On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

2004 ◽  
Vol 24 (1) ◽  
pp. 41 ◽  
Author(s):  
Yuri E. Gliklikh ◽  
Andrei V. Obukhovski
Keyword(s):  
Riemannian Manifolds ◽  
Differential Inclusions ◽  
Velocity Hodograph ◽  
Carathéodory Conditions

Solvability of Langevin differential inclusions with set-valued diffusion terms on Riemannian manifolds

2007 ◽  
Vol 86 (9) ◽  
pp. 1105-1116 ◽  
Author(s):  
Svetlana V. Azarina ◽  
Yuri E. Gliklikh ◽  
Andrei V. Obukhovskiĭ
Keyword(s):  
Riemannian Manifolds ◽  
Differential Inclusions

scholarly journals On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds

2003 ◽  
Vol 2003 (10) ◽  
pp. 591-600 ◽  
Author(s):  
Yuri E. Gliklikh ◽  
Andrei V. Obukhovskii
Keyword(s):  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
Differential Inclusions ◽  
Extreme Values ◽  
Existence Theorems ◽  
Lower Semicontinuous ◽  
Boundary Value ◽  
Second Order ◽  
Configuration Spaces ◽  
Point Boundary

We consider second-order differential inclusions on a Riemannian manifold with lower semicontinuous right-hand sides. Several existence theorems for solutions of two-point boundary value problem are proved to be interpreted as controllability of special mechanical systems with control on nonlinear configuration spaces. As an application, a statement of controllability under extreme values of controlling force is obtained.

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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