Prescribed-time control weak disturbance decoupling problems for strict-feedback-like systems with unknown control coefficients, disturbances and zero dynamics.

In many applications, such as manipulators for an assembly line, a prescribed-time controller is required to complete a task at prescribed-time and to continue operating for long time. However, the existing prescribed-time controllers are not well designed for long time operation because prescribed-time adjustment functions used in controllers are not well-defined in some publications and are not differentiable in others. In addition, disturbance decoupling has not been addressed for prescribed-time control. Therefore, the main objective of the paper is to design an adaptive controller so that the impact of disturbances is attenuated for scenarios with disturbances, while at the same time, the system output error is bounded at prescribed-time by positive constant which can be made arbitrarily small and the bounded stability of states can be ensured for situations without disturbances. To this end, the existing prescribed-time adjustment functions are smoothed by using linear combination of exponential functions so that they are sufficiently differentiable for infinite-time, a new weighted norm is defined, and an adaptive prescribed-time almost disturbance decoupling controller is constructed for uncertain strict-feedback-like nonlinear systems with zero dynamics, disturbances and unknown virtual control coefficients. Unboundedness of high-order derivatives of virtual and actual control signals caused by nondifferentiability of the existing prescribed-time adjustment functions is overcome by the proposed sufficiently differentiable prescribed-time adjustment function. Comparative simulation results show that the proposed controller performs better than the existing controllers before and after prescribed-time and is effective for disturbance attenuation.