Core Concepts
This paper introduces a novel distributed algorithm for tracking ellipsoids that approximate the global intersection, ensuring convergence and robustness against time-varying inputs.
Abstract
The paper presents a distributed algorithm to track ellipsoids approximating the global intersection. It proves convergence and robustness in both static and dynamic cases. The proposed method extends consensus algorithms to positive definite matrices, showcasing improved performance in distributed Kalman filtering.
The outer L¨owner-John method is discussed as a centralized solution for approximating the intersection of ellipsoids. The paper introduces a novel distributed algorithm that ensures finite-time convergence to the global minima in static scenarios and bounded tracking error in dynamic cases. The theoretical properties of the algorithm are analyzed, highlighting its robustness and boundedness.
The content also covers related works on distributed optimization methods, emphasizing challenges posed by non-separable objective functions and global coupling constraints. The proposed algorithm addresses these challenges through a novel distributed reformulation approach.
Overall, the paper provides insights into applying distributed algorithms for tracking ellipsoids in various applications such as stochastic estimation, cooperative control, and computer vision tasks.
Stats
Qi[k] ∈ rebdr(Ci[k])
λ∗i = 1/N ∑ λiP(1 - Pj∈Ni λjl)
Q∗[k] = Σλ∗jPj[k]^-1
Qi[k]=Q∗⪯λiPPi[k]^-1+ΣλijQ∗ → Q*
Quotes
"The proposed algorithm ensures finite-time convergence to the global minima of the centralized problem."
"Our proposal extends min/max dynamic consensus algorithms to positive definite matrices."
"Theoretical properties of the algorithm are analyzed, highlighting its robustness and boundedness."