Geodesic
Optimal control of linear systems with interval constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 758-775

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For linear systems with interval constraints, a method for computing a time-optimal control is proposed. The method is based on transforming a quasi-optimal control. The properties and features of the quasi-optimal control are examined. A technique is described for dividing the domain of initial conditions into reachable sets over different times and for approximating each set by a family of hyperplanes. An iterative method for computing an optimal control with interval constraints is developed. The convergence of the method is proved, and a sufficient condition for the convergence of the computational process is obtained. The radius of local quadratic convergence is found. Numerical results are presented. 
@article{ZVMMF_2015_55_5_a2,
     author = {V. M. Aleksandrov},
     title = {Optimal control of linear systems with interval constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {758--775},
     publisher = {mathdoc},
     volume = {55},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a2/}
}
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V. M. Aleksandrov. Optimal control of linear systems with interval constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 758-775. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a2/