Non-degenerate necessary optimality conditions for the optimal control problem with equality-type state constraints

2015 ◽  
Vol 64 (4) ◽  
pp. 623-647 ◽  
Author(s):  
A. V. Arutyunov ◽  
D. Yu. Karamzin
2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Lihua Li ◽  
Yan Gao ◽  
Gexia Wang

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Benharrat ◽  
Delfim F. M. Torres

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.


2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhen Wu ◽  
Feng Zhang

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.


Author(s):  
Fedor A. Kuterin

We consider the regularization of classical optimality conditions in a convex optimal control problem for a linear system of ordinary differential equations with pointwise state constraints such as equality and inequality, understood as constraints in the Hilbert space of square-integrable functions. The set of admissible task controls is traditionally embedded in the space of square-integrable functions. However, the target functional of the optimization problem is not, generally speaking, strongly convex. Obtaining regularized classical optimality conditions is based on a technique involving the use of two regularization parameters. One of them is used for the regularization of the dual problem, while the other is contained in a strongly convex regularizing addition to the target functional of the original problem. The main purpose of the obtained regularized Lagrange principle and the Pontryagin maximum principle is the stable generation of minimizing approximate solutions in the sense of J. Varga for the purpose of practical solving the considered optimal control problem with pointwise state constraints.


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