Most autonomous systems can be described by Euler–Lagrange (EL) model. This article investigates the problem of prescribed time tracking control for EL systems in the presence of modeling uncertainties, prescribed performance requirements and time-varying state constraints. Two proportional–integral (PI)-like control schemes with time-varying gains are developed with several favorable features: (1) achieving prescribed tracking precision within finite time in the presence of modeling uncertainties; (2) state constraints being obeyed all the time; (3) both the final tracking accuracy and the setting time being preassigned irrespective of initial condition or any other constraining parameter; and (4) bearing simple PI structure with analytical formula for robust-adaptive tuning gains, and demanding inexpensive online computation. The benefits and effectiveness of the proposed control are also validated via numerical simulation.

中文翻译：

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约束欧拉-拉格朗日系统的规定时间跟踪控制：自适应比例积分解

大多数自治系统可以用欧拉-拉格朗日（EL）模型来描述。本文研究了存在建模不确定性、规定的性能要求和时变状态约束的 EL 系统的规定时间跟踪控制问题。开发了两种具有时变增益的类似比例积分（PI）的控制方案，具有几个有利的特征：（1）在存在建模不确定性的情况下，在有限时间内实现规定的跟踪精度；(2) 始终遵守状态约束；(3) 最终跟踪精度和设定时间均预先指定，与初始条件或任何其他约束参数无关；(4) 具有简单的PI结构，具有鲁棒自适应调谐增益的解析公式，需要廉价的在线计算。