arXiv subjects

S. A. Belbas

Publications and source records attributed to S. A. Belbas.

21 records · Page 2Linked to original sources

arXiv2004

New hysteresis operators with applications to counterterrorism

We define two models of hysteresis that generalize the Preisach model. The first model is deterministic, the second model is stochastic and it utilizes disconinuous transition probabilities that satisfy impulsive differential equations. For the first model we prove, among other things, a local version of the "wiping out" property; for the stochastic model, we give methods for the construction of solutions of impulsive differential equations that determine the discontinuous transition probabilities. We also present a game-theoretic problem utilizing a generalized hysteresis operator. These hysteresis operators are motivated by questions of modelling the dynamics of decision making processes of networks of loosely knit terrorist groups.

math.DS↗

arXiv2004

Optimal Control of Volterra Equations with Impulses

We consider an optimal control problem for a system governed by a Volterra integral equation with impulsive terms. The impulses act on both the state and the control; the control consists of switchings at discrete times. The cost functional includes both, an integrated cost rate (continuous part) and switching costs at the discrete impulse times (discrete part). We prove necessary optimality conditions of a form analogous to a discrete maximum principle. For the particular case of a system governed by impulsive ordinary differential equations, we obtain an impulsive maximum principle as a special case of the necessary optimality conditions for impulsive Volterra equations.

math.OC↗

arXiv2003

Identification in models of biochemical reactions

We introduce, analyze, and implement a new method for parameter identification for system of ordinary differential equations that are used to model sets of biochemical reactions. Our method relies on the integral formulation of the ODE system and a method of linear least squares applied to the integral equations. Certain variants of this method are also introduced in this paper.

q-bio.QM↗