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

ABSTRACT 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.