This manuscript introduces the design of a controller that ensures predefined-time convergence for a class of second-order systems. In contrast to finite- and fixed-time controllers, predefined-time schemes allow to prescribe a bound for the convergence time as a control parameter. First, a predefined-time integral sliding mode controller allows rejecting unknown but bounded matched disturbances. Then, the system dynamics evolve free of the effect of disturbances during the integral sliding motion. Finally, an ideal controller enforces convergence also in predefined-time. A Lyapunov-like characterisation for predefined-time stability is conducted, and numerical results are provided to illustrate the validity of the proposed technique.

中文翻译：

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二阶系统的预定义时间积分滑模控制

本手稿介绍了控制器的设计，该控制器可确保一类二阶系统的预定义时间收敛。与有限时间和固定时间控制器相比，预定义时间方案允许规定收敛时间的界限作为控制参数。首先，预定义时间积分滑模控制器允许拒绝未知但有界的匹配干扰。然后，系统动力学在积分滑动过程中不受干扰的影响而发展。最后，理想的控制器也在预定义的时间内强制收敛。对预定义时间稳定性进行了类似李雅普诺夫的表征，并提供了数值结果来说明所提出技术的有效性。