Structured adaptive estimation: reliable "grey box" adaptation

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.