This study proposes an adaptive constraint-following control scheme for an uncertain nonlinear mechanical system. The concerned system is required to follow a class of (holonomic and nonholonomic) equality constraints. Uncertainties (possibly fast time-varying) exist in the dynamics equation and the equality constraints. Meanwhile, the system contains state measurement errors. Both the uncertainties and measurement errors are assumed to be bounded. Based on Udwadia–Kalapa approach and a saturation type adaptive law, an adaptive control scheme is proposed to drive the system to follow the prescribed constraints approximately. Through Lyapunov minimax analysis, it is proved that the resulting control guarantees the uniform boundedness and uniform ultimate boundedness of the closed-loop constrained mechanical system despite the presence of the uncertainties and the measurement errors. Numerical simulations of the vehicle lateral motion control are presented. The results validate the effectiveness of the proposed methodology.

中文翻译：

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具有测量误差的不确定非线性机械系统的自适应约束跟随控制

本研究针对不确定的非线性机械系统提出了一种自适应约束跟随控制方案。相关系统需要遵循一类（完整的和非完整的）等式约束。动力学方程和等式约束中存在不确定性（可能随时间快速变化）。同时，系统包含状态测量误差。假设不确定度和测量误差都是有界的。基于 Udwadia-Kalapa 方法和饱和型自适应律，提出了一种自适应控制方案，以驱动系统近似遵循规定的约束条件。通过李雅普诺夫极小极大分析，结果证明，尽管存在不确定性和测量误差，但所得到的控制保证了闭环约束机械系统的统一有界和统一的最终有界。给出了车辆横向运动控制的数值模拟。结果验证了所提出方法的有效性。