Geodesic
Real-time computation of optimal control
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 10, pp. 1778-1800

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A new approach to the real-time implementation of time-optimal control for linear systems with a bounded control is proposed. The computational costs are separated between preliminary computations and computations in the course of the control process. The preliminary computations are independent of the particular initial condition and are based on the approximation of sets reachable in different times by a collection of hyperplanes. Methods for constructing hyperplanes and selecting a supporting hyperplane are described. Methods are proposed for approximately finding the normalized vector of initial conditions of the adjoint system, the driving time, and the switching times of the time-optimal control, and an iterative method for their refinement is developed. The computational complexity of the method is estimated. The computational algorithm is described, and simulation and numerical results are presented. 
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     author = {V. M. Aleksandrov},
     title = {Real-time computation of optimal control},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1778--1800},
     publisher = {mathdoc},
     volume = {52},
     number = {10},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_10_a3/}
}
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V. M. Aleksandrov. Real-time computation of optimal control. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 10, pp. 1778-1800. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_10_a3/