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Learned dynamical models should be forced to obey control-relevant properties such as dissipativity, monotonicity, and symmetry, because a good data fit alone does not guarantee a usable control model.

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2026-08-03 18:10 UTC pith:ZKIT5SL3

load-bearing objection A useful survey/tutorial whose three-way taxonomy is the real contribution; the headline benefits are plausible but mostly unproven, and the paper itself flags the key caveat. the 1 major comments →

arxiv 2512.06315 v2 pith:ZKIT5SL3 submitted 2025-12-06 eess.SY cs.SYmath.OC

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
show 1 more author
Frank Allg\"ower
This is my paper
classification eess.SY cs.SYmath.OC MSC 93-0293B3093C1093D25
keywords system identificationphysics-informed learningcontrol-oriented identificationdissipativitymonotone systemsport-Hamiltonian modelsdata-driven controlbehavioral systems theory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This survey postulates that system identification—whether classical, machine learning, or data-driven—should preserve control-relevant properties of the true system, such as dissipativity, monotonicity, energy conservation, and symmetry. It frames identification as an optimization problem in which these properties are enforced in one of three ways: building them into the model parameterization, imposing them as hard constraints, or encouraging them through soft penalty terms. The paper supports its thesis with a counter-example showing that a linear model can fit a passive system to 99.6% accuracy yet fail to be passive, and with examples where physics-informed models match or beat unstructured models. If the thesis holds, controllers designed from identified models can inherit provable stability and compositionality guarantees instead of relying on the hope that a good fit implies a dependable model.

Core claim

The paper's central claim is that merging system identification with physics-informed or control-relevant properties—dissipativity, monotonicity, energy conservation, and symmetry-preserving Lagrangian/Hamiltonian structure—yields models with useful inductive bias, explainability, provable control guarantees, and improved sample complexity. Because even an excellent fit does not preserve these properties (Example 3.2 finds a 99.6%-fit model that is not passive), the survey contends that property preservation must be built into identification explicitly. It organizes the field through the optimization problem (21), where properties are enforced by direct parameterization, hard constraints g(θ

What carries the argument

The unifying object is the constrained identification optimization: minimize a fit cost plus regularization over model parameters, subject to property constraints and a chosen model parameterization. The control-relevant properties it packages are dissipativity (an energy-balance inequality, whose QSR form reduces to a linear matrix inequality for linear systems), monotonicity (order preservation), and symmetry or conservation laws, realized through Lagrangian, Hamiltonian, and port-Hamiltonian structures. The paper distinguishes three enforcement mechanisms—direct parameterization, hard constraints, and soft constraints—and treats Willems' fundamental lemma plus set-membership outer approxi

Load-bearing premise

The central premise is that the property being enforced—dissipativity, monotonicity, energy conservation, or symmetry—actually holds for the true system; if the real dynamics deviate from that prior, enforcing the property injects model bias and can invalidate the guarantees.

What would settle it

Train a hard-constrained stable or dissipative model and an unconstrained model on data from a system that only approximately satisfies the property (for example, a pendulum with unmodeled friction), then show the constrained model's out-of-distribution prediction error exceeds the unconstrained model's while its certified property still holds.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Identified models can be certified to be passive, dissipative, stable, or monotone before being used in control synthesis, closing a gap shown by the 99.6%-fit counter-example.
  • Physics-informed architectures (Hamiltonian or Lagrangian neural ODEs, monotone networks) promise better sample efficiency and generalization than unstructured approximators on the same data.
  • Direct data-driven verification via the fundamental lemma or set-membership methods can certify properties from single or noisy trajectories without first building a state-space model.
  • The hard, soft, and direct parameterization taxonomy gives practitioners a menu for trading strict guarantees against model bias and expressiveness.
  • A universal approximation theory for structured model classes would formalize how much expressiveness is lost when properties are enforced.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same three-way enforcement taxonomy could be applied to networked and switched system identification, where the paper notes that properties like dissipativity need redefinition; a natural extension is to use the framework to define mode-dependent storage functions during identification.
  • The counter-example suggests a practical model-selection criterion beyond fit: among models with comparable validation error, prefer ones that satisfy the target property; this could be tested systematically on standard benchmark systems.
  • Enforcing a property in the model does not guarantee robustness if the true system violates that property; a testable extension is to quantify, for a given property and dataset, the error range in which hard-constraint benefit turns into bias harm.
  • The taxonomy could inform experiment design: choose inputs that make the target property identifiable, not just persistently exciting.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 3 minor

Summary. The paper surveys the field of control-oriented system identification with physics-informed and control-relevant constraints. It organizes the literature through the constrained optimization formulation in Eq. (21), classifying approaches into direct parameterization, hard constraints, and soft constraints. The survey covers classical linear and nonlinear identification, deep learning architectures (neural ODEs, RENs, Hamiltonian/Lagrangian and monotone networks, PINNs), and behavioral/data-driven methods, including set-membership verification and online schemes. Several expository examples with accompanying code are provided, and the paper ends with future directions on networked, switched, and time-varying systems, experiment design, and tradeoffs between structure and expressivity.

