Set-Membership Filtering for Nonlinear Dynamic Systems With Quadratic Inequality Constraints

Xiaowei Li,Xuqi Zhang,Xuedong Yuan,Haiqi Liu,Yiwei Liao,Xiaojing Shen,Fanqin Meng

doi:10.1109/access.2020.2966250

Abstract

The present study investigates the problem of set-membership filtering for nonlinear dynamic systems with general nonconvex inhomogeneous quadratic inequality constraints. The investigators propose an ellipsoidal state bounding estimation in the setting of unknown but bounded noise. In order to guarantee the on-line usage, the nonlinear function is linearized by Taylor expansion at each time step, where the bounding ellipsoid of the remainder is updated on-line based on the current state bounding ellipsoid. Furthermore, based on the remainder bounds and the constraints, both the state prediction and measurement update of the filtering can be transformed into a semidefinite programming problem that can be efficiently solved. In order to further reduce the computational complexity, a part-analytical formula of the shape matrix and the center of the bounding ellipsoid is derived using a decoupled technique, which is also helpful to clarify how these constraints affect the state estimation. Finally, typical numerical examples demonstrate the effectiveness of this filtering.

Highlights

Filtering techniques are widely used in target tracking, signal processing, system identification, fault diagnosis, robotics, navigation, etc [1]–[5]
The filtering problem for nonlinear dynamic systems with general nonconvex inhomogeneous quadratic inequality constraints has not been considered under the set-membership filter framework
The present study investigated the problem of setmembership filtering for nonlinear dynamic systems with general nonconvex inhomogeneous quadratic inequality constraints

Summary

INTRODUCTION

Filtering techniques are widely used in target tracking, signal processing, system identification, fault diagnosis, robotics, navigation, etc [1]–[5]. X. Li et al.: Set-Membership Filtering for Nonlinear Dynamic Systems With Quadratic Inequality Constraints. Set-membership filtering for nonlinear equality constrained linear dynamic systems was addressed in a study [34], and linear dynamic systems with state linear equality constraints and a specific positive semidefinite quadratic inequality constraint were given concerned in a study [5]. The filtering problem for nonlinear dynamic systems with general nonconvex inhomogeneous quadratic inequality constraints has not been considered under the set-membership filter framework. Focus was given on the setmembership filtering problem for nonlinear dynamic systems with general nonconvex inhomogeneous quadratic inequality constraints.

PROBLEM FORMULATION

PREDICTION STEP

MEASUREMENT UPDATE STEP

CONCLUSION