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.
Multi-agent systems, as all control processes, are in general sensitive to disturbances. When only relative measurements are available, disturbances may spread through the network. It has for example been shown by @cite_32 that vehicular string formations with only relative measurements cannot maintain coherency under disturbances, as the size of the formation increases. In @cite_29 the robustness of consensus-protocols under disturbances is studied, but limited to the relative states of the agents. However, none of the aforementioned references consider disturbance rejection. In @cite_27 however, the steady-state error for first-order consensus dynamics is minimized by convex optimization over the edge-weights. A similar approach is taken in @cite_25 , where the application is vehicle-platooning. In @cite_1 , an optimal sensor placement problem for consensus problems is formulated, minimizing the @math gain of the system. However, these approaches eliminate output errors if the disturbances are constant only in special cases, as no no integral control is employed.
@cite_29 @cite_1 @cite_32 @cite_27 @cite_25
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In this paper, we study the problem of reaching a consensus among all the agents in the networked control systems (NCS) in the presence of misbehaving agents. A reputation-based resilient distributed control algorithm is first proposed for the leader-follower consensus network. The proposed algorithm embeds a resilience mechanism that includes four phases (detection, mitigation, identification, and update), into the control process in a distributed manner. At each phase, every agent only uses local and one-hop neighbors' information to identify and isolate the misbehaving agents, and even compensate their effect on the system. We then extend the proposed algorithm to the leaderless consensus network by introducing and adding two recovery schemes (rollback and excitation recovery) into the current framework to guarantee the accurate convergence of the well-behaving agents in NCS. The effectiveness of the proposed method is demonstrated through case studies in multirobot formation control and wireless sensor networks. In this paper, multi-agent systems minimizing a sum of objective functions, where each component is only known to a particular node, is considered for continuous-time dynamics with time-varying interconnection topologies. Assuming that each node can observe a convex solution set of its optimization component, and the intersection of all such sets is nonempty, the considered optimization problem is converted to an intersection computation problem. By a simple distributed control rule, the considered multi-agent system with continuous-time dynamics achieves not only a consensus, but also an optimal agreement within the optimal solution set of the overall optimization objective. Directed and bidirectional communications are studied, respectively, and connectivity conditions are given to ensure a global optimal consensus. In this way, the corresponding intersection computation problem is solved by the proposed decentralized continuous-time algorithm. We establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non-smooth analysis. We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2, and higher dimensions, with vehicular platoons corresponding to the 1-D case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent 1-D vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways. This paper examines the close interplay between cooperation and adaptation for distributed detection schemes over fully decentralized networks. The combined attributes of cooperation and adaptation are necessary to enable networks of detectors to continually learn from streaming data and to continually track drifts in the state of nature when deciding in favor of one hypothesis or another. The results in this paper establish a fundamental scaling law for the steady-state probabilities of miss detection and false alarm in the slow adaptation regime, when the agents interact with each other according to distributed strategies that employ small constant step-sizes. The latter are critical to enable continuous adaptation and learning. This paper establishes three key results. First, it is shown that the output of the collaborative process at each agent has a steady-state distribution. Second, it is shown that this distribution is asymptotically Gaussian in the slow adaptation regime of small step-sizes. Third, by carrying out a detailed large deviations analysis, closed-form expressions are derived for the decaying rates of the false-alarm and miss-detection probabilities. Interesting insights are gained from these expressions. In particular, it is verified that as the step-size @math decreases, the error probabilities are driven to zero exponentially fast as functions of @math , and that the exponents governing the decay increase linearly in the number of agents. It is also verified that the scaling laws governing the errors of detection and the errors of estimation over the network behave very differently, with the former having exponential decay proportional to @math , while the latter scales linearly with decay proportional to @math . Moreover, and interestingly, it is shown that the cooperative strategy allows each agent to reach the same detection performance, in terms of detection error exponents, of a centralized stochastic-gradient solution. The results of this paper are illustrated by applying them to canonical distributed detection problems.