Robust stability and suboptimality in nonlinear moving horizon estimation --- From conceptual to practically relevant guarantees

• Applicant: Professor Dr.-Ing. Matthias Müller
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 426459964

Moving horizon estimation (MHE) is an optimization-based state estimation strategy. At each time instant, a fixed finite number of past output measurements is considered in order to determine an estimated state and disturbance trajectory over this past time interval by solving an optimization problem. The main advantages of MHE and reasons for its success in many different applications are that this estimation strategy is applicable to general nonlinear systems and that it is easily possible to incorporate known constraints on states and/or disturbances into the repeatedly solved optimization problem in order to improve the estimator performance. Since disturbances and measurement noise are present in most practical applications, it is of intrinsic importance to establish robust stability and performance guarantees for MHE. To this end, various results have been obtained in recent years in the context of nonlinear systems. These are, however, typically overly conservative and/or require restrictive assumptions, thus limiting their value for practical applications. In the first funding period of this project, we have developed general nonlinear MHE schemes for which less conservative guarantees can be given. In particular, we were able to establish practically relevant conditions using a Lyapunov-based stability analysis and develop methods to verify them systematically. To enhance the real-time capability of MHE, we have developed several suboptimal MHE schemes that do not require a globally optimal solution to the optimization problem solved at each time step. Instead, robust stability can be guaranteed independent of the number of solver iterations performed. The main goal of the second funding period is to further extend the applicability of MHE in practice. This includes joint state and parameter estimation, where we will develop MHE schemes for which rigorous stability guarantees can be given even in the absence of persistently excited data. In addition, we will consider large-scale systems, which are becoming increasingly common, for example, in the context of electricity grids or manufacturing networks. We will develop distributed MHE schemes and derive practically relevant stability guarantees that are structurally independent of changes in network topology or system size. Finally, we will consider MHE in the context of model predictive control with output measurements, which is one of the most important applications of MHE in practice. Since control and estimation algorithms for nonlinear systems cannot generally be separated, it is essential to analyze them in a holistic framework. Here we will establish robustness, stability, and performance guarantees for the closed loop by exploiting the MHE theory we have developed.

• DFG Programme: Research Grants