An analytic solution to the optimal design of information structure and cooperative control in networked systems

In this paper, the optimal design problem of both information structure and cooperative control is investigated for a collection of heterogeneous nonlinear systems. The concept of generalized passivity is presented to not only extend the concept of passivity to dynamical systems of any relative degree but also achieve the decoupling between designing a system-level self-feedback control law for any of the individual systems and designing a network-level distributed cooperative control as the command signal to the system-level control. The separation enables a new formulation in which both communication network topology and network-based cooperative control gains can be optimized in general. The performance indices in the formulation are chosen to minimize the cost of local communication network and to maximize convergence to consensus. Optimal gains in the cooperative controls can analytically be solved in terms of any information structure, and recursive algorithms of polynomial time are provided to find Pareto non-inferior solutions of information structures and the corresponding cooperative control gains.