This article constructs two adaptive control laws to achieve deformation reduction and attitude tracking for a rotary variable-length crane arm with system parameter uncertainties and asymmetric input–output constraints. Two auxiliary systems are given to deal with the input constraints, an asymmetric-logarithm-barrier Lyapunov function is established for achieving the asymmetric output constrains, and five adaptive laws are constructed to handle system parameter uncertainties. Besides, the control design is based on a partial differential equation model, and the S-curve acceleration and deceleration method is used for regulating the arm extension speed. Both the system stability and uniform ultimate boundedness of the controlled crane arm are analyzed. Simulation results validate the effectiveness of our established control laws.

中文翻译：

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具有不对称输入输出约束的柔性变长旋转起重机臂的自适应变形控制


本文构建了两个自适应控制律，以实现具有系统参数不确定性和不对称输入输出约束的旋转变长起重机臂的变形减少和姿态跟踪。给出了两个辅助系统来处理输入约束，建立了非对称对数势垒Lyapunov函数来实现非对称输出约束，并构造了五个自适应律来处理系统参数不确定性。此外，控制设计基于偏微分方程模型，采用S曲线加减速方法调节手臂伸展速度。分析了受控起重机臂的系统稳定性和一致极限有界性。仿真结果验证了我们所建立的控制律的有效性。