrogate LPV State-Space Models with Uncertainty Quantification
This addresses the problem of assessing model reliability for analysis and control in complex nonlinear systems, offering a solution for engineers and researchers, though it is incremental as it builds on existing LPV methods.
The paper tackles the lack of uncertainty quantification in data-driven Linear Parameter-Varying (LPV) models by proposing a Bayesian approach that jointly estimates LPV state-space models and their scheduling, providing confidence bounds on predictions from input-output data.
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.