On the optimal control of rate-independent soft crawlers

Colombo, Giovanni; Gidoni, Paolo

doi:10.1016/j.matpur.2020.11.005

Cited by 17 publications

(12 citation statements)

References 29 publications

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“…These two results are the basis for the study of optimal gaits for our models, as it has been recently proposed in [3].…”

Section: Introductionmentioning

confidence: 66%

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

Colombo¹,

Gidoni²,

Vilches³

2021

Preprint

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We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger W 1,2 convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only convergence.

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“…These two results are the basis for the study of optimal gaits for our models, as it has been recently proposed in [3].…”

Section: Introductionmentioning

confidence: 66%

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

Colombo¹,

Gidoni²,

Vilches³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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“…These two results are the basis for the study of optimal gaits for our models, as it has been recently proposed in [4].…”

mentioning

confidence: 66%

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

Colombo¹,

Gidoni²,

Vilches³

2022

DCDS

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<p style='text-indent:20px;'>We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger <inline-formula><tex-math id="M1">\begin{document}$ W^{1,2} $\end{document}</tex-math></inline-formula> convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only convergence.</p>

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“…Sweeping differential inclusions are highly discontinuous, and the machinery of Lipschitzian variational analysis is not applicable in the sweeping framework. Further developments of this method in various sweeping control settings can be found in [2,9,8,10,13,14] and the references therein. However, neither these publications, nor those of [5,15,35] exploring other approaches to deriving optimality conditions in different models of sweeping optimal control address additional endpoint constraints x(T ) ∈ Ω on sweeping trajectories.…”

Section: Discrete Approximations Of Controlled Sweeping Processesmentioning

confidence: 99%

“…The third topic we investigate here concerns an optimal control problem for the sweeping process in (1.1) and (1.2) under the additional pointwise equality constraint on the u-component of controls and geometric endpoint constraint x (u,b) ∈ Ω on trajectories. Optimal control theory for sweeping processes, with addressing the main issue of deriving necessary optimality conditions, has been started rather recently in [11] and then has been extensively developed in subsequent publications (see, e.g., [2,5,8,9,10,12,13,14,15,35] and the references therein), which did not concern however systems with endpoint constraints. Problems of sweeping optimal control, that are governed by discontinuous dif-ferential inclusions with intrinsic pointwise and irregular state constraints, constitute one of the most challenging class in modern control theory.…”

Section: Introduction and Problem Formulationmentioning

confidence: 99%

Controlled polyhedral sweeping processes: existence, stability, and optimality conditions

Henrion¹,

Jourani²,

Mordukhovich³

2021

Preprint

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This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and suboptimality conditions for sweeping control systems with endpoint constrains by using constructive discrete approximations.

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On the optimal control of rate-independent soft crawlers

Cited by 17 publications

References 29 publications

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

Controlled polyhedral sweeping processes: existence, stability, and optimality conditions

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