An approximate method for solving optimal control problems

An approximate method is presented for solving optimization problems. A truncated series of exponential functions is used to approximate a desired state variable or output of a system. Integral-square error is used as the criterion to be minimized. The coefficients of the series are determined in such a way that the error index is minimum, subject to the physical constraints imposed on the system. In this way, the dynamic problem is converted into a static one. The resulting problem becomes a general problem of mathematical programming which may be solved either by digital or analog computers. Once the coefficients of the approximating signal are determined, the input control signal is determined through the relationship of the process dynamics of the system. This approximate method of optimization is simple, and possesses the important advantage of requiring less computer time than exact optimization methods.