system identification

This paper addresses the problem of improving dynamical system identification accuracy for a target linear system using auxiliary data from a similar—but non-homologous—linear system, particularly under limited target-data regimes. To tackle the challenge of fusing heterogeneous main and auxiliary datasets with scarce target samples, we propose a weighted least-squares identification method. Our key theoretical contribution is the first derivation of a computable, data-dependent finite-sample error upper bound. We rigorously characterize a fundamental trade-off between noise suppression and model discrepancy, yielding an explicit error bound that provably demonstrates substantial reduction in noise-induced estimation error through auxiliary data. Furthermore, we establish an adaptive weighting criterion that optimizes this trade-off. Extensive simulations confirm that the proposed method reduces identification error by over 30% across representative scenarios, providing a robust, analytically tractable framework for cross-system knowledge transfer in dynamical modeling.

This work addresses the problem of unsupervised learning of low-dimensional, manipulable dynamical system representations—namely, compact and smooth state variables coupled with differentiable vector fields—directly from raw video, without prior physical knowledge or domain-specific assumptions. We propose the first end-to-end, video-driven framework for manipulable dynamics discovery, integrating neural implicit state modeling, contrastive spatiotemporal regularization, and differential-geometric constraints to jointly ensure state interpretability, dynamical differentiability, and behavioral analyzability. Evaluated across diverse dynamical systems—including chaotic, limit-cycle, stable fixed-point, and natural oscillatory regimes—the method accurately recovers essential dynamical features (e.g., attractors, bifurcations, conserved quantities) and achieves significantly higher long-horizon prediction accuracy than existing baselines.

Integrating physics-based and machine learning models for dynamic system modeling remains challenging due to difficulties in unifying multi-model representations, handling algebraic loops, and managing discontinuous events within a coherent framework. Method: This paper proposes a learnable and interpretable hybrid modeling paradigm built upon a novel wildcard architecture—the first to enable unified symbolic representation of algebraic, discrete, and differential equations—supporting end-to-end differentiable joint optimization of physics-informed and data-driven components. Grounded in systems theory and symbolic modeling principles, the approach inherently avoids algebraic loops and explicitly models discontinuities. Contribution/Results: Experiments demonstrate that the framework automatically identifies and resolves diverse dual-model compositions, achieving significant improvements over state-of-the-art methods in prediction accuracy, model interpretability, and cross-scenario generalizability.

This paper addresses Bayesian state estimation and prediction for nonlinear dynamical systems with unknown dynamics and no access to ground-truth state labels. Method: We propose a fully model-free, unsupervised framework that derives a closed-form analytical solution for the posterior state distribution directly from raw measurement data—without requiring system equations or labeled states. By integrating a data-driven RNN to implicitly encode the dynamics prior and coupling it with analytical Bayesian updating, our approach bypasses explicit modeling assumptions. A linear observation model ensures tractability while preserving theoretical rigor and computational feasibility. Results: Experiments on high-dimensional chaotic systems (e.g., Lorenz and Chen) demonstrate estimation and prediction accuracy competitive with KF, EKF, UKF, KalmanNet, and DMM—significantly extending the applicability of Bayesian filtering to scenarios where the underlying dynamics are entirely unknown.

This paper addresses the finite-sample identification of the system matrix (A^*) for linear dynamical systems under convex set constraints, based on a single trajectory of length (T). To overcome the low sample efficiency of conventional unconstrained estimators, we propose a constrained least-squares estimation framework. We establish, for the first time, non-asymptotic error bounds for this estimator, explicitly quantifying how local geometric properties—such as the local Rademacher complexity—affect sample complexity. Our method integrates convex optimization with structured modeling to uniformly handle four canonical structural priors: sparsity, subspace constraints, convex regression, and Lipschitz row-wise constraints. Theoretically, we prove that, under such structural constraints, reliable estimation is achievable with significantly fewer samples than required in the unconstrained setting—thereby substantially improving identification efficiency in the small-sample regime.

This study addresses the challenge of global linear modeling and control for highly nonlinear dynamical systems by leveraging Koopman operator theory. By introducing observable functions, the nonlinear dynamics are lifted into a higher-dimensional space where they admit an approximately linear representation. A data-driven surrogate model is constructed through a synergistic integration of Extended Dynamic Mode Decomposition (EDMD), kernelized EDMD, and machine learning techniques. The work innovatively extends the Koopman framework to input-affine systems, proposing a unified modeling approach and a corresponding Koopman-based Model Predictive Control (MPC) design methodology. Numerical simulations demonstrate that the proposed method achieves high-fidelity modeling accuracy and effective closed-loop control performance. Full reproducibility is supported by the accompanying open-source implementation.

This work addresses the challenge of modeling dynamical systems subject to state-dependent, non-i.i.d., and non-Gaussian noise by proposing a general identification framework. By integrating dynamical system embedding theory with random feature mappings, the method extends classical noise-free system identification approaches to complex stochastic environments. It establishes that only \(2p+1\) random features are sufficient to uniquely identify continuous or discrete-time dynamical models containing \(p\) parameters. Theoretical analysis provides identifiability guarantees for a broad class of stochastic dynamical systems, while numerical experiments on the Lorenz-63 system and Hénon map demonstrate the method’s efficacy in accurately recovering underlying system structures from observations corrupted by strongly correlated, non-Gaussian noise.

This work addresses the challenge of high computational complexity in Gaussian process model predictive control (GP-MPC) for time-varying systems, which hinders real-time deployment. To overcome this limitation, the authors propose a spatiotemporal Gaussian process approximation method tailored for MPC optimization. By integrating structured approximations with an efficient online learning mechanism, the approach enables real-time modeling of system dynamics while maintaining constant computational complexity. As the first GP-MPC framework to support constant-complexity real-time online learning, it substantially improves both control accuracy and response speed. The effectiveness of the proposed method is validated through simulations and hardware experiments on an autonomous miniature race car, demonstrating superior control performance and real-time capability compared to existing approaches.

This study addresses the limitations of traditional state-space models, which rely on predefined nonlinear dynamics and struggle with theoretically under-specified complex systems, as well as the high computational cost of Bayesian inference in Gaussian process state-space models for moderately long sequences. To overcome these challenges, the authors propose two enhanced Gibbs sampling strategies that substantially improve sampling efficiency and convergence reliability. By integrating confirmatory factor analysis to construct an identifiable and interpretable measurement structure, they develop a comprehensive framework for learning nonlinear latent dynamical systems. Simulation studies validate the accuracy of posterior inference, while two empirical applications demonstrate the method’s practical utility and interpretability. An open-source implementation is provided, offering researchers an efficient and feasible workflow for empirical analysis.

This work investigates whether an analytic system model, linearly parameterized over a prescribed dictionary (e.g., partial differential operators or dynamical system terms), can be uniquely identified from a single input–response trajectory. By analyzing the linear independence of dictionary elements under a single observation, the authors establish and prove a sharp zero–one law: either no input enables unique identification, or almost every input drawn from a non-degenerate Gaussian measure permits exact recovery. This result reframes one-shot system identification as a problem of detecting degenerate inputs and provides a posteriori verification. Combining tools from linear algebra, measure theory, and system identification, the approach successfully reconstructs dynamical systems, nonlinear partial differential equations, and structured matrix families from a single trajectory, while accurately determining whether additional probing signals are necessary.