Accurate parameter estimation for safety-critical systems with unmodeled dynamics

Sarker, Arnab; Fisher, P. H.; Gaudio, Joseph E.; Annaswamy, Anuradha M.

doi:10.1016/j.artint.2023.103857

Cited by 6 publications

(6 citation statements)

References 23 publications

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“…Intuitively, this assumption says that the higher order terms are dominated by the second order terms, if the arguments of the function are sufficiently close to the origin. Note that it does not require the function h to be Lipschitz (which is the assumption used in [17]). As an example, consider a scalar system with the dynamics given by f…”

Section: Problem Formulation and Systemmentioning

confidence: 99%

“…The key reason is that the random input and process noise can always drive the system states to undesired regions and excite the higher order terms, unless the input is carefully designed. In fact, the paper [17] shows that random inputs in the single trajectory setup could result in inconsistent estimation under certain conditions even for Lipschitz nonlinearity. In the second example, we investigate the performance of the system identification algorithms under strong nonlinearity (where the assumption of lipschitzness used in [17] no longer holds).…”

Section: A System With Mild Nonlinearitymentioning

confidence: 99%

“…In fact, the paper [17] shows that random inputs in the single trajectory setup could result in inconsistent estimation under certain conditions even for Lipschitz nonlinearity. In the second example, we investigate the performance of the system identification algorithms under strong nonlinearity (where the assumption of lipschitzness used in [17] no longer holds). The virtual model we use here is given by x 1,k+1 x 2,k+1 = 0.9 0.5 0 0.8…”

Section: A System With Mild Nonlinearitymentioning

confidence: 99%

“…truly linear, except for [17]. Furthermore, Gaussian random inputs are typically applied to ensure persistent excitation.…”

Section: Introductionmentioning

confidence: 99%

“…Most relevant to our work is the recent paper [17], which provides a finite sample error bound for learning linear models from systems that have unmodeled dynamics that could capture nonlinearities, using a single system trajectory. However, the method proposed in [17] assumes the system is "well-behaved" by requiring the unmodeled dynamics/nonlinear terms to be (globally) Lipschitz [23]. The method also requires the system to satisfy certain additional properties to ensure consistent estimation, supposing the inputs are carefully chosen.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectories

Xin¹,

Chiu²,

Sundaram³

2022

2022 American Control Conference (ACC)

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Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs, and assumes that the underlying dynamics is truly linear. In contrast, we consider the problem of identifying a linearized model when the true underlying dynamics is nonlinear. We provide a multiple trajectories-based deterministic data acquisition algorithm followed by a regularized least squares algorithm, and provide a finite sample error bound on the learned linearized dynamics. Our error bound demonstrates a tradeoff between the error due to nonlinearity and the error due to noise, and shows that one can learn the linearized dynamics with arbitrarily small error given sufficiently many samples. We validate our results through experiments, where we also show the potential insufficiency of linear system identification using a single trajectory with i.i.d random inputs, when nonlinearity does exist.

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Section: Problem Formulation and Systemmentioning

confidence: 99%

Section: A System With Mild Nonlinearitymentioning

confidence: 99%

Section: A System With Mild Nonlinearitymentioning

confidence: 99%

“…truly linear, except for [17]. Furthermore, Gaussian random inputs are typically applied to ensure persistent excitation.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectories

Xin¹,

Chiu²,

Sundaram³

2022

2022 American Control Conference (ACC)

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Towards targeted exploration for non-stochastic disturbances

Venkatasubramanian,

Köhler,

Cannon

et al. 2024

IFAC-PapersOnLine

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A Risk-Based Decision-Making Process for Autonomous Trains Using POMDP: Case of the Anti-Collision Function

Chelouati,

Boussif,

Beugin

et al. 2024

IEEE Access

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As the railway domain progresses towards autonomy, maintaining safety at levels comparable to human-operated systems is a crucial challenge. Autonomous trains require advanced systems capable of real-time risk assessment and decision-making, a task traditionally managed by human situational awareness. This paper introduces a novel risk-based decision-making approach for autonomous trains, using Partially Observable Markov Decision Processes (POMDPs) for continuous monitoring and evaluation of environmental collision risks. By consistently maintaining an acceptable risk level through ongoing risk estimation (in terms of occurrence probability and severity degree), the approach supports the decisionmaking capabilities of the autonomous driving system in autonomous trains, enabling safe and informed decisions despite the uncertainties in the train's operational state and environmental conditions. The approach's relevance and effectiveness are illustrated through its application in an anti-collision function for autonomous trains.

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Accurate parameter estimation for safety-critical systems with unmodeled dynamics

Cited by 6 publications

References 23 publications

Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectories

Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectories

Towards targeted exploration for non-stochastic disturbances

A Risk-Based Decision-Making Process for Autonomous Trains Using POMDP: Case of the Anti-Collision Function

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