Significance. The paper is a timely and well-organized survey that provides a useful map of an emerging area. The proposed taxonomy (direct parameterization / hard constraints / soft constraints) is a practical organizing principle, and the expository examples—especially the non-passivity counterexample in Example 3.2, the passivity-preserving perturbation in Example 4.1, and the stable Koopman model in Example 4.2—concretely illustrate the main ideas. The associated GitHub repository is a valuable asset for reproducibility. The paper states standard results (Lyapunov stability, dissipativity LMIs, Willems' fundamental lemma) accurately and is honest about the tradeoffs in Section 7.6. Its central claims are framed as a research program rather than as established theorems, which is appropriate for a survey. The main limitation is that the advertised benefits are conditional on the correctness of the physical prior and on bridging model-level guarantees to closed-loop guarantees; this should be made more explicit in the abstract and Section 3.1.

major comments (1)
  1. [Abstract and Sec. 3.1 / Sec. 7.6] The paper advertises that property-preserving identification can 'enable control synthesis with provable guarantees' and 'improve sample complexity.' These benefits are conditional on the physical prior actually holding for the true system, and model-level property certificates do not by themselves imply plant-level closed-loop guarantees unless model-error bounds are also available. Section 7.6 acknowledges the bias-variance tradeoff but does not provide a criterion for deciding when enforcing a property helps versus harms. I recommend adding a short paragraph in Sec. 3.1 or 7.6 that explicitly distinguishes model-level properties from closed-loop guarantees and states that the benefits are guaranteed only when the constrained model class contains the true system.
minor comments (3)
  1. [Eq. (30)] The Hamiltonian matrix M_H appears to be missing the bottom-right block in the displayed equation; the second row is also typeset in a garbled way. Please check the formatting and verify the standard expression for the passivity Hamiltonian.
  2. [Definition 2.3] The supply-rate condition is written as 'TR 0 |s(u,y)dt|<∞', which is typeset incorrectly. It should be an integral over [0,T] of |s(u,y)|, likely with a suitable absolute integrability condition.
  3. [Sec. 5.5] There is a typo in 'This aspects will be further discussed'—should be 'This aspect' or 'These aspects.' Also, in the caption of Figure 10, 'V oltage' should be 'Voltage.'

Circularity Check

0 steps flagged

No significant circularity; the central thesis is explicitly a postulate and the examples are illustrative, with limitations disclosed.

full rationale

The paper is a survey and does not derive the central claim. Section 3.1 states: "we postulate that merging system identification algorithms 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." This is a research program, not a result derived from its own inputs. The optimization formulation (21) is a definitional taxonomy (direct parameterization, hard constraints, soft constraints), not a prediction. The expository examples that cite the authors' own work (Duong et al. 2024a/b, Feng et al. 2023, Xu and Sivaranjani 2023) are feasibility illustrations with publicly available code, and the surrounding text also cites independent literature (Cranmer, Greydanus, Zhong, Miller, Ljung, etc.). None of the examples takes a fitted quantity and renames it as a prediction: e.g., Example 5.3 reports that after weight perturbation the model is dissipative, which is a constraint-satisfaction check, and Examples 5.1 and 5.2 evaluate accuracy honestly (Example 5.2 reports MNNs are "comparable but slightly worse" than a standard FNN). The paper's own limitation statement in Section 7.6 — "hard constraints or rigid model parameterizations can introduce model bias" — explicitly bounds the thesis; this is a correctness caveat, not circularity. Similarly, Section 6.1's disclaimer that fundamental-lemma-based verification requires "noise-free measurements, is restricted to finite horizon, and an extension to general nonlinear systems is unknown" is an assumption disclosure, not a circular step. No equation is shown to reduce to its input by construction; no fitted parameter is renamed as a prediction; no uniqueness or ansatz is imported from a self-citation. The conditionality of the claimed benefits is exactly what the paper concedes. Therefore, score 0.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central claim of the survey is a research direction, so the ledger lists the background theorems and domain assumptions on which the surveyed methods rest. No new entities are introduced. The most important unresolved assumption is that the control-relevant properties being enforced are true of the real system; the paper itself notes that hard constraints and rigid parameterizations can introduce model bias (Sec. 7.6).

