Abstract
This paper is concerned with synthesizing, from a standpoint of so called “indirect control approach”, a new scheme of designing an adaptive control for a class of a single-input single-output linear discrete systems in the model reference adaptive control problem. Employing Gram-Schmidt orthogonalization technique, an adaptive identifier is constructed to generate both the estimates of the parameter and the state of the plant, but requires no more knowledge than the input-output signals as available measurements from the plant. Those estimates are proven to converge to the real values of the plant without errors in finite discrete time and are used to change in each step the parameters of a compensator connected ahead with the plant in a cascade. The compensator yields an adaptive control to the plant and is supplied with a reference model input in addition with two different signals. One is produced by feeding back the state estimates of the plant and another by feeding back the state of the compensator. When the identification process completes, the revised close loop transfer function of the plant coincides with the reference model one, namely at this time, the exact model matching is phased out clearly. After then, the output error between the plant and the model converges to zero asympototically.
