The human relations aspects of inaugurating and implementing a program of industrial security

Thesis (M.B.A.)--Boston Universit

Set-Valued Analysis, Viability Theory and Partial Differential Inclusions

Systems of first-order partial differential inclusions -- solutions of which are feedbacks governing viable trajectories of control systems -- are derived. A variational principle and an existence theorem of a (single-valued contingent) solution to such partial differential inclusions are stated. To prove such theorems, tools of set-valued analysis and tricks taken from viability theory are surveyed. This paper is the text of a plenary conference to the World Congress on Nonlinear Analysis held at Tampa, Florida, August 19-26, 1992

Hyperbolic Systems of Partial Differential Inclusions

This paper is devoted to the study of first-order hyperbolic systems of partial differential inclusions which are in particular motivated by several problems of control theory, such as tracking problems. The existence of contingent single-valued solutions is proved for a certain class of such systems. Several comparison and localization results (which replace uniqueness results in the case of hyperbolic systems of partial differential equations) allow to derive useful informations on the solutions of these problems

Dynamic Regulation of Controlled Systems, Inertia Principle and Heavy Viable Solutions

Existence of viable (controlled invariant) solutions of a control problem regulated by absolutely continuous open loop controls is proved by using the concept of viability kernels of closed subsets (largest closed controlled invariant subsets). This is needed to provide dynamical feedbacks, i.e., differential equations governing the evolution of viable controls. Among such differential equations, the differential equation providing heavy solutions (in the sense of heavy trends), i.e., governing the evolution of controls with minimal velocity is singled out. Among possible applications, these results are used to define global contingent subsets of the contingent cones which allow to prove the convergence of a modified version of the structure algorithm to a closed viability domain of any closed subset

Partial Differential Inclusions Governing Feedback Controls

The authors derive partial differential inclusions of hyperbolic type, the solutions of which are feedbacks governing the viable (controlled invariant) solutions of a control system. They show that the tracking property, another important control problem, leads to such hyperbolic systems of partial differential inclusions. They begin by proving the existence of the largest solution of such a problem, a stability result and provide an explicit solution in the particular case of decomposable systems. They then state a variational principle and an existence theorem of a. (single-valued contingent) solution to such an inclusion, that they apply to assert the existence of a feedback control