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—Impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Connections to standard problems in the area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these… (More)

—In 1988 Kennedy and Chua introduced the dynamical canonical nonlinear programming circuit (NPC) to solve in real time nonlinear programming problems where the objective function and the constraints are smooth (twice continuously differen-tiable) functions. In this paper, a generalized circuit is introduced (G-NPC), which is aimed at solving in real time a… (More)

We study the notion of approachability in a repeated game with vector payoffs from a new point of view using techniques recently developed for qualitative differential games. Namely, we relate the sufficient condition for approachability (B-set) to the notion of discriminating domain for a suitably chosen differential game. The other goal of the present… (More)

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in… (More)

We investigate the limit of the average value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it is usually done in the literature.

In this paper, we study two new methods for approximating the viability kernel of a given set for a HH olderian diierential inclusion. We approximate this kernel by viability kernels for discrete dynam-ical systems. We prove a convergence result when the diierential inclusion is replaced by a sequence of recursive inclusions. Furthermore , when the given… (More)