State-space self-tuning regulators for general multivariable stochastic systems

Abstract

The paper presents a state-space approach for the self-tuning control of general linear multivariable discrete-time stochastic systems with the number of inputs (controllability indices) equal to or different from the number of outputs (observability indices). The dynamic system is represented in the state-space innovation form with the Luenberger's canonical structure. The model parameters, as well as the Kalman gain, are identified via the least-squares ladder algorithm, without utilising the standard stateestimation algorithm. Also, to avoid the direct use of the Luenberger's canonical transformations, a long division method is introduced for quickly converting a reducible or irreducible left matrix fraction description (LMFD) to an irreducible right matrix fraction description (RMFD) and for constructing the Luenberger's transformation matrices. In conjunction with the state-space selftuning control, an integral control is used so as to eliminate the steady-state errors and render the closed-loop system less sensitive to modelling errors. The proposed method will enhance the application of the state-space self-tuning concepts to a general class of multivariable stochastic systems.