Distributed control of linear time‐varying systems interconnected over arbitrary graphs

Farhood, Mazen; Di, Zhe; Dullerud, Geir E.

doi:10.1002/rnc.3081

Cited by 39 publications

(34 citation statements)

References 33 publications

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“…We will also denote the resulting distributed LTV plant by

\overset{G}{true}

, its distributed LTV controller by

\overset{K}{true}

, and the closed‐loop system by

\overset{L}{true}

. The following results are the reformulations of analysis and synthesis results developed in the work of Farhood et al…”

Section: Preliminariesmentioning

confidence: 99%

“…Before stating the next reformulated synthesis result from the work of Farhood et al, we make the following definitions:

F_{1} false(R, R^{+} false) = {([], \begin{matrix} array N_{R} & array 0 \\ array 0 & array I \end{matrix})}^{T} ([], \begin{matrix} array A R A^{T} - R^{+} & array A R C_{1}^{T} & array B_{1} \\ array C_{1} R A^{T} & array - γ I + C_{1} R C_{1}^{T} & array D_{11} \\ array B_{1}^{T} & array D_{11}^{T} & array - γ I \end{matrix}) ([], \begin{matrix} array N_{R} & array 0 \\ array 0 & array I \end{matrix}),

F_{2} false(S, S^{+} false) = {([], \begin{matrix} array N_{S} & array 0 \\ array 0 & array I \end{matrix})}^{T} ([], \begin{matrix} array A^{T} S^{+} A - S & array A^{T} S^{+} B_{1} & array C_{1}^{T} \\ array B_{1}^{T} S^{+} A & array - γ I + B_{1}^{T} S^{+} B_{1} & array D_{11}^{T} \\ array C_{1} & array D_{11} & array - γ I \end{matrix}) ([], \begin{matrix} array N_{S} & array 0 \\ array 0 & array I \end{matrix}),

…”

Section: Preliminariesmentioning

confidence: 99%

“…The main contributions of this paper are as follows. A new framework is developed for describing the considered distributed LPV systems, which, unlike the previous works,() does not require operator‐theoretic machinery or transforming the directed graph into a regular one by adding, if necessary, nonexistent, or “virtual”, edges and nodes. This framework is devised to represent the distributed system equations in a form reminiscent of standard state‐space equations, where the interconnections between the subsystems are regarded as spatial states.…”

Section: Introductionmentioning

confidence: 99%

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Distributed control of LPV systems over arbitrary graphs with communication latency

Farhood

2017

Intl J Robust & Nonlinear

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Summary This paper focuses on spatially distributed control systems where the controller sensing and actuation topology is inherited from that of the plant. Specifically, this paper considers distributed systems composed of discrete‐time linear parameter‐varying subsystems interconnected over general graph structures. These distributed systems are subject to a communication latency of one sampling period, where the information sent by a subsystem at the current time step is received by the target subsystem at the next time step. Analysis and synthesis conditions are derived for control design in this setting using a parameter‐dependent Lyapunov approach with the ℓ2‐induced norm as the performance measure. Fast and easy‐to‐implement algorithms are also provided for constructing the controller in real time. The techniques developed are finally applied to a leader‐follower formation problem with intermittent communications.

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“…We will also denote the resulting distributed LTV plant by

\overset{G}{true}

, its distributed LTV controller by

\overset{K}{true}

, and the closed‐loop system by

\overset{L}{true}

. The following results are the reformulations of analysis and synthesis results developed in the work of Farhood et al…”

Section: Preliminariesmentioning

confidence: 99%

“…Before stating the next reformulated synthesis result from the work of Farhood et al, we make the following definitions:

F_{1} false(R, R^{+} false) = {([], \begin{matrix} array N_{R} & array 0 \\ array 0 & array I \end{matrix})}^{T} ([], \begin{matrix} array A R A^{T} - R^{+} & array A R C_{1}^{T} & array B_{1} \\ array C_{1} R A^{T} & array - γ I + C_{1} R C_{1}^{T} & array D_{11} \\ array B_{1}^{T} & array D_{11}^{T} & array - γ I \end{matrix}) ([], \begin{matrix} array N_{R} & array 0 \\ array 0 & array I \end{matrix}),

