Dynamic Programming
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The method proposed in this paper uses direct approach to the control system optimization. In order to reduce variational problem to ordinary extremum problem all state and control variables are approximated by a particular from of power polynomials in which the polynomial coefficients are given by linear combinations of all coordinate of the output state signal x"N(t). Consequently, the performance index reduces to a function of the finite number of variables, while the optimization problem reduces to finding the extremum of a function of several variables. Although, this method is limited to a definite class of control system - linear with quadratic performance index - its merits should be evaluated through the fact it enables very general control problem to be handled adequately. In other words, it makes possible to treat a problem involving simultaneous constraints on both control and state variables as well as integral-type constraints. Finally, the basic property of the method consists in the reduction of dynamic optimization problem to that of nonlinear programming which is more convenient for computer treatment.