Sweeping process with regular and nonregular sets

By Lionel Thibault. 2003

193 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/ae80c17801a793402d12137cebb5a82eb0f9d2d2

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

On optimal control of a sweeping process coupled with an ordinary differential equation (2014, background): “More references to and applications of (1) can be found in [19] or [37].”
Optimal control of the sweeping process over polyhedral controlled sets (2015, background): “Such a boundedness reduction was first established in [42] for the sweeping process with an absolutely continuous moving set C(t), which is not the case here, and then was further developed in [11] for (1.”
Prox-regular sets and epigraphs in uniformly convex Banach spaces: Various regularities and other properties (2011, background): “, [19, 24, 42]), in resource allocation mechanisms in economics (see, e.”
Characterizations of Prox-Regular Sets in Uniformly Convex Banach Spaces (2006, background): “For other recent applications to evolution problems with moving sets putting in light the amenability of prox-regular and proximally smooth sets, we refer to [24, 43].”
Differential variational inequalities (2008, background): “13) to nonconvex K(t, x) can be found, for instance, in [15,39,100].”
A Maximum Principle for the Controlled Sweeping Process (2016, background): “itz as a set-valued map depending on the time t, and the perturbation f is Lipschitz, then it is well known that the Cauchy problem (1.1), (1.2) admits one and only one Lipschitz solution (see, e.g., [23]). Observe that the state constraint x(t) ∈ C(t) for all t ∈ [0,T] is built in the dynamics, bei”
Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems (2010, methodology): “Then the results obtained elsewhere by Thibault and his co-workers [16, 15, 40] on the well-posedness of the sweeping process are used.”
OPTIMAL CONTROL OF THE SWEEPING PROCESS (2012, background): “On the other hand, it is proved by Thibault [18] that the unbounded differential inclusion of the sweeping process (1.”