Prescribed-time control for nonholonomic systems: a fully actuated systems method

This paper addresses the prescribed-time control problem for a class of nonholonomic systems subject to time-varying unknown control coefficients. Firstly, a state transformation is introduced to convert the original system into a fully actuated and decoupled form, which significantly simplifies the subsequent controller design process. In contrast to existing prescribed-time stability theorems, a more generalised stability criterion is proposed in this work, offering greater flexibility and reduced conservatism in the analysis and synthesis of controllers. Subsequently, a time-varying fully actuated controller is developed by integrating a prescribed-time adjustment function with a Nussbaum-type function, effectively handling the unknown control coefficients. Supported by a parameterised Lyapunov function framework, the proposed control scheme guarantees that all system states converge to zero exactly within a user-defined prescribed time. Finally, simulation results performed on a hopping robot model validate the effectiveness and superiority of the proposed control strategy.