Multi-robot systems can accomplish a variety of tasks through the power of coordination.There are mutliple benefits. These systems have many advantages over a single very complex robot in term of scalability, versatility, and adaptability. In many cases, the robots cannot accomplish much by itself, but coordination empowers them the ability to complete various objectives. Even when the individuals robots are very capable, coordination can increase robot efficiency by allocating robots with fitting tasks. In both scenarios, the problem of balancing the system objectives arise naturally, and properly addressing it can lead to better overall performance. Motivated by this observation, this dissertation seek to understand how different objectives can be put together and how to strike a balance between them. We consider control objectives at the most fundamental level to control systems, such as stability, system safety, smoothness of the controller, performance, and resources spent for accomplishing tasks.

This dissertation is divided into two parts. The first part deals with control laws that considerboth stability and safety objectives. We design controllers that can satisfy simultaneously conditions given by control Lyapunov functions and control barrier functions. Depending on the smoothness properties of the given functions, we guarantee the continuity or smoothness of the controller. In particular, we design a continuous controller for connectivity maintenance, and also design a universal formula for smooth safe stabilization. In the second part, we study the resource-efficient implementation of control laws using event-triggered control. We improve the existing event-triggered control framework for stabilization by incorporating prescribed performance into the design. The resulting framework further enhances the advantage of resource conservation characteristic of event-triggered control. We build on the proposed framework to design an intrinsically Zeno-free distributed triggering mechanisms for network systems. In addition, this dissertation also explores unconventional ways to utilize the event-triggered control framework. In one way, we deviate ourselves from trigger conditions that use Lyapunov functions replacing it instead with barrier certificate and develop an event-triggered control framework for safety objectives. Another interesting way we explore to use event-triggered control is in the context of human supervised multiobjective optimization. In this setting, we consider the human as a valuable resource, which should be used sparingly, and use event-triggered control to accommodate various models of human performance, such as constraints on the response time and the interaction frequency.