Cloud-assisted Distributed Nonlinear Optimal Control for Dynamics over Graph

Dynamics over graph are large-scale systems in which the dynamic coupling among subsystems is modeled by a graph. Examples arise in spatially distributed systems (as discretized PDEs), multi-agent control systems or social dynamics. In this paper, we propose a cloud-assisted distributed algorithm to solve optimal control problems for nonlinear dynamics over graph. Inspired by the centralized Hauser's projection operator approach for optimal control, our main contribution is the design of a descent method in which at each step agents of a network compute a local descent direction, and then obtain a new system trajectory through a distributed feedback controller. Such a controller, iteratively designed by a cloud, allows agents of the network to use only information from neighboring agents, thus resulting into a distributed projection operator over graph. The main advantages of our globally convergent algorithm are dynamic feasibility at each iteration and numerical robustness (thanks to the closed-loop updates) even for unstable dynamics. In order to show the effectiveness of our strategy, we present numerical computations on a discretized model of the Burgers’ nonlinear partial differential equation.