Efficient identification of linear, parameter-varying, and nonlinear systems with noise models

2025-04-16

AI Summary

This work addresses the unified identification of linear time-invariant (LTI), linear parameter-varying (LPV), and nonlinear (NL) dynamical systems under complex noise models. Methodologically, it introduces a general state-space framework that is both theoretically consistent and computationally efficient. The core contribution lies in the first extension of the well-established deterministic/stochastic decoupling paradigm—previously confined to LTI systems—to LPV and NL settings, enabling joint optimization and co-adaptation of dynamics structure and noise model. Nonlinear mappings are parameterized via neural networks, while constrained quasi-Newton optimization with automatic differentiation enables end-to-end minimization of prediction error. Empirically, the method achieves significantly higher accuracy than existing ANN-based approaches across diverse benchmark tasks, reduces training time from hours to seconds, and maintains statistical consistency and strong generalization performance.

Technology Category

• Natural Language Processing: Learning & Optimization for NLP
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We present a general system identification procedure capable of estimating of a broad spectrum of state-space dynamical models, including linear time-invariant (LTI), linear parameter-varying} (LPV), and nonlinear (NL) dynamics, along with rather general classes of noise models. Similar to the LTI case, we show that for this general class of model structures, including the NL case, the model dynamics can be separated into a deterministic process and a stochastic noise part, allowing to seamlessly tune the complexity of the combined model both in terms of nonlinearity and noise modeling. We parameterize the involved nonlinear functional relations by means of artificial neural-networks (ANNs), although alternative parametric nonlinear mappings can also be used. To estimate the resulting model structures, we optimize a prediction-error-based criterion using an efficient combination of a constrained quasi-Newton approach and automatic differentiation, achieving training times in the order of seconds compared to existing state-of-the-art ANN methods which may require hours for models of similar complexity. We formally establish the consistency guarantees for the proposed approach and demonstrate its superior estimation accuracy and computational efficiency on several benchmark LTI, LPV, and NL system identification problems.

Problem

• Identify diverse dynamical systems with noise models
• Separate deterministic and stochastic parts in nonlinear systems
• Optimize model estimation using efficient computational methods

Innovation

• General system identification for LTI, LPV, and NL dynamics
• Parameterize nonlinear relations using artificial neural networks
• Efficient optimization via quasi-Newton and automatic differentiation