A multi-agent system is defined as a collection of autonomous agents which are able to interact with each other or with their environments to solve problems that are difficult or impossible for an individual agent. Coordination in multi-agent systems attracts significant interest in the realm of engineering. Examples of cooperative tasks include mobile sensor networks, automated parallel delivery of payloads, region following formation control and coordinated path planning. One common feature for these systems is acting the agents in a distributed manner (using only local information from their neighbors) to complete global tasks cooperatively so as to increase flexibility and robustness. In this work, two distributed tracking issues in multi-agent systems are investigated in detail: leader-follower flocking with a moving leader for Lagrange networks and distributed average tracking of physical agents.

Flocking of multi-agent systems is the motion of a group of agents cohesively to maintain connectivity and avoid collisions. This dissertation proposes novel distributed tracking algorithms to solve the leader-follower flocking problem with a moving leader. The problem is investigated for networked Lagrange systems with parametric uncertainties under a proximity graph. Two cases are considered: i) the leader moves with a constant velocity, and ii) the leader moves with a varying velocity. In the first case, a distributed continuous adaptive control algorithm accounting for unknown parameters is proposed in combination with a distributed continuous estimator for each follower. In the second case, a distributed discontinuous adaptive control algorithm and estimator are proposed to track the varying leader, where only a group of followers have access to the leader. However, in the proposed algorithm the agents use the two-hope neighbors' information and need some global information to determine the control gains. Thus, the algorithm is improved in the next step to use one-hop neighbors' information and to be fully distributed with the introduction of gain adaptation laws. In all proposed algorithms, flocking is achieved as long as the connectivity and collision avoidance are ensured at the initial time and the control gains are designed properly.

In the distributed average tracking problem, each agent uses local information to calculate the average of individual varying input signals, one per agent. In this dissertation, two distributed average tracking problems for physical second-order agents are investigated. First, distributed average tracking problem is studied for double-integrator agents with reduced requirement on velocity measurements and in the absence of correct position and velocity initialization. Two algorithms are introduced, where in both algorithms a distributed discontinuous control input and a filter are proposed. In the first algorithm, the requirement for either absolute or relative velocity measurements is removed. The algorithm is robust to initialization errors and can deal with a wide class of input signals with bounded deviations in input signals, input velocities, and input accelerations. In the second algorithm, the requirement for communication. However, the algorithm can deal with a smaller group of input signals. Second, distributed average tracking problem of physical second-order agents with heterogeneous nonlinear dynamics is investigated, where there is no constraint on input signals. The agents' dynamics satisfy a Lipschitz-like condition that will be defined later and is more general than the Lipschitz-type condition. In the proposed algorithm, a control input and a filter are designed for each agent. Since the input signals are arbitrary and the nonlinear terms in agents' dynamics can be unbounded, novel state-dependent time varying gains are employed in agents' filters and control inputs to overcome these unboundedness effects.

The dissertation provides a rigorous stability analysis of the introduced control algorithms for both issues and presents simulations that validate the effectiveness of the proposed algorithms.