Abstract
A method for calculating the unknown initial state from observed output data and control input data is shown in this paper. These data are dealt with as a batch and not continuously in this method. The essential point of the method is to calculate the initial state by constructing an optimization problem and then solving it by the steepest descent method. The method can be applied to nonlinear systems. Two examples show that the initial state can be estimated without discernible error by this method. In the case of a linear time-fixed system, the optimization problem can be solved analytically and does not require the steepest descent method.
