Aubin cellina differential inclusions pdf

To this purpose, the underlying initial value problem is transformed into a fractional setvalued problem. Jfca2019102 solution sets for fractional differential inclusions 277 for further reading and details on multivalued analysis, we refer the reader to the books of andres and g orniewicz 3, aubin and cellina 6, aubin and frankowska 7, deimling 11, g orniewicz 17, kamenskii et al 19, hu and papageorgiou 28, 29. The corresponding compactness and tangency conditions for the right handside are expressed. Extremal solutions and relaxation problems for fractional. More detailed assumptions and exhaustive survey can be found in aubin and cellina. Recall that a differential inclusion di is a differential equation with multivalued righthand side. Ams proceedings of the american mathematical society. Viability theory is an area of mathematics that studies the evolution of dynamical systems under constraints on the system state. Connections to standard problems in the area of hybrid systems are. In this paper the existence of lyapunov functions for secondorder differential inclusions is analyzed by using the methodology of the viability theory. Cellina introduction there is a great variety of motivations that led mathemati cians to study dynamical systems having velocities not uniquely determined by the state of the system, but depending loosely upon it, i. The differential inclusion di is defined by the following statement. Haddad, monotone trajectories of differential inclusions and functionaldifferential inclusions with memory, israel j.

Existence of solutions to differential inclusions springerlink. Ntouyas, some existence results for boundary value problems of fractional differential inclusions with nonseparated boundary conditions, electronic journal of qualitative theory of differential equations, vol. Differential inclusions with lipschitzean maps and the relaxation theorem. Ornelas, representation of the attainable set for lipschitzean differential inclusions, rocky mountain j. The convergence results obtained by liu are generalized and refined. Cellina, differential inclusions, springerverlag, new yorkberhn. Cellina, differential inclusions, springerverlag, berlin. Caratheodory solutions for a differential inclusion of the form. As a matter of fact, there exist extensive literature concerning differential and integral inclusions in deterministic cases see aubin and. Lyapunov functions for secondorder differential inclusions. We consider discrete penalization schemes for reflecting stochastic differential equations.

However, in contrast to the existing books on the subject i. Indeed, if we introduce the setvalued map ft, x ft, x, uueu then solutions to the differential equations are solutions to the differen tial inclusion xteft, xt, xo. Filippov 1988 systemized the theory of differential inclusions and introduced the main properties of differential inclusions. A necessary assumption on the initial states and sufficient conditions for the existence of local and global lyapunov functions are. Aubin cellina differential inclusions pdf files bitbin. Our uniqueness theorem for differential inclusions is not in terms of the trajectories of 1. Existence results for thirdorder differential inclusions. On unique solution of quantum stochastic differential. The theory of differential inclusions was initiated in 19341936 with 4 pa pers.

Then,an existence theorem of periodic viable trajectories of differential inclu sions in a finite dimensional space is proved. Existence of viable solutions for a class of nonconvex differential inclusions with memory aurelian cernea and vasile lupulescu abstract. In this paper, we are concerned with the possible approach to the existence of solutions for a class of discontinuous dynamical systems of fractional order. Pdf finite time stability of differential inclusions. By using a suitable fixed point theorems, we study the existence of solutions for fractional diffeointegral inclusion of sobolevtype. In fact, an ode is a special case of a di, where the righthand f is a onepoint set. The existence of periodic solutions to nonautonomous differential inclusions article pdf available in proceedings of the american mathematical society 1043. Pdf handbook of multivalued analysis download full pdf. Nonsmooth lyapunov pairs for infinitedimensional firstorder differential inclusions samir adlyy, abderrahim hantoutez, and michel therax abstract. For more details on differential inclusions see the books by aubin and cellina.

Existence results for thirdorder differential inclusions with threepoint boundary value problems. Fractional differential inclusions of hilfer type under weak. The paper provides topological characterization for solution sets of differential inclusions with not necessarily smooth functional constraints in banach spaces. On unique solution of quantum stochastic differential inclusions. This paper discusses the topological structure of the set of solutions for a variety of volterra equations and inclusions. Editorial board antonio ambrosetti, scuola internazionale superiore di studi avanzati, trieste a. In the present paper, we show the some properties of the fuzzy rsolution of the control linear fuzzy differential inclusions and research the optimal time problems for it. Differential inclusions, springerverlag, 1983, and deimling. In the nineties, aubin suggested how to formulate ordinary differential equations and their main existence theorems in metric spaces. It was developed to formalize problems arising in the study of various natural and social phenomena, and has close ties to the theories of. Differential inclusion an overview sciencedirect topics. Haddad, monotone viable trajectories for functionaldifferential inclusions, j. For continuous differential inclusions the classical bangbang property is known to fail, yet a weak form of it is established here, in the case where the right hand side is a multifunction whose.

The corresponding compactness and tangency conditions for the right handside are expressed in terms of the measure of noncompactness and the clarke. Filippov, who studied regularizations of discontinuous equations. A great impetus to study differential inclusions came from the development of control theory, i. In this working, we consider the timedependent differential inclusion involving partial generalized gradient. Firstly,a simplified property of differential inclusions is given. Our results rely on the existence of a maximal solution for an appropriate ordinary differential equation. Differential inclusion solver a differential inclusion is a generalization of an ordinary differential equation. The reader is assumed to be familiar with the theory of multivalued analysis and differential inclusions in banach spaces, as presented in aubin et al. It was developed to formalize problems arising in the study of various natural and social phenomena, and has close ties to the theories of optimal control and setvalued analysis.

A viability approach to hybrid systems jeanpierre aubin, john lygeros, marc quincampoix, shankar sastry, fellow, ieee, and nicolas seube abstract impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Partial differential inclusions of transport type with state. Multifunctions arise in optimal control theory, especially differential inclusions and related subjects as game theory, where the kakutani fixed point theorem for multifunctions has been applied to prove existence of nash equilibria in the context of game theory, a multivalued function is usually referred to as a correspondence. Other readers will always be interested in your opinion of the books youve read. As a matter of fact, there exist extensive literature concerning differential and integral inclusions in deterministic cases see aubin and cellina, 1984. In this paper,the periodic viable trajectories of differential inclusions are discussed. Differential inclusions can be used to understand and suitably interpret discontinuous ordinary differential equations, such as arise for coulomb friction in mechanical systems and ideal switches in power electronics. The focus of interest is how to extend ordinary differential inclusions beyond the traditional border of vector spaces. Haddad, monotone trajectories of differential inclusions and functional differential inclusions with memory, israel j. Their combined citations are counted only for the first article.

Cellina, on the set of solutions to lipschitzian differentia. A necessary assumption on the initial states and sufficient conditions for the existence of local and global lyapunov functions are obtained. In this section you can find some general remarks on differential inclusions. On the qualitative theory of lower semicontinuous differential.

In this paper, we present some results concerning the existence of weak solutions for some functional hilfer and hadamard fractional differential inclusions. Qualitative properties of the set of trajectories of convexvalued differential inclusions. An ordinary differential equation ode in a real vector space can be defined as follows f x,t dt dx where x is an ndimensional vector and f is a vectorvalued function. Regulation of viable and optimal evolutions, springerverlag.

We prove the existence of viable solutions for an autonomus di. Berlinheidelbergnew yorktokyo, springerverlag 1984. Existence of solutions for a class of nonconvex differential inclusions. Haddad, monotone viable trajectories for functional differential inclusions, j. Acta mathematica universitatis comenianae, 852, 3118. We also compare the penalization schemes with a more wellknown recursive projection scheme.