Abstract
In this paper, a computational method for the optimal control of a linear sampled-data control system is described.
In the linear stationary dynamical system x=Ax+Bu, the problem of minimizing the integral type criterion function which has the quadratic form as its integrand J=∫tf0(x'Qx+u'Ru)dt, isconsidered. In this case, the differential equation of the system, the value at each sampling point of variable x0 introduced by the equation dx0/dt=x'Qx+u'Ru and the so-called adjoint equation etc. are reduced to recurrence equations with constant coefficients. And if these coefficients are determined beforehand, the iterative computations to determine the optimal value of u are carried out not by numerical integration. And these coefficients, generally, are computed by numerical integration. But if the method described in this paper is used, computations of numerical integrations can be considerably reduced. Therefore, the time for computations can be shortened.
In this paper this computational method is described.
