We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and outflows. As a preparatory result it is shown how a distributed proportional-integral controller structure, associating with every edge of the graph a controller state, will regulate the state variables of the vertices, irrespective of the unknown constant inflows and outflows, in the sense that the storage variables converge to the same value (load balancing or consensus). This will be proved by identifying the closed-loop system as a portHamiltonian system, and modifying the Hamiltonian function into a Lyapunov function, dependent on the value of the vector of constant inflows and outflows. In the main part of the paper the same problem will be addressed for the case that the input flow variables are constrained to take value in an interval. We will derive sufficient and necessary conditions for load balancing, which only depend on the structure of the network in relation with the flow constraints.

This paper studies multi-agent systems with nonlinear consensus protocols, i.e., only nonlinear measurements of the states are available to agents. The solutions of these systems are understood in Filippov sense since the possible discontinuity of the nonlinear controllers. Under the condition that the nonlinear functions are monotonic increasing without any continuous constraints, asymptotic stability is derived for systems defines on both directed and undirected graphs. The results can be applied to quantized consensus which extend some existing results from undirected graphs to directed ones.

In this paper, the problem of collaborative tracking of an underwater target using autonomous surface vehicles is studied. As a solution, we consider distance-based formation control with a collision-avoidance potential function. The devised formation control protocol is applied to the formation tracking problem, where vehicles form a desired formation around a moving target and estimate its position. More precisely, the centroid of the formation tracks the target. Almost global stability is proved for the case with three tracking agents. A fully operational platform with four autonomous surface vehicles was built to implement the derived algorithms, where one of the vehicles was used to simulate a target and the rest to try to form a triangle formation around the target. Power usage of a naval vessel is highly affected by resistance forces which increases significantly with velocity. To account for this and increase the overall system endurance, the derived formation tracking protocol was furthermore modified with an additional term. Experimental results are presented.

Abstract-The consensus problem for multi-agent systems with quantized communication or sensing is considered. Centralized and distributed self-triggered rules are proposed to reduce the overall need of communication and system updates. It is proved that these self-triggered rules realize consensus exponentially if the network topologies have a spanning tree and the quantization function is uniform. Numerical simulations are provided to show the effectiveness of the theoretical results.

Harmful algal blooms occur frequently and deteriorate water quality. A reliable method is proposed in this paper to track algal blooms using a set of autonomous surface robots. A satellite image indicates the existence and initial location of the algal bloom for the deployment of the robot system. The algal bloom area is approximated by a circle with time varying location and size. This circle is estimated and circumnavigated by the robots which are able to locally sense its boundary. A multi-agent control algorithm is proposed for the continuous monitoring of the dynamic evolution of the algal bloom. Such algorithm comprises of a decentralised least squares estimation of the target and a controller for circumnavigation. We prove the convergence of the robots to the circle and in equally spaced positions around it. Simulation results with data provided by the SINMOD ocean model are used to illustrate the theoretical results.