Adaptive output regulation of unknown linear systems with unknown exosystems

The problems of the output regulations and/or disturbance reductions have attracted a lot of interest and have been actively researched in the consideration of the control problem for systems which are required to have servomechanism and for vibration attenuation in mechanical systems. It is well known that such problems are solvable using the Internal Model Principle in cases where the system to be controlled and the exosystem which generates the output reference signal and external disturbances are known. In the case where the controlled system is unknown and/or the exosystem is unknown, adaptive control strategies have played active roles in solving such problems for systems with uncertainties. For known systems with unknown exosystems, solutions with adaptive internal models have been provided in (Feg & Palaniswami, 1991), (Nikiforov, 1996) and (Marino & Tomei, 2001). In (Marino & Tomei, 2001), an output regulation system with an adaptive internal model is proposed for known non-minimum phase systems with unknown exosystems. Adaptive regulation problems have also been presented for time varying systems and nonlinear systems (Marino & Tomei, 2000; Ding, 2001; Serrani et al., 2001). Most of these methods, however, assumed that either the controlled system or the exosystem was known. Only few adaptive regulation methods for unknown systems with unknown exosystems have been provided (Nikiforov, 1997a; Nikiforov, 1997b). The method in (Nikiforov, 1997a) is an adaptive servo controller design based on the MRAC strategy, so that it was essentially assumed that the order of the controlled system was known. The method in (Nikiforov, 1997b) is one based on an adaptive backstepping strategy. In this method, it was necessary to design an adaptive observer that had to estimate all of the unknown system parameters depending on the order of the controlled system. Further, the controller design based on the backstepping strategy essentially depends on the order of the relative degree of the controlled system. As a result, the controller's structure was quite complex in both methods for higher order systems with higher order relative degrees.