Terminal control problem for affine systems

Крищенко, А. П.; Fetisov, D. A.

doi:10.1134/s0012266113110062

Cited by 5 publications

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“…For nonlinear dynamical systems, approaches to solve problems with fixed ends are known only for some classes of systems. For example, for a statically linearizable system, the system can be transformed to a special form called the regular canonical form [2,3], and then one can find the open-loop trajectory in the terms of time polynomials, the order of which is determined by the number of boundary conditions. For some dynamical systems, it is possible to transform the system to a quasi-canonical form [4], for which a similar approach is applied.…”

Section: Introductionmentioning

confidence: 99%

The Admissible Control Correction Method in a Nonlinear Terminal Perturbed Problem

2021

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A solution of a nonlinear perturbed unconstrained point-to-point control problem, in which the unperturbed system is differentially flat, is considered in the paper. An admissible open-loop control in it is constructed using the covering method. The main part of the obtained admissible control correction in the limit problem is found by expanding the perturbed problem solution in series by the perturbation parameter. The first term of the expansion is determined by A.N. Tikhonov’s regularization of the Fredholm integral equation of the first kind. As shown by numerical experiments, the found structure of an admissible control allows one to find the final form of high precision point-to-point control based on the solution of an auxiliary variational problem in its neighborhood.

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Section: Introductionmentioning

confidence: 99%