The purpose of this paper is to study the
random input in a discrete-time linear optimal
control system. Since the random input includes the measurement noise and disturbance input, it is often referred as white noise when evaluating a quadratic performance functional. With the random input presented in a system, the state variable is impossible determined precisely at the later time. Due to the existence of noise, the state variable is considered as a random
sequence which satisfies the Markov
property and could be described by the
probability transition matrix. Additional, the mean-value and the covariance
matrix of the state give the meaningful information for investigation of the stochastic linear optimal control system. A simple simulation of scalar system is discussed and the graphical optimal solution is represented.
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