Approximate moving horizon estimation for switching conservative linear infinite-dimensional systems

Abstract

This work addresses moving horizon estimation for switching conservative linear infinite-dimensional systems described by partial differential equations (PDE), where the plant and measurement equations are corrupted with bounded disturbances, and the system mode is regarded as an unknown and unpredictable discrete state to be estimated. To address the issues associated with unbounded operators (induced by boundary or point observation and disturbance) and facilitate discrete-time moving horizon estimator design, the Cayley–Tustin transformation is deployed for model time-discretization without any spatial discretization or model reduction while preserving model essential properties. A series of observability concepts along with corresponding properties are proposed and analyzed for the switching linear infinite-dimensional discrete-time systems. A moving horizon estimation algorithm that accounts for state/output and mode estimation and constraint handling is proposed. Based on the proposed observability properties, we prove the stability of the proposed moving horizon estimator. The derived results are demonstrated by an undamped Schrödinger equation with switching group-velocity dispersion.