Adaptive Prescribed-Time Control for Uncertain Nonlinear Cascaded Systems With Time-Varying Constraints

This paper studies the problem of prescribed-time stabilization for uncertain nonlinear cascaded systems consisting of inverse dynamics and the nonholonomic system with time-varying asymmetric constraints. For handling the time-varying asymmetric constraints, the unified tan-type barrier Lyapunov function is constructed, and the parameter separation technique is used to address the nonlinear uncertainties. By combining the integral input-to-state stable Lyapunov function with the changing supply rates technique, the stability of inverse dynamics is achieved. It is noted that the prescribed-time adjustment function is directly embedded into the controllers, reducing the computational burden of the state scaling transformations. The designed adaptive prescribed-time control strategy guarantees that all measurable states of the cascaded system converge to zero within a prescribed time while satisfying the time-varying output constraints. The effectiveness of the proposed scheme can be verified through a simulation example.