Structured adaptive estimation: reliable "grey box" adaptation

状态观测器用于估计系统无法物理测量的内部状态。在控制工程中，使用观测器背后的基本原理是成立的。原则上，观察者需要一个精确的数学模型，在该模型中，系统的动态方程是已知的，只需要估计内部状态。事实上，当对系统动力学了解不多时，观测者的估计性能可能会很差。自适应观测器可以用来估计系统的状态和系统的动态；原则上，它们可以用来从数据中了解关于系统的“一切”。遗憾的是，当前的自适应观测器只有在系统满足一些非常严格的假设时才能可靠地工作，这使得它们不适合于许多实际的现实世界问题。通常，当这些严格的假设不被满足时，特别自适应机制被设计来增加观察者，但结果是虚假的，而且往往很差。这一建议试图通过两个关键方法来扩大人们可以预期其可靠的自适应估计的系统类别。第一个涉及降低自适应估计器的野心：对象将以一种方式被划分，使得已知导致适应问题的动力学的麻烦元素将被排除在适应机制之外，并使用广义上的鲁棒控制(即不确定系统的控制)中的技术来处理。因此，自适应观测器将利用系统结构，并且只更新对其而言“安全”的那些组件。换句话说，为了保证可靠性，一些潜在的性能将被牺牲。扩大系统类别的第二条途径涉及放松系统观察部分(不产生内能)的标准严格要求。这条路将利用无源性条件的放松，该条件源于分析非线性系统的更一般的方法，有时被称为“圆锥扇形”方法，该方法是近年来成熟的，对于无源性是一个特例。该项目也非常强调可用性。事实上，与所有控制系统设计方法一样，需要正确地调整自适应观测器以提供所需的结果。通常，当前自适应控制方法的整定过程明显困难且缺乏直观性。这是自适应控制潜力尚未被挖掘的另一个原因。因此，该项目将处理两个真实世界的案例研究，并建立有效调整适应性观察员的专门知识和指导方针。这种调整方法对于本文开发的研究的未来应用是至关重要的。第一个案例研究将侧重于航空发动机液压机械伺服系统的控制系统的设计，目的是展示相对于该系统目前实施的工业解决方案的改进。第二个案例研究将使用神经生理学记录的实验室数据来估计神经元之间信息转移的分子机制中的隐藏状态。

State observers are used to estimate systems' internal states which cannot be physically measured. In control engineering, the rationale behind the use of observers is well established. In principle, observers require an accurate mathematical model, in which the system's dynamic equations are known and only the internal states need to be estimated. In fact, observers' estimation performance may be poor when not much is known about the system dynamics. Adaptive observers may be used to estimate the system states and the dynamics of the system; in principle they can be used to learn "everything" about a system from just data. Unfortunately, current adaptive observers only work reliably when the system satisfies some very restrictive assumptions, making them unsuitable for many practical real-world problems. Often, ad-hoc adaptive mechanisms are devised to augment observers when these strict assumptions are not satisfied, but results are spurious and often poor. This proposal attempts to expand the class of systems for which one can expect reliable adaptive estimation by two key approaches. The first involves a lowering in ambition of the adaptive estimator: the plant will be partitioned in a way such that troublesome elements of the dynamics, known to cause problems in adaptation, will be excluded from the adaptation mechanism and dealt with using techniques from, broadly speaking, robust control (i.e. the control of uncertain systems). The adaptive observer will therefore exploit system structure and only update those components for which it is "safe" to do so. In other words, some potential performance will be sacrificed for guarantees of reliability. The second path to expanding the class of systems involves loosening the standard strict requirement of passivity of the observed part of the system (no generation of internal energy). This path will exploit a relaxation of the passivity condition which follows from a more general approach to the analysis of nonlinear systems, sometimes referred to as the "conic sector" approach, which has matured in recent years, and for which passivity is a special case.The project has also a strong emphasis on usability. In fact, as with all control system design methods, adaptive observers need to be tuned correctly in order to provide desirable results. In general, tuning procedures for current adaptive control methods are conspicuously difficult and lack intuition. This is one additional reason why the potential of adaptive control has not yet been harvested. The project will therefore address two real-world case studies and establish know-how and guidelines for effective tuning of the adaptive observers. Such a tuning approach is vital for future application of the research developed here. The first case study will focus on the design of the control system for an aero-engine hydro-mechanical servo system aiming at demonstrating improvement with respect to the current industrial solution implemented in the system. The second case study will use lab data from neurophysiology recordings to estimate hidden states in the molecular mechanism of information transfer between neurons.