Retrospective Cost Adaptive Control of Nonlinear Systems Using Ersatz Nonlinear Models

本课题的目标是研究非线性系统在最小建模信息下的自适应控制技术。本工作的基础是回溯成本自适应控制（RCAC），它适用于建模信息极其有限的线性系统。我们的目标是将这种方法扩展到非线性系统。一个典型的例子是一个线性系统，前面有一个不确定的非线性输入，如死区或饱和。这个项目的新颖部分是使用伪非线性模型，它捕捉了其他不确定非线性的关键特征，以确保正确的适应。例如，关于真正非线性的唯一可靠信息可能是它的单调性，即它在增加或减少的区间。伪非线性随后捕捉到这种行为，但在其他所有细节上可能都是不正确的。因此，研究目标是确定非线性的特征，这些知识对RCAC至关重要。影响人类的控制系统必须非常可靠，因为它们的故障可能危及生命和财产。不幸的是，控制系统往往无法在紧急情况下运行，而具有讽刺意味的是，这往往是最需要控制系统的时候。人类无需使用计算机就能控制车辆和机器，而是在系统运行时从经验中学习。因此，我们的目标是将这种能力扩展到计算机上，因为计算机缺乏人类对现实世界的直觉。计算机自适应控制车辆或机器的能力将增加控制系统的可靠性，这在紧急情况下可能至关重要，例如当汽车在结冰的道路上刹车或飞机发生故障时。这项研究的另一个好处是减少了实施可靠控制系统所需的时间和成本。

The goal of this project is to investigate adaptive control techniques for nonlinear systems under minimal modeling information. The basis of this work is retrospective cost adaptive control (RCAC), which is applicable to linear systems under extremely limited modeling information. The goal is to extend this approach to nonlinear systems. A prototypical case is a linear system preceded by an uncertain input nonlinearity, such as a deadzone or saturation. The novel component of this project is the use of ersatz nonlinear models, which capture key features of the otherwise uncertain nonlinearity in order to ensure correct adaptation. For example, the only reliable information about the true nonlinearity may be its monotonicity, that is, intervals within which it is increasing or decreasing. The ersatz nonlinearity then captures this behavior, but may be otherwise incorrect in all other details. The research goal is thus to determine the features of the nonlinearities whose knowledge is essential to RCAC.Control systems that affect humans must be extremely reliable since their failure can endanger lives and property. Unfortunately, control systems are often unable to operate under emergency conditions, which is, ironically, the times when they are often most needed. Humans control vehicles and machines without using computers, but rather by learning from experience as the system operates. Our goal is thus to extend this ability to computers, which lack the intuition about the real world that humans possess. The ability of computers to adaptively control a vehicle or machine will increase the reliability of the control system, which may be crucial in an emergency situation, such as when an automobile brakes on an icy road or an airplane experiences a failure. An additional benefit of this research is the reduced time and cost needed to implement reliable control systems.