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Showing 1 to 6 of 6 for “"Hamiltonian Function"”.
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Optimal control problems on lie groups with symmetry breaking cost functions
… control problem by studying an associated Hamiltonian dynamical system. When the associated Hamiltonian function possess symmetries, we can often study the Hamiltonian system in a vector space whose dimension is lower than the original system. We apply these symmetry reduction techniques to …
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Periodic existence theorems in optimal control
… the constraints are absorbed into the objective function. Rockafellar has established a general existence theorem for such control problems. This existence theorem requires finding bounds on a Hamiltonian function. In his work Rockafellar specialized his results to certain initial value problems. …
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Generalized Characteristics Of A Generic Polytope
… S ⊂ R 2n given by the level set of a Hamiltonian function H, a symplectic form ω on R2n induces a vector field XH which flows tangent to S. By the nondegeneracy of ω, there exists a distinguished line bundle LS whose characteristics are the integral curves of XH. When S is the boundary …
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Optimal, impulsive, time-fixed orbital rendezvous and interception with path constraints
… boundaries, and the continuity of the Hamiltonian function with a scleronomic constraint in infinite control problems have been studied and answered in this research. A bifurcation phenomenon and the non-uniqueness of the extremal solutions having the same cost have been found during …
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Geometric Mechanics of Active Particles
… the dynamical preservation of symplecticity in Hamiltonian systems. In this way, dynamics derived from a Hamiltonian function admit energy-conserving integration schemes with an error that remains bounded in the infinite time limit. Furthermore, the existence of this scalar first integral …
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The Computational Kleinman-Newton Method in Solving Nonlinear Nonquadratic Control Problems
This thesis deals with non-linear non-quadratic optimal control problems in an autonomous system and a related iterative numerical method, the Kleinman-Newton method, for solving the problem. The thesis proves the local convergence of Kleinman-Newton method using the contraction mapping theorem and …