This paper will review some fundamental results in the understanding of several basic problems concerning feedback and uncertainty. First, we will consider adaptive control of linear stochastic systems, in particular, the global stability and optimality of the well-known self-tuning regulators, designed by combining the least-squares estimator with the minimum variance controller. This natural and seemingly simple case had actually been a longstanding central problem in the area of adaptive control, and its solution offers valuable insights necessary for understanding more complex problems. Next, we will discuss the theoretical foundation of the classical proportional-integral-derivative (PID) control, to understand the rationale behind its widespread successful applications in control practice where almost all of the systems to be controlled are nonlinear with uncertainties, by presenting some theorems on the global stability and asymptotic optimality of the closed-loop systems, and by providing a concrete design method for the PID parameters. Finally, we will consider more fundamental problems on the maximum capability and limitations of the feedback mechanism in dealing with uncertain nonlinear systems, where the feedback mechanism is defined as the class of all possible feedback laws. Some extensions and perspectives will also be discussed in the paper.

本文将回顾一些基本结果，以了解有关反馈和不确定性的几个基本问​​题。首先，我们将考虑线性随机系统的自适应控制，尤其是通过结合最小二乘估计器和最小方差控制器来设计的众所周知的自调整调节器的全局稳定性和最优性。这种自然的，看似简单的情况实际上一直是自适应控制领域中一个长期存在的中心问题，它的解决方案为理解更复杂的问题提供了宝贵的见解。接下来，我们将讨论经典比例积分微分（PID）控制的理论基础，通过介绍闭环系统的整体稳定性和渐近最优性的一些定理，并提供具体的设计，以了解其在控制实践中广泛成功应用背后的原理，在控制实践中，几乎所有要控制的系统都是非线性的，具有不确定性PID参数的方法。最后，在处理不确定的非线性系统时，我们将考虑关于反馈机制的最大能力和局限性的更基本的问题，其中将反馈机制定义为所有可能的反馈定律的类别。本文还将讨论一些扩展和观点。通过提供一种针对PID参数的具体设计方法。最后，在处理不确定的非线性系统时，我们将考虑关于反馈机制的最大能力和局限性的更基本的问题，其中将反馈机制定义为所有可能的反馈定律的类别。本文还将讨论一些扩展和观点。通过提供一种针对PID参数的具体设计方法。最后，在处理不确定的非线性系统时，我们将考虑关于反馈机制的最大能力和局限性的更基本的问题，其中将反馈机制定义为所有可能的反馈定律的类别。本文还将讨论一些扩展和观点。