论文标题
贝叶斯关于古典控制的观点
A Bayesian perspective on classical control
论文作者
论文摘要
长期以来,最佳控制与贝叶斯推理之间的连接已被认识到,随机(最佳)控制的领域结合了这些框架,以解决部分可观察到的控制问题。特别是,对于具有二次函数和高斯噪声的线性情况,随机控制在不同领域(包括机器人技术,增强学习和神经科学)显示出了显着的结果,尤其是由于估计和控制过程的既定双重性。遵循这个想法,我们最近引入了PID控制的表述,PID控制是基于主动推理的经典控制方法之一,一种具有变化贝叶斯方法根源的理论以及在生物学和神经科学中的应用。在这项工作中,我们重点介绍了我们以前的配方的优势,并引入了新的,更通用的方法来解决当前控制器设计程序中的一些现有问题。 In particular, we consider 1) a gradient-based tuning rule for the parameters (or gains) of a PID controller, 2) an implementation of multiple degrees of freedom for independent responses to different types of signals (e.g., two-degree-of-freedom PID), and 3) a novel time-domain formalisation of the performance-robustness trade-off in terms of tunable constraints (i.e., priors in a Bayesian model) of a single cost功能性的,各种自由能。
The connections between optimal control and Bayesian inference have long been recognised, with the field of stochastic (optimal) control combining these frameworks for the solution of partially observable control problems. In particular, for the linear case with quadratic functions and Gaussian noise, stochastic control has shown remarkable results in different fields, including robotics, reinforcement learning and neuroscience, especially thanks to the established duality of estimation and control processes. Following this idea we recently introduced a formulation of PID control, one of the most popular methods from classical control, based on active inference, a theory with roots in variational Bayesian methods, and applications in the biological and neural sciences. In this work, we highlight the advantages of our previous formulation and introduce new and more general ways to tackle some existing problems in current controller design procedures. In particular, we consider 1) a gradient-based tuning rule for the parameters (or gains) of a PID controller, 2) an implementation of multiple degrees of freedom for independent responses to different types of signals (e.g., two-degree-of-freedom PID), and 3) a novel time-domain formalisation of the performance-robustness trade-off in terms of tunable constraints (i.e., priors in a Bayesian model) of a single cost functional, variational free energy.