Some extremal problems for elliptical discrete and differential inclusions with distributed parameters and duality

Cybernetics ◽  
1990 ◽  
Vol 26 (2) ◽  
pp. 215-226 ◽  
Author(s):  
�. N. Makhmudov
Keyword(s):  
Differential Inclusions ◽  
Extremal Problems ◽  
Distributed Parameters

scholarly journals ON THE EXACT PENALTY OF HIGH ORDER FOR EXTREME PROBLEMS OF DIFFERENTIAL INCLUSIONS

2021 ◽  
Vol 6 (2(52)) ◽  
pp. 75-86
Author(s):  
Misraddin Allahverdi oglu Sadygov
Keyword(s):  
Distance Function ◽  
Differential Inclusions ◽  
Continuous Functions ◽  
Extremal Problems ◽  
High Order ◽  
Necessary Condition ◽  
Exact Penalty ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Locally Lipschitz

In this paper, using theorems on the continuous dependence of the solution of differential inclusions on the perturbation, we obtain high-order exact penalty theorems for nonconvex extremal problems of differential inclusions in the space of Banach-valued absolutely continuous functions. Using the type of the distance function in the classes of 𝜙 − (𝜙, 𝜙, 𝜙, 𝜙, 𝜙) locally Lipschitz functions, the nonconvex extremal problem for differential inclusions is reduced to a variational problem and the necessary condition for the extremum of a high-order is obtained. The paper also shows that the used functions type of distance function satisfy the 𝜙 − (𝜙, 𝜙, 𝜙, 𝜙, 𝜙) locally Lipschitz conditions.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Sign in / Sign up

Export Citation Format

Share Document