Abstract
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.
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Original Russian Text © V.M. Aleksandrov, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 5, pp. 758–775.
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Aleksandrov, V.M. Optimal control of linear systems with interval constraints. Comput. Math. and Math. Phys. 55, 749–765 (2015). https://doi.org/10.1134/S0965542515050048
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DOI: https://doi.org/10.1134/S0965542515050048