Distributed moving horizon estimation via dual decomposition

Abstract

This paper presents a distributed moving horizon estimator (DMHE) based on dual decomposition. The DMHE is equivalent to a centralized Kalman filter and allows the distributed implementation of any centralized controller. This equivalence is achieved by formulating the estimation problem as a suitable convex optimization problem. The cost function is defined on a sliding window involving a finite number of past measurements. These measurements are allocated to the estimators without requiring local observability of the complete state. The communication topology of the estimators is represented by a graph and reflected in the optimization problem by additional consensus constraints. A subgradient method is used for solving the decoupled dual optimization problem. The resulting distributed algorithm alternates between updating and transmitting the primal and dual variables. Simulation results of a closed-loop weir system are provided in order to show the main features of the proposed method.

Distributed robust moving horizon estimation for multisensor systems with stochastic and norm‐bounded uncertainties

“… i 2 , and  i 1 are defined in (19). To achieve our goal, we rewrite the cost function (34) as follows…”

“…Our goal is to reach a recursive algorithm for computing the weighting matrices Π i t−N∕t−1 through the steps mentioned above. Using the lemmas and theorems presented in this section, we finally achieve the cost function (55), which in comparison with the cost function (34) does not have uncertain terms. Now, solving the cost function ( 34) for an uncertain system is similar to minimizing the cost function (55) for a nominal system.…”

“…Then, they developed this method for handling time‐varying communication delays in Reference 31, and both data loss and communication delays in Reference 32. The consensus problem for multisensory systems based on a distributed moving horizon estimation has been presented in References 33‐35. Moreover, decentralized moving horizon estimation has been presented for a group of networked spatial‐navigation systems in References 36 and 37.…”

Distributed MHE for Multi-Sensors Based on Measurements Compensation

“…To this end, the moving horizon estimation (MHE) approach [12,13] which can be used for the estimation of control system with constraints is adopted to solve this problem. In [14], the global cost function is decentralized by dual decomposition, then dual variables are communicated according to the network topology to guarantee the consensus and stability of the system. Focused on a class of nonlinear systems which are composed of several subsystems and each subsystem interacts with others via their states, [15] designed the distributed estimation algorithm and the local moving horizon estimation scheme for each subsystem.…”