Search results for "differential inclusion"
showing 10 items of 21 documents
Constrained differential inclusions with nonlocal initial conditions
2017
International audience; We show existence for the perturbed sweeping process with nonlocal initial conditions under very general hypotheses. Periodic, anti-periodic, mean value and multipoints conditions are included in this study. We give abstract results for differential inclusions with nonlocal initial conditions through bounding functions and tangential conditions. Some applications to differential complementarity systems and to vector hysteresis are given.
Game-Theoretic Learning and Allocations in Robust Dynamic Coalitional Games
2019
The problem of allocation in coalitional games with noisy observations and dynamic environments is considered. The evolution of the excess is modeled by a stochastic differential inclusion involvin...
The interrelation between stochastic differential inclusions and set-valued stochastic differential equations
2013
Abstract In this paper we connect the well established theory of stochastic differential inclusions with a new theory of set-valued stochastic differential equations. Solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty, bounded, convex and closed subsets of the space L 2 consisting of square integrable random vectors. We show that for the solution X to a set-valued stochastic differential equation corresponding to a stochastic differential inclusion, there exists a solution x for this inclusion that is a ‖ ⋅ ‖ L 2 -continuous selection of X . This result enables us to draw inferences about the reachable sets of solutio…
Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity
2021
We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex value…
Necessary Optimality Conditions in Multiobjective Dynamic Optimization
2004
We consider a nonsmooth multiobjective optimal control problem related to a general preference. Both differential inclusion and endpoint constraints are involved. Necessary conditions and Hamiltonian necessary conditions expressed in terms of the limiting Frechet subdifferential are developed. Examples of useful preferences are given.
Controllability and strong controllability of differential inclusions
2012
Abstract In this paper, we prove sufficient conditions for controllability and strong controllability in terms of the Mordukhovich subdifferential for two classes of differential inclusions. The first one is the class of sub-Lipschitz multivalued functions introduced by Loewen–Rockafellar (1994) [10] . The second one, introduced recently by Clarke (2005) [18] , is the class of multivalued functions which are pseudo-Lipschitz and satisfy the so-called tempered growth condition. To do this, we establish an error bound result in terms of the Mordukhovich subdifferential outside Asplund spaces.
Measure differential inclusions: existence results and minimum problems
2020
AbstractWe focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possible due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to…
Extremal solutions and strong relaxation for nonlinear multivalued systems with maximal monotone terms
2018
Abstract We consider differential systems in R N driven by a nonlinear nonhomogeneous second order differential operator, a maximal monotone term and a multivalued perturbation F ( t , u , u ′ ) . For periodic systems we prove the existence of extremal trajectories, that is solutions of the system in which F ( t , u , u ′ ) is replaced by ext F ( t , u , u ′ ) (= the extreme points of F ( t , u , u ′ ) ). For Dirichlet systems we show that the extremal trajectories approximate the solutions of the “convex” problem in the C 1 ( T , R N ) -norm (strong relaxation).
Relaxation result for differential inclusions with Stieltjes derivative
2023
The aim of this paper is to provide a Filippov-Wa\.{z}ewski Relaxation Theorem for the very general setting of Stieltjes differential inclusions. New relaxation results can be deduced for generalized differential problems, for impulsive differential inclusions with multivalued impulsive maps and possibly countable impulsive moments and also for dynamic inclusions on time scales.
Adaptation, coordination, and local interactions via distributed approachability
2017
This paper investigates the relation between cooperation, competition, and local interactions in large distributed multi-agent\ud systems. The main contribution is the game-theoretic problem formulation and solution approach based on the new framework\ud of distributed approachability, and the study of the convergence properties of the resulting game model. Approachability\ud theory is the theory of two-player repeated games with vector payoffs, and distributed approachability is here presented for\ud the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local\ud information and interaction structure. The game model turns i…