Learning Surrogate LPV State-Space Models with Uncertainty Quantification

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.

Figures (7)

• Figure 1: Graphic representation of the two-dimensional interconnection of mass-spring-damper systems.
• Figure 2: Input and output trajectories of the training data set.
• Figure 3: Input and output trajectories of the test data set.
• Figure 4: Frequency response of the estimated LTI models $S_{\mathrm{ssest}}$ and $S_{\mathrm{n4sid}}$ where the shaded area shows the uncertainty interval for confidence level 95%.
• Figure 5: Simulated output trajectories of the estimated LTI models for $u_{\mathrm{test}}$.