This thesis applies predictor-based methods for the distributed consensus control of multi-agent systems with input delay. "Multi-agent systems" is a term used to describe a group of agents which are connected together to achieve specified control tasks over a communication network. In many applications, the subsystems or agents are required to reach an agreement upon certain quantities of interest, which is referred to as "consensus control". This input delay may represent delays in the network communication. The main contribution of this thesis is to provide feasible methods to deal with the consensus control for general multi-agent systems with input delay. The consensus control for general linear multi-agent systems with parameter uncertainties and input delay is first investigated under directed network connection. Artstein reduction method is applied to deal with the input delay. By transforming the Laplacian matrix into the real Jordan form, delay-dependent conditions are derived to guarantee the robust consensus control for uncertain multi-agent systems with input delay. Then, the results are extended to a class of Lipschitz nonlinear multi-agent systems and the impacts of Lipschitz nonlinearity and input delay in consensus control are investigated. By using tools from control theory and graph theory, sufficient conditions based on the Lipschitz constant are identified for proposed protocols to tackle the nonlinear terms in the system dynamics. Other than the time delay, external disturbances are inevitable in various practical systems including the multi-agent systems. The consensus disturbance rejection problems are investigated. For linear multi-agent systems with bounded external disturbances, Truncated Predictor Feedback (TPF) approach is applied to deal with the input delay and the H_infinity consensus analysis is put in the framework of Lyapunov analysis. Sufficient conditions are derived to guarantee the H_infinity consensus in time domain. Some disturbances in real engineering problems have inherent characteristics such as harmonics and unknown constant load. For those kinds of disturbances in Lipschitz nonlinear multi-agent systems with input delay, Disturbance Observer-Based Control (DOBC) technique is applied to design the disturbance observers. A new predictor-based control scheme is constructed for each agent by utilizing the estimate of the disturbance and the prediction of the relative state information. Sufficient delay-dependent conditions are derived to guarantee consensus with disturbance rejection.

The decentralized consensus control of a formation of rigid-body spacecraft is studied in the framework of geometric mechanics while accounting for a constant communication time delay between spacecraft. The relative position and attitude (relative pose) are represented on the Lie group SE(3) and the communication topology is modeled as a digraph. The consensus problem is converted into a local stabilization problem of the error dynamics associated with the Lie algebra se(3) in the form of linear time-invariant delay differential equations with a single discrete delay in the case of a circular orbit, whereas it is in the form of linear time-periodic delay differential equations in the case of an elliptic orbit, in which the stability may be assessed using infinite-dimensional Floquet theory. The proposed technique is applied to the consensus control of four spacecraft in the vicinity of a Molniya orbit.

This research focuses on developing novel approaches in load balancing and restoration problems in electrical power distribution systems. The first approach introduces an inter-connected network topology, referred to as (n, k)-star topology. While power distribution systems can be constructed in different communication network topologies, the performance and fault assessment of the networked systems can be challenging to analyze. The (n, k)-star topologies have well defined performance and stability analysis metrics. Typically, these metrics are defined based on: i) degree, ii) diameter, and iii) conditional diagnosability of a faulty node. These parameters could be evaluated and assessed before a physical (n, k)-star topology power distribution system is constructed. Moreover, in the second approach, we evaluate load balancing problems by using a decentralized algorithm, i.e., the Multi-Agent System (MAS) based consensus algorithm on an (n, k)-star power topology. With aforementioned research approaches, an (n, k)-star power distribution system can be assessed with proposed metrics and assessed with encouraging results compared to other topology networked systems. Other encouraging results are found in efficiency and performance enhancement during information exchange using the decentralized algorithm. It has been proven that a load balance solution is convergent and asymptotically stable with a simple gain controller. The analysis can be achieved without constructing a physical network to help evaluate the design. Using the (n, k)-star topology and MAS, the load balancing/restoration problems can be solved much more quickly and accurately compared to other approaches shown in the literature. / Electrical and Computer Engineering

This dissertation aims at solving the consensus control problem of multi-agent systems with Lipschitz nonlinearity. This depends on the design of the controller that enables each agent or subsystem in multi-agent systems with Lipschitz nonlinearity to reach consensus; using the understanding of the agents' connection network from the knowledge of graph theory as well as the control system design strategy. The objective is achieved by designing a type of distributed control, namely the consensus control, which manipulates the relative information of each agent in a multi-agent systems in order to arrive at a single solution. In addition, containment control is also developed to solve containment problem. It is an extension of consensus control via leader-follower configuration, aimed at having each agent contained by multiple leaders in a multi-agent systems with Lipschitz nonlinearity. Four types of controllers are proposed - state-feedback consensus controller, observer-based consensus controller, state-feedback containment controller and observer-based containment controller; each provides the stability conditions based on Lyapunov stability analysis in time domain which enabled each agent or subsystem to reach consensus. The observer-based controllers are designed based on the consensus observer that is related to Luenberger observer. Linear Matrix Inequality (LMI) and Algebraic Riccati Equation (ARE) are utilized to obtain the solutions for the stability conditions. The simulation results of the proposed controllers and observers have been carried out to prove their theoretical validity. Several practical examples of flexible robot arm simulations are included to further validate the theoretical aspects of the thesis.

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