Abstract
The mathematical studies of optimal control processes are based on many idealized assumptions. When disturbances that are not known even statistically are considered, the optimum-controller must be readjusted every time the disturbances occur and the parameters of the plant must be compensated so as to maintain the deviation from the expected optimal state within some allowable limit. The control scheme can be realized only by using a high speed digital computer on its feedback circuit. This study presents all the mathematical conditions that are necessary to the scheme and accessible to modern high speed computers. The magnitude of disturbances (plant parameter variation) is estimated by solving an equation of observation that relates the parameter disturbances to the plant dynamic sensitivity coefficients. The deviation of the performance index (PI) is also calculated by means of the coefficients of PI variation. To a given margin for the deviation of PI, one simple procedure by which the deviation can be reduced to a value within the margin is proposed as an example.
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