Duality Between the Control of Processes Subject to Randomly Occurring Deterministic Disturbances and ARIMA Stochastic Disturbances

The problem of process control in the presence of deterministic disturbances occurring rather infrequently, but at random intervals, is considered. It is shown that these processes can be represented by the same structural form of model as autoregressive-integrated-moving-average (ARIMA) processes, the only difference being in the probability distribution of the shocks. These models are useful in the important industrial problem of designing optimal-control algorithms for processes perturbed by such disturbances. As might be anticipated from the duality in structure of these processes, the linear optimal-control laws for processes subject to either ARIMA or randomly occurring deterministic disturbances are identical for models of the equivalent structure. This important result allows for a unification of the theory of optimal control.