Numerical Analysis and Applications

, Volume 5, Issue 1, pp 1–16 | Cite as

Forming an approximating construction for calculation and implementation of optimal control in real time



A new approach to realization of the time-optimal control in real time for linear systems under control with a constraint is proposed. It is based on dividing the computer costs into those made in advance of the control process and those carried out as it proceeds. The preliminary computations do not depend on a particular initial condition and rely on approximation of attainability sets in different periods of time by a union of hyperplanes. Methods of their construction and identification of the support hyperplane are given. Methods of approximate finding and subsequent refining of the normalized vector of the initial conditions of the adjoint system as well as switching times and instants of switching of time-optimal control are proposed. Results of modeling and numerical calculations are presented.


optimal control attainability sets hyperplane real time adjoint system edge point first approximation approximating construction 


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© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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