Neighbor Approximations for Distributed Optimal Control of Nonlinear Networked Systems

This paper concerns the distributed solution of optimal control problems for the class of nonlinear neighbor-affine systems, for which the dynamics can be written as sum of terms that depend only on the states and controls of two neighboring agents. The proposed distributed optimization algorithm is based on the introduction of local copies of states and controls that are coupled via additional consistency constraints. Formulating the augmented Lagrangian function for the consistency constraints then allows to solve the problem in a distributed manner using the alternating direction method of multipliers (ADMM). This paper proposes to approximate parts of the neighbors optimization problem using local copies of states and controls. While this increases the complexity of the local problems, an extensive numerical evaluation for several benchmark examples shows that the convergence behaviour of the ADMM algorithm is improved significantly and thus the total computation time and the communication effort are decreased.