Learning Surrogate LPV State-Space Models with Uncertainty Quantification

• URL: http://arxiv.org/abs/2603.29532v1
• Date: Tue, 31 Mar 2026 10:13:25 GMT
• Title: Learning Surrogate LPV State-Space Models with Uncertainty Quantification
• Abstract summary: The Linear -Varying (LPV) framework enables the construction of surrogate models of complex nonlinear and high-dimensional systems.<n>Existing approaches do not quantify the uncertainty of the obtained LPV models.<n>This paper proposes a Bayesian approach for the joint estimation of LPV state-space models.
• Score: 0.815557531820863
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

Related papers

• Joint Model and Data Sparsification via the Marginal Likelihood [53.29070892356214]
  We propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification.<n>This symmetric pruning of model and data offers a natural extension that preserves conjugacy.<n> Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.
  arXiv  Detail & Related papers  (2026-05-28T13:26:53Z)
• Quantifying and Attributing Submodel Uncertainty in Stochastic Simulation Models and Digital Twins [0.1234398109349733]
  This paper investigates how submodel uncertainty affects the estimation of system performance metrics.<n>We develop a framework for quantifying submodel uncertainty in simulation models and extend the framework to digital-twin settings.
  arXiv  Detail & Related papers  (2026-02-18T00:06:39Z)
• Safety Beyond the Training Data: Robust Out-of-Distribution MPC via Conformalized System Level Synthesis [3.5174884177930448]
  We present a novel framework for robust out-of-distribution planning and control using conformal prediction (CP) and system level synthesis (SLS)<n>We first derive high-confidence model error bounds using weighted CP with a learned, state-control-dependent covariance model.<n>These bounds are integrated into an SLS-based robust nonlinear model predictive control (MPC) formulation, which performs constraint tightening over the prediction horizon via volume-optimized forward reachable sets.
  arXiv  Detail & Related papers  (2026-02-12T15:11:44Z)
• Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification [6.5745172279769255]
  We propose a neural network-based state-space model that simultaneously learns latent states and internal scheduling variables.<n>The state-transition matrix is guaranteed to be stable through a Schur-based parameterization.<n>The proposed NN-SS is evaluated on benchmark nonlinear systems, and the results demonstrate that the model consistently matches or surpasses classical subspace identification methods.
  arXiv  Detail & Related papers  (2025-10-21T10:25:54Z)
• Model Correlation Detection via Random Selection Probing [62.093777777813756]
  Existing similarity-based methods require access to model parameters or produce scores without thresholds.<n>We introduce Random Selection Probing (RSP), a hypothesis-testing framework that formulates model correlation detection as a statistical test.<n>RSP produces rigorous p-values that quantify evidence of correlation.
  arXiv  Detail & Related papers  (2025-09-29T01:40:26Z)
• Efficient identification of linear, parameter-varying, and nonlinear systems with noise models [1.6385815610837167]
  We present a general system identification procedure capable of estimating a broad spectrum of state-space dynamical models.<n>We show that for this general class of model structures, the model dynamics can be separated into a deterministic process and a noise part.<n>We parameterize the involved nonlinear functional relations by means of artificial neural-networks (ANNs)
  arXiv  Detail & Related papers  (2025-04-16T11:23:30Z)
• Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study [56.283944756315066]
  We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman modeling and state estimation. A case study demonstrates that our approach provides accurate control models and enables real-time capable nonlinear model predictive control of a high-purity cryogenic distillation column.
  arXiv  Detail & Related papers  (2024-01-09T11:54:54Z)
• End-to-End Reinforcement Learning of Koopman Models for Economic Nonlinear Model Predictive Control [45.84205238554709]
  We present a method for reinforcement learning of Koopman surrogate models for optimal performance as part of (e)NMPC. We show that the end-to-end trained models outperform those trained using system identification in (e)NMPC.
  arXiv  Detail & Related papers  (2023-08-03T10:21:53Z)
• Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty [68.00748155945047]
  Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. Our contribution is a novel abstraction-based controller method for continuous-state models with noise, uncertain parameters, and external disturbances.
  arXiv  Detail & Related papers  (2022-10-12T07:57:03Z)
• COMBO: Conservative Offline Model-Based Policy Optimization [120.55713363569845]
  Uncertainty estimation with complex models, such as deep neural networks, can be difficult and unreliable. We develop a new model-based offline RL algorithm, COMBO, that regularizes the value function on out-of-support state-actions. We find that COMBO consistently performs as well or better as compared to prior offline model-free and model-based methods.
  arXiv  Detail & Related papers  (2021-02-16T18:50:32Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)
• DISCO: Double Likelihood-free Inference Stochastic Control [29.84276469617019]
  We propose to leverage the power of modern simulators and recent techniques in Bayesian statistics for likelihood-free inference. The posterior distribution over simulation parameters is propagated through a potentially non-analytical model of the system. Experiments show that the controller proposed attained superior performance and robustness on classical control and robotics tasks.
  arXiv  Detail & Related papers  (2020-02-18T05:29:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.