Matrix power series method for nonlinear problems of optimal regulator construction

We propose a relatively simple and efficient method for solving the problem of analytic construction of optimal regulators for multidimensional control objects with polynomial nonlinearities based on the A. A. Krasovskii's generalized work criterion. Our method employs an extension of the power series method which is based on using matrix theory with Kroneker (direct) product. The matrix formalism has let us establish a simple recursive relation for the matrices of coefficients of the Bellman–Lyapunov function, with which the control problem can be solved with any reasonable precision on modern computers.