输入增益未知非参数不确定系统的准最优学习控制

Suboptimal Learning Control for Nonparametric Systems With Uncertain Input Gains

为解决一类非参数不确定系统在任意初态且输入增益未知情形下的轨迹跟踪问题,提出准最优误差跟踪学习控制方法.该方法综合准最优控制和迭代学习控制两种技术设计控制器,在构造期望误差轨迹的基础上,根据控制Lyapunov函数及Sontag公式给出标称系统的优化控制,以鲁棒方法和学习方法相结合的策略处理非参数不确定性.闭环系统经过足够次迭代运行后,经由实现系统误差对期望误差轨迹在整个作业区间上的精确跟踪,获得系统状态对参考信号在预设的部分作业区间上的精确跟踪.仿真结果表明所设计学习系统在收敛速度方面快于非优化设计.

This paper presents a suboptimal error-tracking iterative learning control(ILC)scheme to solve the trajectorytracking problem for a class of nonparametric systems with uncertain input gains in the presence of arbitrary initial states.The ILC controller is developed by integrating ILC with suboptimal control.Firstly,a desired error trajectory is constructed according to the given method,and then Sontag formula is employed for the control design of nominal system,while robust control and learning control are synthetically applied to deal with nonparametric uncertainties.While the closed-loop system operates,as iteration number increases,the controller can render system error to perfectly follow its desired error trajectory over the entire time interval,by which,the system state can precisely track its reference signal in the pre-specified part of above-mentioned interval.Numerical simulations demonstrate that our suboptimal error-track ILC scheme improves convergence performance in comparison with conventional solutions.