Sufficient conditions for a strong relative minimum in an optimal control problem

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

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Sufficient Conditions for a Relaxed Optimal Control Problem

Dynamical Systems ◽

10.1016/b978-0-12-164901-2.50037-4 ◽

1976 ◽

pp. 331-332

Author(s):

RUSSELL D. RUPP

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Sufficient Conditions

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Dynamic Analysis of a Two-Language Competitive Model with Control Strategies

Mathematical Problems in Engineering ◽

10.1155/2013/654619 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Lin-Fei Nie ◽

Zhi-Dong Teng ◽

Juan J. Nieto ◽

Il Hyo Jung

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Numerical Simulations ◽

Control Strategy ◽

Sufficient Conditions ◽

Positive Order ◽

State Dependent ◽

Competitive Model ◽

The Impact

The dynamic behavior of a two-language competitive model is analyzed systemically in this paper. By the linearization and the Bendixson-Dulac theorem on dynamical system, some sufficient conditions on the globally asymptotical stability of the trivial equilibria and the existence and the stability of the positive equilibrium of this model are presented. Nextly, in order to protect the endangered language, an optimal control problem relative to this model is explored. We derive some necessary conditions to solve the optimal control problem and present some numerical simulations using a Runge-Kutta fourth-order method. Finally, the languages competitive model is extended to this model assessing the impact of state-dependent pulse control strategy. Using the Poincaré map, differential inequality, and method of qualitative analysis, we prove the existence and stability of positive order-1 periodic solution for this control model. Numerical simulations are carried out to illustrate the main results and the feasibility of state-dependent impulsive control strategy.

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An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients

Georgian Mathematical Journal ◽

10.1515/gmj-2015-0012 ◽

2015 ◽

Vol 22 (2) ◽

Author(s):

Hamlet F. Guliyev ◽

Vera B. Nazarova

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Fourth Order ◽

Hyperbolic Equations ◽

Sufficient Conditions ◽

Constant Coefficients ◽

Gradient Of The Functional ◽

Necessary And Sufficient ◽

Hyperbolic Differential Equations

AbstractIn this paper, an optimal control problem is considered for a system of fourth order hyperbolic equations with constant coefficients. The gradient of the functional is calculated and the necessary and sufficient conditions of optimality in the form of an integral inequality are derived.

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On an optimal control problem involving second order hyperbolic systems with boundary controls

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700011564 ◽

1983 ◽

Vol 27 (1) ◽

pp. 139-148 ◽

Cited By ~ 2

Author(s):

K.G. Choo ◽

K.L. Teo ◽

Z.S. Wu

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Hyperbolic Systems ◽

Sufficient Conditions ◽

Second Order ◽

Optimal Controls ◽

Convergence Properties ◽

Boundary Controls ◽

Necessary And Sufficient

In this paper, we consider an optimal control problem involving second-order hyperbolic systems with boundary controls. Necessary and sufficient conditions are derived and a result on the existence of optimal controls is obtained. Also, a computational algorithm which generated minimizing sequences of controls is devised and the convergence properties of the algorithm are investigated.

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