Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches
S. Sivaranjani, Yuanyuan Shi, Nikolay Atanasov, Thai Duong, Jie Feng, Tim Martin, Yuezhu Xu, Vijay Gupta, Frank Allgöwer
TL;DR
The paper surveys how physics-informed and control-oriented priors can be integrated into system identification to produce models with provable control guarantees and better data efficiency. It categorizes approaches into direct parametrization, hard constraints, and soft constraints across classical linear/nonlinear SI and deep learning methods, highlighting examples like Lyapunov/QSR dissipativity, Koopman/Mueller, SINDy, port-Hamiltonian, and Hamiltonian/Lagrangian networks. It demonstrates that vanilla data-driven models may fail to preserve essential control properties and presents optimization- and data-driven verification techniques (behavioral, set-membership) to enforce or certify these properties. The work also outlines future directions including networked, switched, and time-varying systems, experiment design, and tighter integration of ML with control-theoretic representations to achieve scalable, interpretable, and certifiable models for complex physical systems.
Abstract
We survey classical, machine learning, and data-driven system identification approaches to learn control-relevant and physics-informed models of dynamical systems. Recently, machine learning approaches have enabled system identification from noisy, high-dimensional, and complex data. However, their utility is limited by their ability to provide provable guarantees on control-relevant properties. Meanwhile, control theory has identified several properties that are useful in analysis and control synthesis, such as dissipativity, monotonicity, energy conservation, and symmetry-preserving structures. We posit that merging system identification with such control-relevant or physics-informed properties can provide useful inductive bias, enhance explainability, enable control synthesis with provable guarantees, and improve sample complexity. We formulate system identification as an optimization problem where control-relevant properties can be enforced through direct parameterization (constraining the model structure to satisfy a desired property by construction), soft constraints (encouraging control-relevant properties through regularization or penalty terms), and hard constraints (imposing control-relevant properties as constraints in the optimization problem). Through this lens, we survey methods to learn physics-informed and control-relevant models spanning classical linear and nonlinear system identification, machine learning approaches, and direct identification through data-driven and behavioral representations. We also provide several expository examples that are accompanied by code and brief tutorials on a public Github repository. We also describe challenging directions for future research, including identification in networked, switched, and time-varying systems, experiment design, and bridging the gaps between data-driven, learning-based, and control-oriented approaches.