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This paper proposes three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We first propose two model-independent algorithms for a subclass of Euler-Lagrange agents without the vector of gravitational potential forces. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent self-dynamics. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work studying event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities, which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information, and bounds on the initial conditions. When the Euler-Lagrange agents have dynamics that include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain parameters associated with the agent self-dynamics. For each algorithm, a trigger function is proposed to govern the event update times. The controller is only updated at each event, which ensures that the control input is piecewise constant and thus saves energy resources. We analyze each controller and trigger function to exclude Zeno behavior.

The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show that for a social network with constant topology, each individual's social power converges to its equilibrium value exponentially fast, whereas previous results only concluded asymptotic convergence. Second, when the network topology is dynamic (i.e., the relative interaction matrix may change between any two successive issues), we show that the initial (perceived) social power of each individual is exponentially forgotten. Specifically, individual social power is dependent only on the dynamic network topology, and initial social power is forgotten as a result of sequential opinion discussion. Finally, we provide an explicit upper bound on an individual's social power as the number of issues discussed tends to infinity; this bound depends only on the network topology. Simulations are provided to illustrate our results.

This paper discusses the problem of controlling formation shapes for a group of nonholonomic unicycle-type agents with constant speeds. The control input is designed to steer their orientations and the aim is to achieve a desired formation configuration for all the agents subject to constant-speed constraints. The circular motion center is adopted as a virtual position for each agent to define the desired formation shape. We consider several different formation design approaches based on different formation specifications under different interaction graphs. In particular, two different formation design approaches, namely, a displacement-based approach and a distance-based approach, are discussed in detail to coordinate constant-speed agents in achieving a desired formation shape with stable circular motions via limited interactions. The communication and measurement requirements for each approach are also discussed. Furthermore, we propose a combined controller to stabilize a formation shape and synchronize the heading of each agent simultaneously. The effectiveness of the proposed formation control schemes is validated by both numerical simulations and real experiments with actual unmanned fixed-wing aircraft.