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Distributed Control of Networked Dynamical Systems: Static Feedback, Integral Action and Consensus

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4 Author(s)
Andreasson, M. ; ACCESS Linnaeus Centre, KTH R. Inst. of Technol., Stockholm, Sweden ; Dimarogonas, D.V. ; Sandberg, H. ; Johansson, K.H.

This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain, and a sum of nonlinear interaction functions. By using integral Lyapunov functions, we prove the stability of the proposed control protocols, and explicitly characterize the equilibrium set. We also propose a distributed proportional-integral (PI) controller for networked dynamical systems. The PI controllers successfully attenuate constant disturbances in the network. We prove that agents with single-integrator dynamics are stable for any integral gain, and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double-integrator dynamics. Throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites, power systems and building temperature control.

Published in:

Automatic Control, IEEE Transactions on  (Volume:59 ,  Issue: 7 )