ISSUES REGARDING SYNCHRONIZATION PROBLEMS FOR NETWORKS AND INTERNAL STABILITY OF LINEAR SYSTEMS WITH CONSTRAINTS
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My Ph.D. thesis research accomplishments span two different disciplines. The first one is synchronization in multi-agent systems and the other one is internal stabilization of linear systems with constraints. These two disciplines are studied respectively in Part I and Part II in this thesis.In Part I, I solve the synchronization problems toward generality of network structure, from homogeneous networks (i.e., the agent models in the network are identical) to heterogeneous networks (i.e., the agent models in the network are non-identical). For homogeneous networks, I propose dierent design methodologies for solving the state synchronization problems for both full-state coupling (i.e., each agent measures its own state relative to that of neighboring agents) and partial-state coupling (i.e., each agent measures its own output relative to that of neighboring agents). For heterogeneous networks, I consider the output synchronization problem and the output regulation problem for two scenarios based on the information available for each agent: introspective agents and non-introspective agents. While in both cases, each agent collects information of its own output relative to that of neighboring agents, an introspective agent also acquires some sortof self-knowledge. I also consider the semi-global regulation of output synchronization for heterogeneous networks of introspective, invertible linear agents subject to actuator saturation. Finally, I consider the case that the network communications are subject to unknown uniform constant communication delay.In Part II, I study the issues regarding the internal stabilization of linear systems subject to actuator saturation. I design saturated globally stabilizing linear static state feedback control laws for continuous-time linear systems mixed with single integrators, double integrators, and neutrally stable dynamics. I also completely characterize the dynamic behavior of the discrete-time double integrator with a saturated locally stabilizing linear state feedback law. These are the first step toward my further goal: to completely characterize under what conditions one canutilize a linear static/dynamic state feedback control laws to globally asymptotically stabilize linear systems subject to actuator saturation.