Brogliato, Bernard Tanwani, Aneel

This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations (ODEs) is coupled with a static and time-varying set-valued operator in the feedback. Interconnections of this form model certain classes of nonsmooth systems including sweeping processes, differential inclusions with maximal...

Palladino, Michele Vinter, Richard B.

This paper concerns state constrained optimal control problems, in which the dynamic constraint takes the form of a differential inclusion. If the differential inclusion does not depend on time, then the Hamiltonian, evaluated along the optimal state trajectory and the co-state trajectory, is independent of time. If the differential inclusion is Li...

alsaedi, ahmed ahmad, bashir alghanmi, madeaha ntouyas, sotiris k.

We establish sufficient criteria for the existence of solutions for a nonlinear generalized Langevin-type nonlocal fractional-order integral multivalued problem. The convex and non-convex cases for the multivalued map involved in the given problem are considered. Our results rely on Leray&ndash / Schauder nonlinear alternative for multivalued maps ...

Logachov, A. V. Makhno, S. Ya.
Published in
Siberian Advances in Mathematics

In the present article, we consider a stochastic differential equation that contains an integral with respect to a Poisson measure but avoids the diffusion term. The integrand need not be continuous. We introduce a definition of a solution and prove the existence and uniqueness theorems.

Liu, Jian Xu, Rui
Published in
Advances in Difference Equations

This paper is concerned with the problem of passivity analysis for a class of memristive neural networks with mixed time-varying delays and different state-dependent memductance functions. By employing the theories of differential inclusions and set-valued maps, delay-dependent criteria in terms of linear matrix inequalities are obtained for the pa...

Cubiotti, Paolo Yao, Jen-Chih
Published in
Advances in Difference Equations

We provide a new proof of a classical result by Bressan on the Cauchy problem for first-order differential inclusions with null initial condition. Our approach allows us to prove the result directly for kth order differential inclusions, under weaker regularity assumptions on the involved multifunction. Our result is the following: let a, b, M be p...

Bortolussi, Luca Gast, Nicolas

—We consider stochastic models in presence of uncertainty , originating from lack of knowledge of parameters or by unpredictable effects of the environment. We focus on population processes, encompassing a large class of systems, from queueing networks to epidemic spreading. We set up a formal framework for imprecise stochastic processes, where som...

Filippova, T. F.
Published in
Proceedings of the Steklov Institute of Mathematics

We consider estimation techniques for trajectory tubes of a nonlinear control system with uncertainty in the initial data and under the assumption of quadratic nonlinearity of the velocity vectors with respect to the states of the system. It is assumed that the uncertain initial states and admissible controls are subject to ellipsoidal constraints....

Graef, John R. Henderson, Johnny Ouahab, Abdelghani
Published in
Fractional Calculus and Applied Analysis

In this paper we study fractional differential inclusions in the sense of Almgren. We begin with a discussion of multiple-valued functions in the Almgren sense and include the basic results needed to make the paper selfcontained. Sufficient background on the fractional calculus is provided to make the material accessible also to the non-specialist ...

Chalco-Cano, Y. Rodriguez-Lopez, R. Silva, Geraldo N. Alonso, J. M. Bustince, H. Reformat, M.

In this paper we present a procedure to obtaining the solution of a fuzzy differential equation via differential inclusions. This procedure is an alternative approach, based on optimal control tools, to obtaining a description exact of a fuzzy solution for a large class of nonlinear fuzzy differential equations.