基于初态学习的非仿射非线性系统的开闭环PD型迭代学习控制

Open-closed-loop PD-type iterative learning control with initial state learning for non-affine nonlinear system

针对非仿射非线性系统,提出了新的学习控制算法,即初态未知情况下系统的输入和初态都需要进行学习的开闭环PD型迭代学习控制,并给出了该算法的收敛性充分条件.初态学习允许系统在每次迭代开始时有一定的定位误差,不严格要求其初态与期望初态重合或固定于某一具体位置上.该算法允许初态在收敛性条件范围内任意设置,从而保证了学习控制系统具有初始定位误差的鲁棒收敛性.依据此收敛性条件,可确定输入学习律及初态学习律的学习增益.利用压缩映射分析方法,证明了系统在任意初始状态下经过迭代后,其输出能够完全跟踪期望轨迹.该算法解决了初始值未知情况下的收敛性问题,且放宽了收敛条件,并通过仿真结果验证了所提算法的有效性.

For non-affine nonlinear system,a new learning control algorithm is proposed,namely an open-closed-loop PD-type iterative learning control principle with input and initial state all needed to learn under initial state unknown,and the sufficient condition for convergence is put forward.The learning algorithm will not fix the initial condition on the expected condition or on the specific position at the beginning of iteration.A certain degree of orientation bias in the initial condition is allowed.The learning control system under initial alignment errors are of robust convergence,which allow initial value any set within convergence conditions.Based on this convergence condition,the learning gain of initial learning principle and input learning principle can be determined.Using the contraction mapping method,it is proved that the output of the system with an arbitrary initial state can track the expected trajectory completely after iteration.The problem of convergence with initial state unknown is solved,and the convergent condition is relaxed.The simulation results testify that the proposed algorithm is effective.