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摘要: 针对存在参数不确定性、外部扰动和输入饱和约束的移动机械臂跟踪控制问题, 提出一种基于自适应动态规划的鲁棒$H_{\infty} $控制方案. 首先, 通过设计神经网络辨识器, 对跟踪误差动力学中的不确定性进行在线估计. 然后, 考虑外部扰动、目标运动扰动和辨识误差, 将鲁棒$H_{\infty} $控制转化为零和博弈问题进行求解, 并在值函数中引入广义非二次泛函来处理输入饱和约束. 进一步, 构建评价网络逼近最优值函数, 获得近似最优控制律及最坏情况下的总扰动估计, 实现闭环系统跟踪误差和评价网络权值估计误差的一致最终有界. 仿真结果验证了所提方案的有效性.Abstract: A robust $H_{\infty} $ control scheme is proposed for the tracking control problem of mobile manipulators based on adaptive dynamic programming under parametric uncertainties, external disturbances and input saturation constraints. First, a neural network identifier is designed to estimate the uncertain dynamics of the tracking error online. Then, considering external disturbances, target motion perturbations and identification error, the robust $H_{\infty} $ control is formulated as a zero-sum game problem for solution, in which a generalized non-quadratic functional is introduced into the value function to address the input saturation constraints. A critic network is further constructed to approximate the optimal value function, and the nearly optimal control law and the estimated worst-case lumped disturbances are obtained. The proposed scheme can achieve the uniform ultimate boundedness of the closed-loop system tracking error and the weight estimation error of the critic network. Simulation results validate the effectiveness of the proposed scheme.
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Key words:
- Mobile manipulator /
- robust H∞ control /
- adaptive dynamic programming /
- visual servoing
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图 4 $H_\infty $控制方案作用下位置和姿态跟踪误差的时间响应
Fig. 4 Time response of position and attitude tracking error with $H_\infty $ control scheme
图 5 LSMC方法作用下位置和姿态跟踪误差的时间响应
Fig. 5 Time response of position and attitude tracking error with LSMC method
图 6 $H_\infty $控制方案作用下相对线速度和角速度的时间响应
Fig. 6 Time response of relative velocity and angular velocity with $H_\infty $ control scheme
图 7 LSMC方法作用下相对线速度和角速度的时间响应
Fig. 7 Time response of relative velocity and angular velocity with LSMC method
图 8 $H_\infty $控制方案作用下控制输入的时间响应
Fig. 8 Time response of control input with $H_\infty $ control scheme
表 1 两种方法的控制成本对比
Table 1 Comparison of control costs between two methods
控制方案 0 ~ 5 s 0 ~ 20 s $ H_\infty $ 控制方案 5.1867 × 1031.6188 × 104LSMC方法 6.3742 × 1031.7338 × 104
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