Abstract
This paper deals with a certain optimal control problem of linear time-invariant systems whose outputs are described by the form of convolution integral of impulse responses and inputs.
The problem dealt here is to determine such inputs that the integral of the quadratic form of input variables is minimized and output variables are settled to certain desired values in a specified time duration.
The authors propose a new effective method to solve this kind of problems and consider 1-input and 1-output systems in the first half of the paper and m-input and m-output systems in the latter half.
Considering the fact that the impulse response of a system is not necessarily given in an analytic form but is described by a set of discrete data, the authors formulate this optimal control problem without using derivatives of the impulse response.
Accordingly, if a set of discrete values of the impulse response is given, the optimal input is determined only by numerical integration and algebraic computation.
Some examples computed by a digital computer are also presented.
