scholarly journals On boundary optimal control problem for an arterial system: First-order optimality conditions

2018 ◽  
Vol 13 (4) ◽  
pp. 585-607 ◽  
Author(s):  
Ciro D'Apice ◽  
◽  
Olha P. Kupenko ◽  
Rosanna Manzo ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Arterial System ◽  
First Order ◽  
First Order Optimality Conditions

scholarly journals Mean-field optimal control for biological pattern formation

2021 ◽  
Author(s):  
Martin Burger ◽  
Lisa Maria Kreusser ◽  
Claudia Totzeck
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Mean Field ◽  
Wasserstein Distance ◽  
Descent Method ◽  
Gradient Descent Method ◽  
First Order ◽  
First Order Optimality Conditions

We propose a mean-field optimal control problem for the parameter identification of a  given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The first-order optimality conditions corresponding to the optimal control problem are derived using a Lagrangian approach on the mean-field level. Based on these conditions we propose a gradient descent method to identify relevant parameters such as angle of rotation  and force scaling which may be spatially inhomogeneous. We discretize the first-order optimality conditions in order to employ the algorithm on the particle level.  Moreover, we prove a rate for the convergence of the controls as the number of particles used for the discretization tends to infinity. Numerical results for the spatially homogeneous case demonstrate the feasibility of the approach.

scholarly journals Necessary Optimality Conditions for a Class of Impulsive and Switching Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Lihua Li ◽  
Yan Gao ◽  
Gexia Wang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Necessary Optimality Conditions ◽  
Switching Systems ◽  
Jump Conditions ◽  
Fréchet Subdifferential ◽  
Extended State ◽  
Adjoint Variables

An optimal control problem for a class of hybrid impulsive and switching systems is considered. By defining switching times as part of extended state, we get the necessary optimality conditions for this problem. It is shown that the adjoint variables satisfy certain jump conditions and the Hamiltonian are continuous at switching instants. In addition, necessary optimality conditions of Fréchet subdifferential form are presented in this paper.

scholarly journals Optimal Control with Time Delays via the Penalty Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Benharrat ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Calculus Of Variations ◽  
Convergence Theorem ◽  
Unknown Function ◽  
Time Delays ◽  
Penalty Method ◽  
Necessary Optimality Conditions

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.

scholarly journals Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhen Wu ◽  
Feng Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Linear Quadratic ◽  
Regular Control

We consider a stochastic recursive optimal control problem in which the control variable has two components: the regular control and the impulse control. The control variable does not enter the diffusion coefficient, and the domain of the regular controls is not necessarily convex. We establish necessary optimality conditions, of the Pontryagin maximum principle type, for this stochastic optimal control problem. Sufficient optimality conditions are also given. The optimal control is obtained for an example of linear quadratic optimization problem to illustrate the applications of the theoretical results.

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