Real-time computation of resource optimal control

For linear systems with bounded control, a new approach to real-time implementation of a resource-optimal control is proposed. The computational costs are separated between preliminary computations and computations in 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 family of hyperplanes. Methods for constructing an approximating family and selecting a supporting hyperplane are described. A method for finding an approximate optimal control time and correctly specifying the transfer time in resource consumption minimization is proposed. A technique specifying an initial approximation for low-cost iterative computations of a resource optimal control is developed. A computational algorithm is described, and simulation and numerical results are presented.