F_{2} false(S, S^{+} false) = {([], \begin{matrix} array N_{S} & array 0 \\ array 0 & array I \end{matrix})}^{T} ([], \begin{matrix} array A^{T} S^{+} A - S & array A^{T} S^{+} B_{1} & array C_{1}^{T} \\ array B_{1}^{T} S^{+} A & array - γ I + B_{1}^{T} S^{+} B_{1} & array D_{11}^{T} \\ array C_{1} & array D_{11} & array - γ I \end{matrix}) ([], \begin{matrix} array N_{S} & array 0 \\ array 0 & array I \end{matrix}),

…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Distributed control of LPV systems over arbitrary graphs with communication latency

Farhood

2017

Intl J Robust & Nonlinear

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“…Furthermore, the methodology developed here provides a unifying viewpoint for our previous and related work on distributed control. The research is reported in [17].…”

Section: Distributed Controlmentioning

confidence: 99%

Hybrid Control for Multi-Agent Systems in Complex Sensing Environments

Dullerud¹

2012

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“…The use of an XBee 900-Pro radio modem onboard the platform allows for data transmission among multiple vehicles, and thus the testbed also supports multi-vehicle operations. This UAV research platform is to be used to implement systematic and rigorous approaches, developed in our research lab, on controlled maneuvers, tracking along trajectories, and distributed control, e.g., [4,[12][13][14][15], and further validate formal methods for mathematically certified control software design. As the control design methodology pursued is model based, it is important that we derive reasonably accurate models that capture the rigid-body dynamics of the vehicle and any relevant subsystems.…”

Section: Introductionmentioning

confidence: 99%

Development and Modeling of a Low-Cost Unmanned Aerial Vehicle Research Platform

Arifianto

Farhood

2014

J Intell Robot Syst

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This paper describes the development and modeling of a low-cost and reliable small unmanned aerial vehicle research platform for advanced control implementation. The platform is mostly constructed of low-cost commercial-off-the-shelf (COTS) components. The only non-COTS components are the airdata probes, which are manufactured and calibrated in-house. The airframe used is the commercially available radio-controlled (R/C) 6-foot Telemaster airplane from Hobby Express, chosen mainly for its adequately spacious fuselage and for being reasonably stable and sufficiently agile. One noteworthy feature of this platform is the use of two separate low-cost onboard computers for handling the data management/hardware interfacing and control computation. Specifically, the single board computer, Gumstix Overo Fire, is used to execute the control algorithms, whereas the open source autopilot, Ardupilot Mega, is mostly used to interface the Overo computer with the sensors and actuators. The platform supports multi-vehicle operations through the use of a radio modem that enables multi-point communications. As the goal of this platform is to implement rigorous control algorithms for real-time trajectory tracking and distributed control, it O. Arifianto · M. Farhood ( ) is important to derive an appropriate flight dynamic model of the platform, based on which the controllers will be synthesized. For that matter, the paper provides reasonably accurate models of the vehicle, servomotors, and propulsion system. Namely, the output error method is used to estimate the longitudinal and lateraldirectional aerodynamic parameters from flight test data. The moments of inertia of the platform are determined using the simple pendulum test method, and the frequency response of each servomotor is also obtained experimentally. The Javaprop applet is used to obtain lookup tables relating airspeed to propeller thrust at constant throttle settings.

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Distributed control of linear time‐varying systems interconnected over arbitrary graphs

Cited by 39 publications

References 33 publications

Distributed control of LPV systems over arbitrary graphs with communication latency

Distributed control of LPV systems over arbitrary graphs with communication latency

Hybrid Control for Multi-Agent Systems in Complex Sensing Environments

Development and Modeling of a Low-Cost Unmanned Aerial Vehicle Research Platform

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