An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The f...

In this paper, the minimum time problem for differential systems of parabolic type with distributed control and control state constraints are considered. The minimum time problem is replaced by an equivalent one with fixed time and the necessary optimality conditions of time-optimal control are obtained by using the generalized Dubovitskii-Milyutin Theorem (see [1]).

An optimal control problem is studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end...

This article is concerned with optimal control problems subject to a second order elliptic PDE and additional pointwise constraints on the gradient of the state. In particular, existence of solutions on nonsmooth polygonal or polyhedral domains is analyzed. In this situation the solution operator for the partial differential equation does not provide enough regularity to state the pointwise con...

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, suucient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L 1-norm. It is shown that these conditions are also necessary, provided that the ...

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled b...

Optimal incomplete block designs are pursued through the E-criterion of minimizing maximal variance. Methodology is developed for design choice based on graphs and an extensive catalog of downloadable designs compiled. Along with the general methodology, a near complete solution for E-optimal block designs is provided for up to 15 treatments. E-optimality is revealed as a flexible criterion tha...

Abstract. We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminaltime triplet to be optimal are obtained. Situations with constraints present at the end time are also considered. Under appropriate assumptions, it is shown that the o...

In this paper we derive necessary optimality conditions involving Mordukhovich coderivatives for optimal control problems of strongly monotone variational inequalities.

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form of stochastic maximum principle. AMS Subject Classification. 93Exx