With the advancement of communication technology, more and more control processes happen in networked environment. This makes it possible for us to deploy multiple systems in a spatially distributed way such that they could finish certain tasks collaboratively. While it brings about numerous advantages over conventional control, challenges arise in the mean time due to the imperfection of communication. This thesis is aimed to solve some problems in cooperative control involving multiple agents in the presence of communication constraints.

Overall, it is comprised of two main parts:​ Distributed consensus in multi-agent systems and bilateral teleoperation. Chapter 2 to Chapter 4 deal with the consensus problem in multi-agent systems. Our goal is to design appropriate control protocols such that the states of a group of agents will converge to a common value eventually. The robustness of multi-agent systems against various adverse factors in communication is our central concern. Chapter 5 copes with bilateral teleoperation with time delays. The task is to design control laws such that synchronization is reached between the master plant and slave plant. Meanwhile, transparency should be maintained within an acceptable level.

Chapter 2 investigates the consensus problem in a multi-agent system with directed communication topology. The time delays are modeled as a Markov chain, thus more characteristics of delays are taken into account. A delay-dependent approach has been proposed to design the Laplacian matrix such that the system is robust against stochastic delays. The consensus problem is converted into stabilization of its equivalent error dynamics, and the mean square stability is employed to characterize its convergence property. One feature of Chapter 2 is redesign of the adjacency matrix, which makes it possible to adjust communication weights dynamically. In Chapter 3, average consensus in single-integrator agents with time-varying delays and random data losses is studied. The interaction topology is assumed to be undirected. The communication constraints lie in two aspects:​ 1) time-varying delays that are non-uniform and bounded;​ 2) data losses governed by Bernoulli processes with non-uniform probabilities. By considering the upper bounds of delays and probabilities of packet dropouts, sufficient conditions are developed to guarantee that the multi-agent system will achieve consensus. Chapter 4 is concerned with the consensus problem with double-integrator dynamics and non-uniform sampling. The communication topology is assumed to be fixed and directed. With the adoption of time-varying control gains and the theory on stochastic matrices, we prove that when the graph has a directed spanning tree and the control gains are properly selected, consensus will be reached.

Chapter 5 deals with bilateral teleoperation with probabilistic time delays. The delays are from a finite set and each element in the set has a probability of occurrence. After defining the tracking error between the master and slave, the input-to-state stability is used to characterize the system performance. By taking into account the probabilistic information in time delays and using the pole placement technique, the teleoperation system has achieved better position tracking and enhanced transparency.