Adaptive control of linear multivariable systems without any prior knowledge

This paper presents a method to design a unity feed-back system for a multivariable discrete-time plant to have a desired denominator matrix. The only available information about the plant is that it is describable by a proper transfer matrix. The design consists of two steps: First, compute a polynomial fraction description of the plant from its input-output data and then design a compensator to achieve arbitrary denominator matrix assignment. The compensator is designed so that the plant input sequence is persistently exciting in the closed-loop connection. Thus the plant transfer matrix can be continuously monitored from the closed-loop input-output data and the compensator can be, if necessary, adjusted to maintain the assigned closed-loop denominator matrix. The entire design requires essentially the manipulation of two numerical matrices. Therefore the design can be easily programmed and implemented on a digital computer.