Prescribed-Time Control for Nonholonomic Systems: A Fully Actuated Systems Method

This paper investigates the prescribed-time control problem for nonholonomic systems with time-varying unknown control coefficient. First, by employing a state transformation, a fully actuated and decoupled nonholonomic system is obtained. Different from existing prescribed-time stability theorem, a more general one is presented in this paper to facilitate controller designing. Then, a time-varying fully actuated controller is constructed by using the prescribed-time adjustment function and the Nussbaum function. With the aid of the solution parameter Lyapunov function, it can ensure that all states converge to zero within the prescribed time. Finally, the simulation studies on hopping robot demonstrate the effectiveness of the proposed scheme.