Iterative learning control (ILC) is a powerful technique for high performance tracking in the presence of modeling errors for optimal control applications. There is extensive prior work showing its empirical effectiveness in applications such as chemical reactors, industrial robots and quadcopters. However, there is little prior theoretical work that explains the effectiveness of ILC even in the presence of large modeling errors, where optimal control methods using the misspecified model (MM) often perform poorly. Our work presents such a theoretical study of the performance of both ILC and MM on Linear Quadratic Regulator (LQR) problems with unknown transition dynamics. We show that the suboptimality gap, as measured with respect to the optimal LQR controller, for ILC is lower than that for MM by higher order terms that become significant in the regime of high modeling errors. A key part of our analysis is the perturbation bounds for the discrete Ricatti equation in the finite horizon setting, where the solution is not a fixed point and requires tracking the error using recursive bounds. We back our theoretical findings with empirical experiments on a toy linear dynamical system with an approximate model, a nonlinear inverted pendulum system with misspecified mass, and a nonlinear planar quadrotor system in the presence of wind. Experiments show that ILC outperforms MM significantly, in terms of the cost of computed trajectories, when modeling errors are high.
翻译:在模拟最佳控制应用的模型错误的情况下,迭代学习控制(ILC)是高性能跟踪的有力技术,在最佳控制应用模型错误的情况下,是一种高性能跟踪高性能的强大技术; 先前的大量工作表明,在化学反应堆、工业机器人和四氯底管等应用方面,它的经验性效力; 然而,即使存在大型建模错误,也很少进行理论工作来解释国际法委员会的效力,即使存在大型建模错误的情况下,使用错误指定模型(MMM)的最佳控制方法往往效果不佳; 我们的工作是对LILC和MMM在Linear Quaberatic 调控管(LQR)问题上的性能进行这种理论性研究; 我们表明,在最佳LQR控制器控制器的最佳 LQQR控制器方面,其亚优性差比MMC值低,因为高的订单性能条件在高的建模模型(MMMM)环境中的离心线方方程式。 解决方案不是固定点,而需要用回溯线追踪错误。 我们的理论发现,在ILCLCLC Firal Studal Studal Priformex系统中, listreformodrodu,在模型的不甚高性能系统上进行实验性实验性实验。