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Additional file 1. More clinical features of the subjects.

Over the past decades, coordinated control of multi-agent systems has received increasing attention for its potential in applications such as cooperation of robots, coordination of unmanned air vehicles, management of distributed database and synchronization of networked oscillators. Flocking behavior is said to be achieved if both position aggregation and heading alignment are achieved. Collision avoidance is an additional control objective in most flocking applications involving physical subjects. Formation control is a widely used method to create flocking behavior in a multi-agent system. Since formation control requires a virtual leader and a predefined geometric configuration of the flock, the resulting closed-loop multi-agent system is sensitive to agent ordering and individual agent failure. An alternative approach to enforcing the aggregation of agents is to define an artificial potential function. The artificial potential function determines the attractive-repulsive interaction between the agents. Then, a control law based on the gradient of the potential function drives the system into a desired configuration. In this case, no a priori knowledge is needed and the closed-loop system is more robust. Consensus control is another important problem in coordinated control. It is concerned with reaching a networkwide agreement on some quantities of interest while each agent can only access local information. Many of the existing studies address the consensus of multi-agent systems with linear dynamics, and both linear and nonlinear controllers have been proposed. Regardless of the control algorithm employed, coordinated control highly relies on interactions among agents and for this reason communication delays are inevitable and should be taken into consideration during the development of the control algorithm. Control of individual dynamic systems with time delays has been studied extensively in the literature. In particular, the low gain feedback method has been demonstrated to be effective in developing control laws for the stabilization of linear and nonlinear delayed systems. In this dissertation, we firstly consider the flocking of nonholonomic vehicles in the presence of communication delays. In both continuous-time and discrete-time scenarios, distributed control laws are developed based on artificial potential functions. Aggregation of positions and alignment of headings are proved separately through the Lyapunov functional approach. Then, we study the consensus of a class of nonlinear affine systems in the presence of communication delays. In both continuous-time and discrete-time settings, distributed control laws are constructed and consensus is proved as well.