Estimation and Control of Nonlinear Hybrid Systems and Nonaffine Control

Abstract

This dissertation consists of three parts which present new results in three areas of nonlinear estimation and control. The first part presents systematic methods to synthesize interval observers, which are set-based state estimators, for nonlinear switched systems and nonlinear impulsive systems. Interval observers are designed to ensure positivity and input-to-state (ISS) stability of the error dynamics. The observer gains and other interval observer parameters are synthesized by solving convex programming problems in the forms of linear programs and linear matrix inequalities (LMIs). In general, it is a difficult task to ensure both the positivity and stability of the error dynamics. To overcome this challenge, a common approach is to find a different set of coordinates where the interval observer can be synthesized to ensure positivity and stability more easily. Interval observers for hybrid systems usually require multiple coordinate transformations to be incorporated into the design. For example, in impulsive systems, two coordinate systems are required: one for the continuous part, and one for the jump part. The second part of this dissertation is focused on estimation and control of nonlinear systems that are implemented on digital platforms. Traditionally, digital control systems are implemented in a periodic fashion. In contrast, self-triggered and event-triggered control/estimation is implemented in an aperiodic fashion by introducing feedback into the sensing and actuation. The goal is to reduce the amount of sampling compared to periodically sampled controllers/estimators. Systematic methods to design self-triggered estimators and periodic event-triggered controllers for nonlinear systems are presented. These methods guarantee a reduction of sampling. The final part proposes constructive methods to design controllers for Coulomb spacecraft formations. Coulomb formations are controlled by manipulating the charges of the the spacecraft in the formation, so, by Coulomb's law, the dynamics are nonlinear in the control.