A time-varying high-gain approach to feedback regulation of uncertain time-varying nonholonomic systems

Abstract

In this paper, novel state feedback and output feedback control strategies are proposed to regulate a class of uncertain time-varying nonholonomic systems with lower-triangular nonlinearities. The nonlinearities admit an incremental rate depending on an unknown parameter and an essential time-varying function. By means of the input-state-scaling technique, the involved systems are firstly transformed into a class of lower-triangular systems. The time-varying high-gain method is then introduced to tackle the system uncertainties and essential time-varying features simultaneously, and based on this, the time-varying state feedback controllers are constructed to achieve the state feedback regulation of the involved systems. Finally a time-varying high-gain observer is proposed to effectively compensate for system uncertainties and essential time-varying features, and on the basis of this, the time-varying output feedback controllers are constructed to achieve the output feedback regulation of the involved systems. Two illustrative examples are provided to demonstrate the effectiveness of the proposed control strategies.

Keywords: Feedback regulation; High-gain method; Nonholonomic systems; Time-varying systems; Uncertainty.