scholarly journals Optimization of fully controlled sweeping processes

2021 ◽  
Vol 295 ◽  
pp. 138-186
Author(s):  
Tan H. Cao ◽  
Giovanni Colombo ◽  
Boris S. Mordukhovich ◽  
Dao Nguyen
Keyword(s):  
Sweeping Processes

Optimal Control Involving Sweeping Processes

2018 ◽  
Vol 27 (2) ◽  
pp. 523-548 ◽  
Author(s):  
M. d. R. de Pinho ◽  
M. M. A. Ferreira ◽  
G. V. Smirnov
Keyword(s):  
Optimal Control ◽  
Sweeping Processes

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

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Giovanni Colombo ◽  
Paolo Gidoni ◽  
Emilio Vilches
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Finite Time ◽  
Dry Friction ◽  
Average Velocity ◽  
Well Posedness ◽  
Asymptotic Velocity ◽  
Sweeping Processes

<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>

scholarly journals One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model

2020 ◽  
Vol 15 ◽  
pp. 25
Author(s):  
Ivan Gudoshnikov ◽  
Mikhail Kamenskii ◽  
Oleg Makarenkov ◽  
Natalia Voskovskaia
Keyword(s):  
Stability Analysis ◽  
Cyclic Loading ◽  
Finite Time ◽  
Stability Result ◽  
Stress Evolution ◽  
Time Stability ◽  
Elastoplastic Model ◽  
Finite Time Stability ◽  
Sweeping Processes ◽  
Simple Network

We offer a finite-time stability result for Moreau sweeping processes on the plane with periodically moving polyhedron. The result is used to establish the convergence of stress evolution of a simple network of elastoplastic springs to a unique cyclic response in just one cycle of the external displacement-controlled cyclic loading. The paper concludes with an example showing that smoothing the vertices of the polyhedron makes finite-time stability impossible.

Airside Velocity Measurement Above the Wind-Generated Water Waves

2007 ◽  
Author(s):  
Nasiruddin Shaikh ◽  
Kamran Siddiqui
Keyword(s):  
Water Waves ◽  
Flow Behavior ◽  
Momentum Exchange ◽  
Mean Velocity ◽  
Wind Speeds ◽  
Velocity Magnitude ◽  
Image Velocimetry ◽  
Sweeping Processes ◽  
High Level ◽  
The Waves

An experimental study conducted to investigate the airside flow behavior within the crest-trough region over wind generated water waves is reported. Two-dimensional velocity field in a plane perpendicular to the surface was measured using particle image velocimetry (PIV) at wind speeds ranging from 1.5 m s−1 to 4.4 m s−1. The results show a reduction in the mean velocity magnitude when gravity waves appear on the surface. A sequence of consecutive velocity fields has shown the bursting and sweeping processes and the flow separation above the waves. The results also indicate that the flow dynamics in the crest-trough region are significantly different than that at greater heights. High level of turbulence was observed in this region which could not be predicted from the measurements at greater heights. Thus, it is concluded that the quantitative investigation of the flow in the immediate vicinity of the interface is vital for an improved understanding of the heat, mass and momentum exchange between air and water.

scholarly journals Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Messaoud Bounkhel
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Growth Conditions ◽  
Existence Results ◽  
Nonlinear Growth ◽  
Upper Semicontinuous ◽  
Set Valued Mapping ◽  
Sweeping Processes

In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is,ẋ(t)∈F(t,x(t))a.e. onI,x(t)∈S,∀t∈I,x(0)=x0∈S, (*), whereSis a closed subset in a Banach space𝕏,I=[0,T],(T>0),F:I×S→𝕏, is an upper semicontinuous set-valued mapping with convex values satisfyingF(t,x)⊂c(t)x+xp𝒦,∀(t,x)∈I×S, wherep∈ℝ, withp≠1, andc∈C([0,T],ℝ+). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.

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