Discrete-time adaptive control of a class of linear time-varying(LTV) systems is investigated. For this, a modified least squares algorithm, called sliding-windowed weighted recursive least squares (SWRLS), is first presented for parameter estimation of rapidly time-varying systems. Two windowing techniques are simultaneously used: one is the exponentially weighted window to emphasize recent data, and the other is the sliding window to discard old data. These windowing technique ensure that the presented method has a fast tracking property of the Sliding Rectangular Recursive Least Squares method and good steady state behaviour of the Weighted Recursive Least Squares method. And, the presented method is a generalised version of LS method.
In the adaptive systems, the input signal is generated by feedback. Under such circumstances, there is no guarantee that the process will be properly excited. To avoid this problem, a modified scheme of the presented method is introduced on which the parameter updating should switched off when the system is not properly excited.
An adaptive control algorithm using the Sliding-Windowed weighted Recursive Least Squares method for the linear time invariant (LTI) system is proposed which results in a globally stable closed loop system. Then, the qualititive stability analysis of adaptive controller for LTV system having two types of parameter variation (jump parameter and drift parameter) is also performed.
Simulation results are presented to compare various algorithms with the proposed one for the parameter estimation and the adaptive control of time varying system.
