A method for the parametrization of optimal control problems

Gorbunov, V. K.

doi:10.1016/0041-5553(79)90003-x

Cited by 5 publications

(3 citation statements)

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“…Introduce the Hamilton-Pontrjagin function The first derivatives (11) can be calculated [3] by formulas:…”

Section: Parameterization Methodsmentioning

confidence: 99%

“…The second variations ∂ 2 z/∂w k ν,β ∂w j µ,α as well as the first (12) are defined by some Cauchy problems [3,11]. It resolves, in principle, the problem of the second derivatives (13) calculation and using the Newton method.…”

Section: Parameterization Methodsmentioning

confidence: 99%

“…In the paper [3] the parameterization method (PM) of optimal control problems was created. This method is based on sequential development of a simple idea to account that as a rule solutions of real optimal control (OC) or calculus of variation (CV) problems have a rather simple structure and control functions can be well approximated in some parametric function class, for example, by splines with moving knots.…”

Section: Introductionmentioning

confidence: 99%

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The Parameterization Method in Singular Differential-Algebraic Equations

Gorbunov

Lutoshkin

2003

Lecture Notes in Computer Science

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The paper is devoted to the circumstantiation of the parameterization method for classical calculus of variation problems corresponding to the non-linear ODEs. The method is based on a finite parameterization of "control" functions (finitely entering in initial system) and on derivation of the problem functional with respect to control parameters. The first and the second derivatives are calculated with the help of adjoint vector and matrix impulses. The problems of arising degeneration of gradients and optimality conditions of the first order are overcome by using the Newton method. Results of the solution to degenerate DAEs, particularly with non-unique solutions, are presented.

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“…Introduce the Hamilton-Pontrjagin function The first derivatives (11) can be calculated [3] by formulas:…”

Section: Parameterization Methodsmentioning

confidence: 99%

Section: Parameterization Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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