Robust Stability and Performance of Nonlinear Moving Horizon Estimation

Having access to the internal state of a dynamical system is of crucial importance for many control applications. In most practical cases, however, the state cannot be completely measured for various reasons, demanding the use of appropriate reconstruction methods. This represents a challenging problem, especially in the presence of nonlinear systems and when robustness to model errors and measurement noise must be ensured. Moving horizon estimation (MHE) is a modern optimization-based state estimation strategy that is naturally suitable for this purpose. In this thesis, we develop various new results in the field of nonlinear MHE. We establish desired robust stability guarantees under realistic conditions, propose MHE schemes for real-time applications, and investigate methods for joint state and parameter estimation -- particularly tailored to applications in which weak excitation occurs frequently and unpredictably. Moreover, we draw connections to optimal control and turnpike theory, leading to a new perspective on MHE and ultimately to novel performance estimates and regret guarantees. We illustrate our theoretical results with various numerical examples from the literature, which highlight the applicability and practical relevance of the developed theory.