A Bayesian perspective on classical control
A Bayesian perspective on classical control
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DOI：
10.1109/ijcnn48605.2020.9206617
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Manuel Baltieri
中科院分区：
文献类型：
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作者：
Manuel Baltieri
最优控制和贝叶斯推理之间的联系早已被认识到，随机（最优）控制领域结合了这些框架来解决部分可观察的控制问题。特别是，对于具有二次函数和高斯噪声的线性情况，随机控制在包括机器人、强化学习和神经科学在内的不同领域中显示出显着的成果，特别是由于估计和控制过程的二元性。遵循这个想法，我们最近引入了 PID 控制的公式，这是经典控制中最流行的方法之一，基于主动推理，一种源于变分贝叶斯方法的理论，以及在生物和神经科学中的应用。在这项工作中，我们强调了先前公式的优点，并引入了新的、更通用的方法来解决当前控制器设计过程中存在的一些问题。特别是，我们考虑 1）PID 控制器参数（或增益）的基于梯度的调整规则，2）对不同类型信号独立响应的多自由度实现（例如，二自由度 PID），以及 3）在单一成本函数、变分自由的可调约束（即贝叶斯模型中的先验）方面，性能鲁棒性权衡的新颖时域形式化能量。
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.