Cooperative control of multi-agent systems stability, optimality and robustness

In this work design methods are given for distributed synchronization control of multi-agent systems on directed communication graphs. Conditions are derived based on the relation of the graph eigenvalues to a region in a complex plane that depends on the single-agent system and the solution of the local Riccati equation. The synchronizing region concept is used. Cooperative observer design, guaranteeing convergence of the local estimates to their true values, is also proposed. The notion of convergence region for distributed observers is introduced. A duality principle is shown to hold for distributed observers and controllers on balanced graph topologies. Application of cooperative observers is made to the distributed synchronization problem. Three dynamic regulator architectures are proposed for cooperative synchronization.;In the second part this work brings together stability and optimality theory to design distributed cooperative control protocols, which guarantee consensus and are globally optimal with respect to a structured performance criterion. Here an inverse optimality approach is used together with partial stability to consider cooperative consensus and synchronization algorithms. A new class of digraphs is defined admitting a distributed solution to the global optimal control problem.;The third part of this work investigates cooperative control performance under disturbances, and distributed static output-feedback control. Control design for the state consensus in presence of disturbances is investigated. Derived results are also applicable to multi-agent systems with heterogeneous agents. If, on the other hand, one constrains the control to be of the static output-feedback form, one needs to redefine the synchronizing region as the output-feedback synchronizing region.;Contributions to Discrete-time Multi-agent Consensus Problem: The main contribution to the discrete-time multi-agent consensus problem is the proposed design method based on local Riccati feedback gains, guaranteeing cooperative stability and convergence to consensus.;Contributions to Globally Optimal Distributed Control Problem: The globally optimal distributed synchronization control protocols are investigated. The main contribution is in merging the notions of inverse optimality and partial stability to guarantee robust stabilization to the noncompact consensus manifold. Furthermore, second contribution is the introduction of the class of digraphs that gives a distributed solution to a structured global optimal control problem.;Contributions to Cooperative Robustness of Multi-agent Systems: The robustness properties of asymptotic and exponential stability are applied in the context of cooperative stability for consensus. The results are based on Lyapunov functions for noncompact manifolds, and the pertinent stability and robustness properties are further elaborated. Distributed and local observers are utilized for disturbance compensation.;Contributions to Distributed Output-feedback for State Synchronization: An application of the cooperative stability analysis, via synchronizing region, to the distributed output-feedback is presented. It is shown that the guaranteed synchronizing region for output-feedback can be both bounded and unbounded.