A Theory of Dynamics, Control and Optimization in Layered Architectures

The controller of a large-scale distributed system (e.g., the internet, the power-grid and automated highway systems) is often faced with two complementary tasks: (i) that of finding an optimal trajectory with respect to a functional or economic utility, and (ii) that of efficiently making the state of the system follow this trajectory despite model uncertainty, process and sensor noise and distributed information sharing constraints. While each of these tasks has been addressed individually, there exists as of yet no controller synthesis framework that treats these two problems in a holistic manner. This paper proposes a unifying optimization based methodology that jointly addresses these two tasks by leveraging the strengths of well established frameworks for distributed control: the Layering as Optimization (LAO) framework and the distributed optimal control framework. We show that our proposed control scheme has a natural layered architecture composed of a low-level tracking layer and top-level planning layer. The tracking layer consists of a distributed optimal controller that takes as an input a reference trajectory generated by the top-level layer, where this top-level layer consists of a trajectory planning problem that optimizes a weighted sum of a utility function and a "racking penalty" regularizer. We further provide an exact solution to the tracking layer problem under a broad range of information sharing constraints, discuss extensions to the proposed problem formulation, and demonstrate the effectiveness of our approach on a numerical example