Reduced-order optimal controller for discrete-time stochastic systems

The solution of the l. q. g. regulator problem is given by the separation principle and involves a Kalman filter with the same dimension as that of the plant. It is shown that, for a class of systems where the input subsystem states are measurable, the Kalman filter may be reduced in dimension considerably. An example of a steel-mill shape control problem is discussed where the number of states required in the filter is halved. The proposed optimal system includes direct state-feedback from the measurable states, which improves the performance of the system and reduces the effects of modelling errors. The optimal controller for the discrete-time system is derived in the z-domain. The solution of the above multivariable regulator problem has not previously been obtained in this form. The z-domain controller is particularly suitable for implementation on a microprocessor or digital computer.