离散非线性系统的迭代学习轨迹跟踪鲁棒算法优化及应用

Robust Optimization and Application of Iterative Learning Trajectory Tracking Algorithm for Discrete Nonlinear Systems

针对一类存在随机输入状态扰动、输出扰动及系统初值与给定期望值不严格一致的离散非线性重复系统,提出了一种P型开闭环鲁棒迭代学习轨迹跟踪控制算法.基于λ范数理论证明了算法的严格鲁棒稳定性,并通过多目标函数性能指标优化P型开闭环迭代学习控制律的增益矩阵参数,保证了优化算法下系统输出期望轨迹跟踪误差的单调收敛性,达到提高学习算法收敛速度和跟踪精度的目的.最后应用于二维运动移动机器人的实例仿真,验证了本文算法的可行性和有效性.

For a class of discrete nonlinear repeated systems with random input and output disturbances, we propose an open-closed loop P-type robust iterative learning trajectory tracking control .algorithm for cases in which the initial states are not strictly identical to given expected values. Based on the A norm theory, we prove the robust stability of the iterative learning algorithm, and optimize the gain matrix parameters of the P-type openclosed control law based on the performance of the multiple objective function. In this way, the monotonic convergence of the trajectory output tracking error can be guaranteed by the optimization ＇algorithm, which improves the convergence speed and tracking accuracy. Lastly, our simulation results of a mobile robot in twodimensional motion show the effectiveness and feasibility of the proposed algorithm.