In recent years, cooperative control of multi-agent systems has drawn increasing interest in the robotics and control community. In particular, the cooperative coverage control technique has been extensively applied to networked mobile agents such as surveillance robotic networks and autonomous ocean sampling networks. The cooperative coverage control law aims to maximize coverage performance in the mission space by coordinating the positions of agents. Though most existing work on coverage control problems have focused on planar fields, the coverage control problem on a circle is also important for boundary mission space in the application of monitoring or enclosing problems. For example, in forest fire surveillance, target-capturing, or target-enclosing problem, mobile agents are supposed to be deployed on a circle such that any point can be reached by agents as soon as possible.

This thesis aims to investigate coverage control problems on a circle subject to various real-world constraints. Cooperative coverage control strategies for multi-agent systems are proposed considering unknown terrain roughness, communication delays, measurement errors, limited interaction ranges, and more general agent dynamics. With the increased number of reported attack events, preserving data privacy has become an urgent need in networked systems. Thus, privacy preservation is also considered in this thesis. The main contributions of this thesis are as follows.

1. The coverage control problem on a circle is investigated with unknown terrain roughness and nonuniform time-varying communication delays.
By using the basis function approximation approach, adaptive coverage control laws are proposed for mobile agents to estimate the unknown roughness function in a collaborative way. Moreover, unlike existing research, nonuniform time-varying communication delays are also taken into consideration. Under the proposed adaptive coverage control laws, the agent network can be driven to the optimal configuration while minimizing the coverage cost function in the presence of nonuniform communication delays, and the true roughness function can be learned by each agent.

2. The coverage control problem for heterogeneous mobile agents is investigated with multiplicative measurement errors and limited interaction ranges. To cooperatively achieve the optimal coverage configuration of networked mobile agents on a circle, a distributed coverage control law is proposed based on only the agents' limited interaction ranges and the lower bounds on the multiplicative measurement errors. Then, the thesis proves that the agent network will be driven to a neighborhood of the optimal positions if the agents' interaction ranges are larger than a given threshold. To evaluate the effect of multiplicative measurement errors on the performance of the proposed coverage control law, an upper bound on the difference between the limit of the coverage cost function and its optimal value is also provided.

3. The coverage control problem for mobile agent networks with privacy preservation and limited interaction ranges is considered. A new confidential interaction protocol is proposed to drive the multi-agent system to the optimal configuration. Moreover, the process required to implement the confidential interaction protocol is provided to handle the limited interaction ranges during coverage tasks. Under the privacy-preserving coverage control law, it is shown that networked mobile agents with limited interaction ranges can be driven to the optimal configuration with guaranteed privacy preservation.

4. The coverage control problem for mobile agents with double-integrator dynamics and different maximum velocities on a circle is investigated. A generalized energy function is introduced in the proposed coverage control laws to guarantee the order preservation of the agents despite the existence of unknown but bounded disturbances. The velocity constraint of each agent is shown to always be satisfied throughout the coverage task. It is shown that the agent network can be driven to a neighborhood of the optimal configuration while minimizing the coverage cost function, and an upper bound on the coverage cost function when time goes to infinity is also provided.

In conclusion, these contributions propel the field of mobile agent coverage control on a circle forward by providing practical insights and approaches that address complex real-world challenges. Finally, it is our hope that these results inspire further research and investigation on cooperative control of multi-agent systems, thus accelerating its application to real-world scenarios.