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

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.