Discontinuous Solutions to Unbounded Differential Inclusions under State Constraints. Applications to Optimal Control Problems

We consider a nonconvex and unbounded differential inclusion derived from a control system whose control sets are time and space-dependent. We extend the inclusion in order to allow discontinuous trajectories. We prove that the set of solutions of the original inclusion is dense in the set of solutions of the extended inclusion and, moreover, these last solutions are stable with respect to the initial data. Both of these results are also proven in the presence of state and integral constraints (assuming suitable conditions at the boundary of the constraining set). As an application, the value function of a Mayer problem is shown to be continuous and the unique viscosity solution of a Hamilton–Jacobi equation with suitable boundary conditions.     

Banach 空间微分包含在闭集上的生存性

本文在抽象Banach空间中研究非自治微分包含系统x（t）∈A（t,x）;x（0）＝x0在闭集上的生存性．在假定A是上半连续,满足一定的模条件与紧性条件之下,获得微分包含初值问题在闭集上的生存定理．     

Banach空间无界时滞的脉冲发展中立泛函积分微分包含的存在性

本文建立了Banach空间中无界时滞的脉冲发展中立泛函积分微分包含温和解存在的充分条件，我们利用由Dhage建立的多值混合不动点定理与发展系统证明了解的存在性．     

Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation

In this paper we present an extension of Moreau’s sweeping process for higher order systems. The dynamical framework is carefully introduced, qualitative, dissipativity, stability, existence, regularity and uniqueness results are given. The time-discretization of these nonsmooth systems with a time-stepping algorithm is also presented. This differential inclusion can be seen as a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary-slackness variables. Applications of such high-order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes.     

Existence theorems of systems of variational inclusion problems with applications

In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results, we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems of variational inclusion constraints, bilevel problem with systems of constraints.     

Effective properties of a piezocomposite containing shape memory alloy and inert inclusions

Received July 2, 2001 / Published online February 4, 2002     

Finite time stability of differential inclusions

^** Email: emmanuel.moulay{at}ec-lille.fr^*** Email: wilfrid.perruquetti{at}ec-lille.fr In this paper, the problem of finite time stability is investigatedfor differential inclusion. Two sufficient conditions for finitetime stability, using a smooth Lyapunov function and a non-smoothone, are established. Then, the same idea is used to give twonecessary conditions. Examples are developed using the conceptof Krasovskii solutions for differential equation with discontinuousright-hand sides.     

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without con-vexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the sys-tems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vec-tor quasi-optimization problems.