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

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. INDEX TERMS Set-membership filter, quadratic inequality constraints, nonlinear dynamic systems, ellipsoidal estimation. I. INTRODUCTION Filtering techniques are widely used in target tracking, signal processing, system identification, fault diagnosis, robotics, navigation, etc [1]-[5]. For linear dynamic systems, Kalman filter (KF) [6] is the minimum-variance linear state estimator for both Gaussian and non-Gaussian noise [7]. However, this is not possible for general nonlinear dynamic systems. Furthermore, estimation for nonlinear systems is quite extensive in practice. Nonlinearities are widely included in vehicle navigation, dialysis machines, and many other areas [8]. In the present case, a few modifications of KF, including the extended Kalman filter (EKF) [9], the unscented Kalman filter (UKF) [10], and the particle filter (PF) [11], were used to estimate the state. Constrained dynamic systems frequently occur in practical applications [12]-[14]. The constraints may arise from physical laws or mathematical properties. For instance, civil The associate editor coordinating the review of this manuscript and approving it for publication was Qichun Zhang .

Nonlinear Set Membership Filter with State Estimation Constraints via Consensus-ADMM

“…Therefore, it is significant to consider state estimators with various estimation constraints. Previous studies on set membership filters mainly focus on state constraints, such as [27,28,29] and the references therein. However, even if the state constraint information is used in the filtering process to ensure that the state bounding ellipsoids take into account the state constraint, the state estimates that are given by the ellipsoidal SMF (the center of the state bounding ellipsoids) generally do not satisfy the constraint.…”