Convex Nonparametric Formulation for Identification of Gradient Flows

Khosravi, Mohammad; Smith, Roy S.

doi:10.1109/lcsys.2020.3000176

Cited by 12 publications

(14 citation statements)

References 15 publications

(27 reference statements)

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“…Due to Theorem 12 and Corollary 13, we know that this solution coincides with the solution of (23) provided that m ≥ m * . Nevertheless, compared to (23), the main optimization problem (19) has an additional constraint on the rank of resulting Hankel operator being finite. In the remainder of this section, we fill this gap by employing the notion of finite Hankel rank kernels.…”

Section: Proof See Appendix Bmentioning

confidence: 80%

“…Theorem 16 offers a practical way to solve problem (39). Due to Theorem 12 and Corollary 13, we know that this solution coincides with the solution of (23) provided that m ≥ m * . Nevertheless, compared to (23), the main optimization problem (19) has an additional constraint on the rank of resulting Hankel operator being finite.…”

Section: Proof See Appendix Bmentioning

confidence: 88%

“…Accordingly, any accurate mathematical modeling approach is expected to include this feature and construct an internally positive system. The second aspect is informed system identification [20]- [23] and concerns utilizing the internal positivity side-information and integrating features of this knowledge in the model to improve the estimation accuracy. Indeed, disregarding the positivity information can lead to models, which are not physically interpretable and explainable, or behaviors in contradiction with our expectations [6], [24].…”

Section: Introductionmentioning

confidence: 99%

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Regularized Identification with Internal Positivity Side-Information

Khosravi¹,

Smith²

2021

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In this paper, we present an impulse response identification scheme that incorporates the internal positivity side-information of the system. The realization theory of positive systems establishes specific criteria for the existence of a positive realization for a given transfer function. These transfer function criteria are translated to a set of suitable conditions on the shape and structure of the impulse responses of positive systems. Utilizing these conditions, the impulse response estimation problem is formulated as a constrained optimization in a reproducing kernel Hilbert space equipped with a stable kernel, and suitable constraints are imposed to encode the internal positivity side-information. The optimization problem is infinitedimensional with an infinite number of constraints. An equivalent finite-dimensional convex optimization in the form of a convex quadratic program is derived. The resulting equivalent reformulation makes the proposed approach suitable for numerical simulation and practical implementation. A Monte Carlo numerical experiment evaluates the impact of incorporating the internal positivity side-information in the proposed identification scheme. The effectiveness of the proposed method is demonstrated using data from a heating system experiment.

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Section: Proof See Appendix Bmentioning

confidence: 80%

Section: Proof See Appendix Bmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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Regularized Identification with Internal Positivity Side-Information

Khosravi¹,

Smith²

2021

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“…Due to Lemma 5, we know that L u t : H k → R is a continuous linear map, for each t ∈ T . Therefore, function E D : H k → R, defined in (8), is a convex and continuous function. Since λ > 0, we know that J is a proper and lower semi-continuous strongly convex function.…”

Section: B the Estimation Problem In Stable Reproducing Kernel Hilber...mentioning

confidence: 99%

“…, where E D is defined in (8). Also, we know that the feasible set in ( 29) is a subset of feasible set of (53).…”

Section: Towards a Tractable Schemementioning

confidence: 99%

Kernel-Based Identification with Frequency Domain Side-Information

Khosravi¹,

Smith²

2021

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This paper discusses the problem of system identification when frequency domain side-information is available. Initially, we consider the case where the side-information is provided as the H∞-norm of the system being bounded by a given scalar. This framework allows considering different forms of frequency domain side-information, such as the dissipativity of the system. We propose a nonparametric identification approach for estimating the impulse response of the system under the given side-information. The estimation problem is formulated as a constrained optimization in a stable reproducing kernel Hilbert space, where suitable constraints are considered for incorporating the desired frequency domain features. The resulting optimization has an infinite-dimensional feasible set with an infinite number of constraints. We show that this problem is a well-defined convex program with a unique solution. We propose a heuristic that tightly approximates this unique solution. The proposed approach is equivalent to solving a finite-dimensional convex quadratically constrained quadratic program. The efficiency of the discussed method is verified by several numerical examples.

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