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 a number of inputs equal or different from the number of outputs. The dynamic system is represented in the state-space innovation form with 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.