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Measure differential inclusions
2018 IEEE Conference on Decision and Control (CDC), 2018When modeling dynamical systems with uncertainty, one usually resorts to stochastic calculus and, specifically, Brownian motion. Recently, we proposed an alternative approach based on time-evolution of measures, called Measure Differential Equations, which can be seen as natural generalization of Ordinary Differential Equations to measures.
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Differential Inclusions for fuzzy maps
Fuzzy Sets and Systems, 2000From the authors abstract: The authors introduce the problems of differential inclusions for fuzzy maps, and prove the existence of solutions to these problems by the continuous selection theorem and fixed point theorems, respectively.
Yuanguo Zhu, Ling Rao
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Stochastic Differential Inclusions
2013A stochastic differential inclusion is formulated in terms of stochastic differentials of continuous semimartingales. In particular, concepts of strong and weak solutions of the inclusion \[ dx_t\in F(t,x_t)dt+G(t,x_t)dw_t \] are introduced. Here \(F,G:[0,1]\times R^n\to \text{Comp} (R^n)\) are Borel measurable set-valued mappings.
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CHAOS IN NONAUTONOMOUS DIFFERENTIAL INCLUSIONS
International Journal of Bifurcation and Chaos, 2005The existence of a continuum of many chaotic solutions are shown for certain differential inclusions which are small nonautonomous multivalued perturbations of ordinary differential equations possessing homoclinic solutions to hyperbolic fixed points. Applications are given to dry friction problems.
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Differential Inclusions and $$\mathcal A$$ A -quasiconvexity
Mediterranean Journal of Mathematics, 2017The paper considers problems of the form \[ v(x)\in E,\quad {\mathcal A}v=0, \] where \( {\mathcal A}\) is a first-order linear partial differential operator and the sets \(E\) are of the form \[ E=\{\xi \in {\mathbb R}^n;\quad F_i(\xi )=0,\quad i=1,\dots,N\}, \] where \(F_i:{\mathbb R}^n\to {\mathbb R}\), \(i=1,\dots,N\) are continuous and \({\mathcal
Ana Cristina Barroso +2 more
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On Copulas and Differential Inclusions
2013We construct a class of differential inclusions such that their solutions are horizontal sections of copulas. Furthermore we show that the horizontal sections of any copula can be obtained in such a way.
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Stochastic Invariance for Differential Inclusions
Set-Valued Analysis, 2000The first objective of this paper is to combine two ways for representing uncertainty through stochastic differential inclusions: a stochastic uncertainty driven by a Wiener process and a contingent uncertainty driven by a set-valued map. The second point consists to extend to stochastic differential inclusions the invariance theorem for nonstochastic ...
Aubin, Jean-Pierre +2 more
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On the implicit fuzzy differential inclusions
2012 9th International Conference on Fuzzy Systems and Knowledge Discovery, 2012In this paper, the implicit fuzzy differential inclusions is introduced and studied. The existence theorem of this implicit inclusion is proved by using barycentric selection theorem and Banach fixed point theorem. The result presented in this paper improves and extends some known results for the fuzzy differential inclusion.
Chao Min +3 more
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ε-approximation of differential inclusions
Proceedings of 1995 34th IEEE Conference on Decision and Control, 1996For a Lipschitz differential inclusion x ∈ f(x), we give a method to compute an arbitrarily close approimation of Reachf(X0, t) — the set of states reached after time t starting from an initial set X0. For a differential inclusion x ∈ f(x), and any e>0, we define a finite sample graph A∈. Every trajectory φ of the differential inclusion x ∈f(x) is also
Anuj Puri, Vivek Borkar, Pravin Varaiya
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