A design of continuous-time model reference adaptive control based on a function estimation of periodically time varying linear system

The author presents a design for stable continuous-time model reference adaptive control based on function estimation of periodically time-varying linear systems with known variation period and unknown system degree. This control system uses a nonminimum representation of the controlled object, where the controlled object is combined with an observer, thus eliminating direct use of a state and a filter to compensate for the relative degree of the controlled object. The controlled object should be uniformly observable, that is, observable in a finite interval of time. The observer and the filter are realized by convolution integrals in a finite span of time. Integral kernel functions of the observer are periodically time-varying functions with the same variation period as that of the controlled object; the representation consists of convolution integrals similar to those used in the observer. The global stability of the proposed adaptive control system is analyzed and a simple numerical simulation is performed for verification of the viability of the proposed control system