A novel strategy for identification and control of a class of linear systems

Control of time-varying systems has become increasingly popular in recent years, as various domains such as aviation, automobile and manufacturing industries require a quick and precise response in the presence of uncertainties. Adaptive control, a popular strategy is used to control systems with unknown or time-varying properties. Classic adaptive control is insufficient to cope with time-varying parameters to produce desired results with minimal parametric error. Furthermore, for these strategies to work, identification model must be initialised closer to the plant. Else the transient response of the plant is likely to grow unbounded. This paper mainly concentrates on employing adaptive control for a type of linear time-invariant (LTI) and linear time-varying (LTV) systems. The time variations in LTV plant parameters are either slow, rapid or fast. This research in turn proposes a two-stage adaptive scheme which swiftly determines the compact region in which plant parameters reside. This method in turn ensures atleast one model to be initialised closer to the plant which significantly reduces parametric estimation error. The uniform boundedness of identification error, tracking error as well as the parametric error of LTI and LTV systems, are deduced. Sufficient examples are also considered to demonstrate the efficacy of the proposed two-stage scheme.