Average Tracking Algorithm Research Articles

Delay and Packet-Drop Tolerant Multistage Distributed Average Tracking in Mean Square.

This article studies the distributed average tracking (DAT) problem pertaining to a discrete-time linear time-invariant multiagent network, which is subject to, concurrently, input delays, random packet drops, and reference noise. The problem amounts to an integrated design of delay and a packet-drop-tolerant algorithm and determining the ultimate upper bound of the tracking error between agents' states and the average of the reference signals. The investigation is driven by the goal of devising a practically more attainable average tracking algorithm, thereby extending the existing work in the literature, which largely ignored the aforementioned uncertainties. For this purpose, a blend of techniques from Kalman filtering, multistage consensus filtering, and predictive control is employed, which gives rise to a simple yet comepelling DAT algorithm that is robust to the initialization error and allows the tradeoff between communication/computation cost and stationary-state tracking error. Due to the inherent coupling among different control components, convergence analysis is significantly challenging. Nevertheless, it is revealed that the allowable values of the algorithm parameters rely upon the maximal degree of an expected network, while the convergence speed depends upon the second smallest eigenvalue of the same network's topology. The effectiveness of the theoretical results is verified by a numerical example.

Design of Distributed Event-Triggered Average Tracking Algorithms for Homogeneous and Heterogeneous Multiagent Systems

This article addresses the design problem of distributed event-triggered average tracking (DETAT) algorithms for homogeneous and heterogeneous multiagent systems. The objective of the DETAT problem is to develop a group of distributed cooperative control algorithms with event-triggered strategies for agents to track the average of multiple time-varying reference signals. First, for homogeneous linear multiagent systems, based on sampling measurements and model-relied holding techniques, a class of static-gain DETAT algorithms is proposed with a couple of local event-triggered functions for estimators and controllers, respectively. Compared with the existing distributed average tracking (DAT) algorithms, the static-gain DETAT algorithms greatly reduce the cost over communication networks and the frequency of control protocol updates. Second, to reduce the chattering phenomenon caused by nonsmooth items in static-gain algorithms and requirements of the global information of networks, smooth dynamic-gain DETAT algorithms are introduced based on boundary layer approximation methods and self-adaptive principles. Third, for heterogeneous linear multiagent systems, a new algorithm is established by using the output regulation techniques for the heterogeneous DETAT problem. The outputs of heterogeneous agents can ultimately track the average of multiple time-varying reference signals. To the best of our knowledge, it is the first time to study the DETAT problem for heterogeneous multiagent systems. Finally, some examples are presented to show the validity of theoretical results.

Design Fixed-Time Practical Distributed Average Tracking Algorithms for Nonlinear Signals With Bounded- and Lipschitz-Type Derivatives

In this brief, the fixed-time practical distributed average tracking (DAT) problem for multiple nonlinear signals is studied, where the nonlinear signals are with bounded- and Lipschitz-type derivatives respectively. Two fixed-time practical DAT algorithms are proposed for agents with local interactions to track the average of the multiple nonlinear signals within a fixed convergence time by using time-base generator techniques. Different from existing results, the proposed DAT algorithms in this brief are applicable to DAT problems for nonlinear signals with both bounded- and Lipschitz-type derivatives, which keeps more reality. Also, the proposed fixed-time practical DAT algorithms are able to provide an explicit estimation of the upper-bounded convergence time without dependence on initial conditions. The fixed convergence time in the proposed algorithms can be adjusted more flexibly. Finally, some illustrative examples are shown to manifest the validity of the fixed-time practical DAT algorithms.

Distributed Dynamic Averaging Tracking Without Rate Measurements

This article introduces a dynamic average tracking algorithm for multiagent systems over weight-balanced direct graphs. Toward the end, we propose a proportional-integral distributive observer for each system with exponential convergence. In particular, the proposed algorithm only requires mild initialization conditions, does not rely on the time derivatives of reference signals and can ensure average consensus tracking with bounded steady-state error. The simulation results verified the performance of the proposed scheme.

Distributed Kalman–Bucy Filter With Embedded Dynamic Averaging Algorithm

This paper focuses on distributed estimation using networked sensor agents with local measurements and local communication. A distributed Kalman–Bucy filter implementation is proposed and analyzed for the general case of continuous-time linear time-varying systems as compared to linear time-invariant systems. The sensor agents employ a distributed average tracking algorithm and its extension that accounts for bounded noise to estimate the averages of certain time-varying signals by communicating with their local neighbors in the network. Such estimates are then used to recover certain information in the implementation of the distributed Kalman–Bucy filter. It is shown that using the proposed distributed filter, in the absence of measurement noise, the distributed local estimates approach the centralized filter's estimate asymptotically. In the presence of bounded measurement noise, the distributed local estimates asymptotically approach the centralized filter's estimate within some bound. Simulation results illustrate the good performance of the distributed filter.

SU‐FF‐J‐30: Experimental Investigation of Moving Average Algorithm for Tracking Organ Motion

Purpose: To investigate the geometric and dosimetric properties of the moving average tracking algorithm compared with real time tracking and static beam. Method and Materials: Patient motion traces from the Cyberknife Synchrony™ were categorized into 3 types of motion: a regular motion with/without baseline drift and irregular motion. Each motion trace was reproduced with the help of a 4D motion platform. Time averaged mean position of the phantom was used to control dMLC position in the perpendicular direction to the leaf travel. Geometric accuracy, delivery efficiency and dose distribution were evaluated for static, IMRT step‐and‐shoot and sliding window plan using simulated and patient motion traces. The geometric accuracy was calculated from the displacement between the target center and the beam center using a real‐time beam's‐eye‐view videos with a circular aperture. For dosimetric measurements, PTW ion chamber array (model 729) was sandwiched between 2 cm thickness of solid water phantoms and irradiated for one field. Dosimetric impact was quantified via gamma index with a 3% dose‐3mm criterion. Results: The difference of RMS geometric error (mm) between the real‐time tracking and moving average tracking was about 3 mm which was similar to errors caused by random motion. The percentages of failing points in the gamma analysis for moving average tracking were reduced by above half of the percent difference between no compensation and real‐time tracking. Delivery efficiencies for moving average tracking were above 97% comparable to static delivery case. Conclusions: Mean position tracking was useful for compensating a baseline drift to improve a geometric and delivery accuracy with high delivery efficiency.