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.
Consensus with integral action is studied in @cite_4 for agents with single-integrator dynamics. It was shown that the proposed controller attenuates constant disturbances. In @cite_3 , the authors take a similar approach to attenuate unknown disturbances. In both references the analysis is limited to agents with single-integrator dynamics. Our proposed PI controller is related to the consensus controllers in @cite_10 @cite_8 . However, these references do not consider the influence of disturbances.
@cite_10 @cite_4 @cite_3 @cite_8
2143156927 2100431085 2013200328 1977509696
In the paper, an extension of LaSalle's Invariance Principle to a class of switched linear systems is studied. One of the motivations is the consensus problem in multi-agent systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows that the switching modes are only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle's Invariance Principle for global asymptotic stability is obtained. Then it is used to solve the consensus reaching problem of certain multi-agent systems in which each agent is modeled by a double integrator, and the associated interaction graph is switching and is assumed to be only jointly connected. We analyze two different estimation algorithms for dynamic average consensus in sensing and communication networks, a proportional algorithm and a proportional-integral algorithm. We investigate the stability properties of these estimators under changing inputs and network topologies as well as their convergence properties under constant or slowly-varying inputs. In doing so, we discover that the more complex proportional-integral algorithm has performance benefits over the simpler proportional algorithm This paper focuses on the consensus and formation problems of multiagent systems under unknown, persistent disturbances. Specifically, we propose a method that combines an existing consensus (or formation) algorithm with a new controller. The new controller has an integral action that produces a control input based on an error signal locally projected onto the column space of the graph Laplacian. This action allows agents to achieve a consensus or a predetermined formation objective under constant or time-varying disturbances. This note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies. Neighbor-based rules are adopted to realize local control strategies for these continuous-time autonomous agents described by double integrators. Although the interagent connection structures vary over time and related graphs may not be connected, a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed Lyapunov-based approach and related space decomposition technique