free parameters (4)
  • Soft-constraint penalty λ = 200
    Chosen by hand in Example 4.2 (Koopman/Duffing) to balance fit and stability; illustrative, not a fitted physical constant.
  • Number of RBF centers N_rbf = 8
    Hand-chosen in Example 4.2 for the Koopman lifting function; illustrative.
  • Noise bound ε = 0.002–0.04
    Assumed known in Example 6.2; controls the size of the set membership and the quality of the dissipativity inference.
  • Perturbation weights λ1, λ2, λ = 10, 10, 27.822
    Used in Example 5.3 (after Xu and Sivaranjani 2023) to enforce passivity via weight perturbation; illustrative.
axioms (6)
  • standard math Lyapunov stability theorem and LaSalle's invariance principle
    Invoked in Sec. 2.3.1 to define and certify stability; standard textbook results (Khalil 2002) relied on without proof.
  • domain assumption Willems' fundamental lemma
    Underpins Sec. 6 data-driven verification; assumes LTI dynamics, persistently exciting input, and noise-free data over finite horizons. Paper flags these restrictions at the end of Sec. 6.1.
  • standard math LMI dissipativity characterization for LTI systems (Eq. 16)
    Used throughout to impose passivity/dissipativity via P≻0 and LMI constraints; standard result from dissipativity theory.
  • standard math Positive real lemma
    Used in Example 4.1 to certify passivity of the RLC model; standard frequency-domain/state-space equivalence.
  • standard math Universal approximation by feedforward and recurrent neural networks
    Assumed in Sec. 5.1 to justify FNN/RNN as flexible model classes for system identification.
  • domain assumption Physics/control properties actually hold for the systems being identified
    Central motivation; if false, enforcing these properties injects bias. The paper acknowledges this tradeoff in Sec. 7.6.

pith-pipeline@v1.3.0-alltime-deepseek · 55317 in / 14874 out tokens · 137266 ms · 2026-08-03T18:10:16.722888+00:00 · methodology

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read the original 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.

Figures

Figures reproduced from arXiv: 2512.06315 by Frank Allg\"ower, Jie Feng, Nikolay Atanasov, S. Sivaranjani, Thai Duong, Tim Martin, Vijay Gupta, Yuanyuan Shi, Yuezhu Xu.

Figure 1
Figure 1. Figure 1: Pendulum dynamics identification using an [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Linear system vs model trajectories for Example [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Approaches to impose control-oriented properties in optimization-based formulation of system identification. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Passive linear model vs system trajectories for for Example [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Koopman operator model with soft constraints vs Koopman Model [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Learning a piecewise-linear dynamics function [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Overview of the deep learning architectures and control-oriented architectures for system identification. [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Real experiments with S E(3) port-Hamiltonian neural ODE network Duong et al. (2024b). Example 5.1 (Quadrotor Dynamics Identification using Port-Hamiltonian Neural ODE Network). To illustrate a Hamiltonian neural network for system identification, we pro￾vide an example from Duong et al. (2024b) where both Hamilto￾nian structure and the state manifold constraints are encoded in the neural network architect… view at source ↗
Figure 9
Figure 9. Figure 9: S E(3) port-Hamiltonian neural ODE network on a Crazyflie quadro￾tor in the PyBullet simulator (Panerati et al., 2020). (f(x) − f(x ′ ))⊤(x − x ′ ) ≥ 0. In this case, Cui et al. (2024) is in￾spired by the fact that gradients of convex functions are mono￾tone, and constructs MIMO monotone neural networks (MNN) using gradients of strictly convex neural networks (termed MNN1 in [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 10
Figure 10. Figure 10: Voltage trajectories of the ground truth using real-world load data, [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Trajectories of the ground truth, the fit for baseline model, model [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of hard projection and soft penalty approach for learn [PITH_FULL_IMAGE:figures/full_fig_p026_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Projected set membership (83) for ϵ = 0.005 and different data length N (top) and (83) for N = 21 and different noise bounds ϵ (bottom). True coefficients are depicted by a black dot [PITH_FULL_IMAGE:figures/full_fig_p029_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Data-driven inference on the L2-gain. 0.2 0.5 1 2 3 4 ·10−2 −8 −6 −4 −2 0 ϵ ρ Model-based Data-driven N = 21 Data-driven N = 7 Data-driven N = 5 [PITH_FULL_IMAGE:figures/full_fig_p030_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Data-driven inference on the input-feedforward passivity parameter. [PITH_FULL_IMAGE:figures/full_fig_p030_16.png] view at source ↗

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