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

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. Most of these results are, however, only applicable under restrictive conditions and/or in special situations (such as no or asymptotically vanishing disturbances).For the practically relevant case of general nonlinear detectable systems subject to unknown and bounded (and possibly persistent) disturbances, some first few theoretical guarantees have been obtained very recently by us and others. These results are, however, of rather conceptual nature since they are typically overly conservative and/or require restrictive assumptions, thus limiting their value for practical applications.

The main goal of this project is the development of general nonlinear MHE schemes for which desired robust stability and performance guarantees can be established under realistic conditions. This includes the development of suboptimal MHE approaches, which do not require a globally optimal solution to the repeatedly solved optimization problem. This is crucial in practical applications, since one can in general not assume to solve the underlying nonlinear, nonconvex optimization problem to (global) optimality in real-time online. Furthermore, within this project we will develop an “economic” MHE framework where we exploit recently obtained insights from the “dual” field of economic model predictive control. This will result in novel tools and techniques for the design and analysis of nonlinear MHE schemes with desired robust stability and performance guarantees.