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 Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 87–118 (Mi semr474)

Differentical equations, dynamical systems and optimal control

Construction of initial approximation and method of computing optimal control

V. M. Aleksandrov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: A method of reducing computational cost in the course of the control is considered. It is based on subdividing the whole computational process into the computations performed beforehand and those that are carried on while the control takes place. A method of calculation of initial approximation is proposed. Used here are the quasi-optimal control and subdividing of the range of initial conditions into the attainability domains. The ways for finding the support hyperplane and for computing approximate values of the switching times and the time of translating the system under the time-optimal control are given. It is developed an iterative procedure that allows the integrating to be carried out only over the displacement intervals of the switching times and that of the control completion time. It is proved that the sequence of quasi-optimal controls converges to the optimal control. The radius of the local convergence at the quadratic rate is obtained. The evaluation of computational working time of the method is given. The computational algorithm and the results of numerical calculations are presented.

Keywords: optimal control, quasi-optimal control, speed, switching time, attainability domain, approximation, support hyperplane, edge points, normalized adjoint system, iterative method, initial approximation, variation, computational cost.

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Document Type: Article
UDC: 519.626.1
MSC: 49N05
Received September 3, 2013, published February 6, 2014

Citation: V. M. Aleksandrov, “Construction of initial approximation and method of computing optimal control”, Sib. Èlektron. Mat. Izv., 11 (2014), 87–118

Citation in format AMSBIB
\Bibitem{Ale14} \by V.~M.~Aleksandrov \paper Construction of initial approximation and method of computing optimal control \jour Sib. \Elektron. Mat. Izv. \yr 2014 \vol 11 \pages 87--118 \mathnet{http://mi.mathnet.ru/semr474} `

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This publication is cited in the following articles:
1. V. M. Aleksandrov, “Optimal control of linear systems with interval constraints”, Comput. Math. Math. Phys., 55:5 (2015), 749–765
2. V. M. Aleksandrov, “Quasi-optimal control of dynamic systems”, Autom. Remote Control, 77:7 (2016), 1163–1179
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