A direct method for a class of optimal control problems

A direct method is developed for the solution of a class of minimum energy control problems. The method is applicable to linear and nonlinear, stationary and time-varying systems described by input-output functional relations. It is based on the expansion of the kernels of the system and of the input, the control, in terms of a set of functions that are characteristic of the kernels. The optimality is measured by the integral of a positive definite quadratic form of the input over the control time interval. The characteristic expansions reduce the optimal control problem to that of solving a finite set of algebraic equations.