Arrow-type sufficient conditions for optimality of age-structured control problems

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Vladimir Krastev
Keyword(s):  
Boundary Conditions ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Infinite Time ◽  
Time Intervals ◽  
Sufficient Conditions For Optimality ◽  
Age Structured

AbstractWe consider a class of age-structured control problems with nonlocal dynamics and boundary conditions. For these problems we suggest Arrow-type sufficient conditions for optimality of problems defined on finite as well as infinite time intervals. We examine some models as illustrations (optimal education and optimal offence control problems).

scholarly journals Variational control problems for linear differential systems with Stieltjes boundary conditions

1978 ◽  
Vol 20 (4) ◽  
pp. 434-445 ◽  
Author(s):  
W. L. Chan ◽  
S. K. Ng
Keyword(s):  
Boundary Conditions ◽  
Bounded Variation ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Sufficient Conditions For Optimality ◽  
Quadratic Performance ◽  
Linear Differential ◽  
Necessary And Sufficient

Necessary and sufficient conditions for optimality in the control of linear differential systems ẋ = Ax + Bu with Stieltjes boundary conditions , where ν is an r × n matrix valued measure of bounded variation, are obtained, Feedback-like control is given in the case of quadratic performance.

scholarly journals Control of stage by stage changing linear dynamic systems

2012 ◽  
Vol 22 (1) ◽  
pp. 31-39 ◽  
Author(s):  
V.R. Barseghyan
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Time Intervals ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Necessary And Sufficient ◽  
Total Controllability

In this paper, the control problems of linear dynamic systems stage by stage changing and the optimal control with the criteria of quality set for the whole range of time intervals are considered. The necessary and sufficient conditions of total controllability are also stated. The constructive solving method of a control problem is offered, as well as the definitions of conditions for the existence of programmed control and motions. The explicit form of control action for a control problem is constructed. The method for solving optimal control problem is offered, and the solution of optimal control of a specific target is brought.

scholarly journals Optimality conditions for systems driven by nonlinear evolution equations

1995 ◽  
Vol 1 (1) ◽  
pp. 27-36
Author(s):  
N. Papageorgiou
Keyword(s):  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Optimal Control Problems ◽  
Nonlinear Evolution ◽  
Sufficient Conditions ◽  
Nonlinear Evolution Equations ◽  
Control Problems ◽  
Terminal Constraints ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

Using the Dubovitskii-Milyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or terminal constraints. An example of a parabolic control system is also included.

Caputo fractional differential equations with non-instantaneous impulses and strict stability by Lyapunov functions

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5217-5239 ◽  
Author(s):  
Ravi Agarwal ◽  
Snehana Hristova ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Intervals ◽  
Dini Derivative ◽  
Comparison Results ◽  
Strict Stability ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

In this paper the statement of initial value problems for fractional differential equations with noninstantaneous impulses is given. These equations are adequate models for phenomena that are characterized by impulsive actions starting at arbitrary fixed points and remaining active on finite time intervals. Strict stability properties of fractional differential equations with non-instantaneous impulses by the Lyapunov approach is studied. An appropriate definition (based on the Caputo fractional Dini derivative of a function) for the derivative of Lyapunov functions among the Caputo fractional differential equations with non-instantaneous impulses is presented. Comparison results using this definition and scalar fractional differential equations with non-instantaneous impulses are presented and sufficient conditions for strict stability and uniform strict stability are given. Examples are given to illustrate the theory.

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