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Brachistochrone Problem with State Constraints of a Certain Typeтезисы доклада
- Авторы: CHERKASOV OLEG, SMIRNOVA N.V.
- Сборник: DSTA-2021 Conference Books – Abstracts
- Том: 1
- Тезисы
- Год издания: 2021
- Место издания: Lodz University of Technology Press
- Первая страница: 647
- Последняя страница: 648
- DOI: 10.34658/9788366741201
- Аннотация: Abstract: The problem of maximizing the horizontal coordinate of a point mass moving in avertical plane under the action of gravity forces, viscous friction, support reaction of the curveand thrust is considered, as well as the interrelated Brachistochrone problem. Two cases areaddressed. The first is when the thrust applied is constant. The second is when the penalty forthe control expenditures is included in the goal function. Assumed that inequality-type constraintsare imposed on the slope angle of the trajectory. The system of equation belongs to acertain type that allows reduce the optimal control problem with state constraints to the optimalproblem with control constraints. The maximum Principle procedure is applied, and thequalitative analysis of the boundary-value problem is presented. As a result, the sequence andthe number of the arcs with motion along the phase constraints are determined and the synthesisof the optimal control is designed. The results of numerical simulation for the case ofquadratic resistance are presented to illustrate the theoretical conclusions. It is shown that optimaltrajectory of the Brachistochrone problem with viscous friction contains no more thanone section of motion along the lower constraint and no more than two sections of motionalong the upper one. For the frictionless Brachistochrone the extremal trajectory reaches foreach constraint no more than once.
- Добавил в систему: Черкасов Олег Юрьевич