Distributed Nonlinear Control Design Using Separable Control Contraction Metrics

This paper gives convex conditions for the synthesis of a distributed control system for large-scale networked nonlinear dynamic systems. It is shown that the technique of control contraction metrics can be extended to this problem by utilizing separable metric structures, resulting in controllers that only depend on information from local sensors and communications from immediate neighbors. The conditions given are pointwise linear matrix inequalities, and are necessary and sufficient for linear positive systems and certain monotone nonlinear systems. Distributed synthesis methods for systems on chordal graphs are also proposed based on semidefinite program decompositions. The results are illustrated on a problem of vehicle platooning with heterogeneous vehicles, and a network of nonlinear dynamic systems with over 1000 states that is not feedback linearizable and has an uncontrollable linearization.