scholarly journals Optimal control of Sturm-Liouville type evolution differential inclusions with endpoint constraints

2020 ◽  
Vol 16 (5) ◽  
pp. 2503-2520 ◽  
Author(s):  
Elimhan N. Mahmudov ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Differential Inclusions ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Endpoint Constraints

scholarly journals On controllability for a class of second-order differential inclusions

2011 ◽  
Vol 27 (1) ◽  
pp. 34-40
Author(s):  
AURELIAN CERNEA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusion ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Second Order ◽  
Sufficient Condition ◽  
Liouville Type ◽  
Sturm Liouville ◽  
The Right

By using a suitable fixed point theorem a sufficient condition for controllability is obtained for a Sturm-Liouville type differential inclusion in the case when the right hand side has convex values.

scholarly journals On controllability for Sturm-Liouville type differential inclusions

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1321-1327
Author(s):  
Aurelian Cernea
Keyword(s):  
Differential Inclusion ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Local Controllability ◽  
Reference Trajectory ◽  
Liouville Type ◽  
Sturm Liouville

We consider a second-order differential inclusion and we obtain sufficient conditions for h-local controllability along a reference trajectory.

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.

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