State-Space Self-Tuning Controllers for General Multivariable Stochastic Systems

This paper presents a state-space approach for self-tuning control of a more general class of multivariable stochastic systems having number of inputs (controllability indices) equal or different from number of outputs (observability indices). The dynamic system is represented in the state-space innovation form with the Luenberger´s canonical structures. The model parameters and the Kalman gain are identified via either the extended least-squares algorithm or the least-squares ladder algorithm. The Kalman gain matrix and states can be estimated from the identified parameters without utilizing the standard state estimation algorithm. A long division method is introduced for finding the similarity transformation matrix, which links the observer canonical form and the controller canonical form, without heavily using the system matrix and input-output matrices. The full-order as well as the reduced-order state-space self-tuning controllers, such as the LQG self-tuning controller and the state-feedback pole-placement self-tuning controller, etc., have successfully been developed and applied to a more general class of multivariable stochastic systems.