Impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Connections to standard problems in the area of systems discussed. Conditions derived that allow one determine whether set states is viable or invariant under action an impulse inclusion. For sets violate these conditions, methods developed approximating their viability and invariance kernels, largest subset The results demonstrated on examples.

In 1988 Kennedy and Chua introduced the dynamical canonical nonlinear programming circuit (NPC) to solve in real time problems where objective function constraints are smooth (twice continuously differentiable) functions. this paper, a generalized is (G-NPC), which aimed at solving much wider class of nonsmooth assumed satisfy only weak condition being regular G-NPC, derives from natural extension NPC, has neural-like architecture also features presence constraint neurons modeled by ideal...

We investigate relationships between the deterministic infinite time horizon optimal control problem with discounting, in which state trajectories remain a given compact set Y, and certain dimensional linear programming (IDLP) problem. introduce dual respect to this IDLP obtain some duality results. construct necessary sufficient optimality conditions for under consideration, we give characterization of viability kernel Y. also indicate how one can use finite approximations its construction...

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic (QP) and nonconvex QP problems where an indefinite objective function is subject to set affine constraints. The NNs are characterized by constraint neurons modeled ideal diodes with vertical segments in their characteristic, which enable implement exact penalty method. A new method exploited address convergence trajectories, based on nonsmooth Lojasiewicz inequality the...

We study a zero-sum differential game where the players have only an unperfect information on state of system. In beginning random distribution initial is available. The main result paper existence value obtained through uniqueness for Hamilton-Jacobi-Isaacs equations stated space measure in ℝ n . This first step future work games with lack information.

We prove the existence of a value for pursuit games with state constraints. also that this is lower semicontinuous.MSC codes90D25Keywordsdifferential gamespursuit gamesstate constraints

In this paper, we revisit the problem of designing controllers to meet safety specifications for hybrid systems, whose evolution is affected by both control and disturbance inputs. The formulated as a dynamic game an appropriate notion strategy inputs developed. design strategies based on iteration alternating discrete continuous calculations. We show that, under certain assumptions, converges fixed point, which turns out be maximal set states can met. part calculation relies computation...

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

Where and how solutions associated to a differential inclusion can or cannot enter given target is studied. For this purpose, partitions of the boundary are with dynamic system. The behaviour these qualitatively described in terms viability invariance kernels sets. These determine points such that there exist (respectively, all) starting at remain set constraints. sets reached finite time by viable system also Finally, some applications control systems one provided, concept semipermeable...

The goal of this paper is to give a representation formula for the mean curvature motion in terms value function some stochastic optimal control problem. This result generalized several geometric evolution equations.

This paper studies stability properties of the solutions optimal control problems for linear systems. The analysis is based on an adapted concept metric regularity, strong bi-metric which introduced and investigated in paper. It allows one to give a more precise description effect perturbations terms Hölder-type estimate investigate robustness this estimate. Hölder exponent depends natural number $k$, known as controllability index reference solution. An inverse function theorem strongly...