7 papers
Optimal control of Goursat-Darboux systems in domains with curvilinear boundaries
S. A. Belbas
We derive necessary conditions for optimality in control problems governed by hyperbolic partial differential equations in Goursat-Darboux form. The conditions consist of a set of…
A hybrid Volterra-type equation with two types of impulses
S. A. Belbas, ; Jong Seo Park
We formulate and analyze a hybrid system model that involves Volterra integral operators with multiple integrals and two types of impulsive terms. We give a constructive proof, via…
On series solutions of Volterra equations
S. A. Belbas
We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or wit…
Dynamic programming in mixed continuous-discrete time scales
S. A. Belbas
We obtain the dynamic programming equations and optimality conditions akin to Pontryagin's extremum principle for certain mathematical models of hybrid control systems.
New hysteresis operators with applications to counterterrorism
S. A. Belbas
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 prob…
Optimal Control of Volterra Equations with Impulses
S. A. Belbas, W. H. Schmidt
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 c…