Optimal Resource Consumption Control of Disturbed Dynamic Systems

A numerical method of solving a problem of resource consumption minimization for linear dynamic systems with disturbances is considered. The method is based on generating finite control moving for fixed time a linear system from any initial state to the desired final state and allowing the structure of optimal resource consumption control to be determined. A way of defining an initial approximation is given and an iterative algorithm of computing the optimal control is proposed. A system of linear algebraic equations is obtained that relates the increments of initial conditions of an adjoint system to the increments of phase coordinates concerning the desired final state. The computational algorithm is given. Local convergence is determined to take place at a quadratic rate and its radius is found. Computing process and a sequence of controls are proved to converge to optimal resource consumption control.