Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations

TLDR

Constrained state estimation for nonlinear discrete‑time systems is challenging, especially with inequality constraints, and a deterministic framework using moving horizon optimization is a common strategy. The paper proposes a general theory for constrained moving horizon estimation. The authors develop a practical algorithm based on moving horizon approximation for constrained linear and nonlinear state estimation. The theory provides sufficient conditions for asymptotic and bounded stability, and examples demonstrate the benefits of constrained state estimation.

Abstract

State estimator design for a nonlinear discrete-time system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ online optimization using a moving horizon approximation. We propose a general theory for constrained moving horizon estimation. Sufficient conditions for asymptotic and bounded stability are established. We apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation. Examples are used to illustrate the benefits of constrained state estimation. Our framework is deterministic.