In the paper we derive new necessary optimality conditions for optimal control of differential equations systems with discontinuous right hand side. The main attention is paid to a situation when an optimal trajectory slides on the discontinuity surface. The new conditions, derived in the paper, are essential and do not follow from any known necessary conditions for such systems.

Reformulation of the M-Stationarity Conditions as a System Discontinuous Equations and Its Solution by Semismooth Newton Method

Abstract-The extensions of Reissner’s two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces (“interelement boundaries”) in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence...

In this paper, we study deterministic limits of Markov processes having discontinuous drifts. While most results assume that the limiting dynamics is continuous, we show that these conditions are not necessary to prove convergence to a deterministic system. More precisely, we show that under mild assumptions, the stochastic system is a stochastic approximation algorithm with constant step size ...

Recently, the use of special local test functions other than polynomials in Discontinuous Galerkin (DG) approaches has attracted a lot of attention and became known as DG-Trefftz methods. In particular, for the 2D Helmholtz equation plane waves have been used in [10] to derive an Interior Penalty (IP) type Plane Wave DG (PWDG) method and to provide an a priori error analysis of its p-version wi...