A discrete-time adaptive controller for time-varying systems

In the last two decades, adaptive control for time-invariant systems has achieved rapid development. Simulation and application have shown that the adaptive controllers based on the time-invariant dynamic assumption are able to deal with three types of systems. Several adaptive control algorithms based on the time-varying models have appeared and improved simulation results have been reported. However, the results are restricted to the stably invertible systems. Unlike the time-invariant plants, even for the stably invertible time-varying systems, there may be some periods in which the systems act as though they were unstably invertible systems. The plant input under the minimum covariance controller will grow rapidly to track a bounded reference output in these periods. The second obstacle to the application of the minimum covariance controller is due to the difficulty of distinguishing between stably invertible and unstably invertible time-varying systems. In this paper, an adaptive controller for time-varying systems is presented. It is shown that the controller can be applied to unstably invertible systems