Measurements and Observability Analysis for Biological and Aerospace Applications

Abstract

Improving the observability properties of a system allows us to better estimate the system's states, hence design efficient robust controllers. However, every system is unique with its dynamics and measurement functions, and the existing numerical/analytical observability analysis tools may fail to complete the task because of the sometimes unusual forms of these functions. In this dissertation, we mainly study two questions from an observability point of view: optimal sensor placement on a flapping wing with neural-inspired measurements, and optimal trajectory planning for the estimation of inertial parameters of a rigid body such as spacecraft, airliner, or satellite. The former requires the development of observability analysis tools for systems with output delay and for systems with composite output functions. We pose observability-based optimization problems to achieve the latter task. After studying these problems using deterministic tools, we consider the process noise in the observability analysis, which can reveal observability in systems that would be otherwise regarded as unobservable and use a numerical tool, the stochastic empirical Gramian, to address the problem of sensor placement for systems in the presence of noise.