Sample-based Moving Horizon Estimation
This addresses state estimation challenges in control systems with non-uniform sampling, offering a theoretical guarantee for stability, but it is incremental as it extends existing MHE methods to irregular sampling scenarios.
The paper tackles state estimation for nonlinear systems with irregular or infrequent measurements by proposing a sample-based moving horizon estimation scheme, achieving robust global exponential stability under a detectability condition and demonstrating effectiveness through simulation.
In this paper, we propose a sample-based moving horizon estimation (MHE) scheme for general nonlinear systems to estimate the current system state using irregularly and/or infrequently available measurements. The cost function of the MHE optimization problem is suitably designed to accommodate these irregular output sequences. We also establish that, under a suitable sample-based detectability condition known as sample-based incremental input/output-to-state stability (i-IOSS), the proposed sample-based MHE achieves robust global exponential stability (RGES). Additionally, for the case of linear systems, we draw connections between sample-based observability and sample-based i-IOSS. This demonstrates that previously established conditions for linear systems to be sample-based observable can be utilized to verify or design sampling strategies that satisfy the conditions to guarantee RGES of the sample-based MHE. Finally, the effectiveness of the proposed sample-based MHE is illustrated through a simulation example.