Optimal Co-Design of Wireless Resource Management and Multi-Loop Networked Control

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Physical entities that are controlled or monitored by computational algorithms and supported by a communication network providing information exchange are typically called cyber-physical systems (CPS). Smart grids, autonomous driving and robotics are some of the most prominent examples to CPS. From a system theoretic viewpoint, CPS consist of multiple control loops closed over shared a communication network, also called networked control systems (NCS). In typical NCS scenarios, the control and communication layers strongly affect the performance of each other. Novel flexible and scalable cross-layer solutions are required, which are responsive to the real-time variations of the individual layers. The development of such communication and control strategies is in the focus of our research project. During the first phase of our project in the DFG SPP Cyber Physical Networking (CPN), we have investigated the control and communication co-design as an optimization problem in shared wireless single-hop and two-hop networks with a focus on multiple linear-quadratic regulator (LQR) feedback control loops and medium access control (MAC) layer with a packet erasure channel model. We have developed control and communication policies such that the overall quality-of-control (QoC) is maximized and presented an initial fundamentally novel systematic solution for the optimal co-design of control and MAC policies in NCS. Moreover, in cooperation with partners in the SPP CPN, we have developed a lightweight open source control and communication platform for initial benchmarking.In this second phase of the project, our goal is to solve a more general global optimization problem that finds optimal joint policies for control and communication taking forwarding delay, queuing, and packet loss in a multi-hop network as well as heterogeneous control task criticalities into account. As part of our approach we introduce the novel concept of utility-of-information (UoI). We aim at developing UoI functions that unify the coupling effects, inter-layer dependencies and heterogeneous task requirements in one single function. UoI functions and their approximations support the decomposition of the global problem into local sub-problems that are solved in a decentralized fashion. In the course of our project we will develop a fundamental understanding of the UoI for various control task criticalities and communication contexts of different layers. We develop a framework for multi-hop and multi-loop control networks that analytically models control and network states and corresponding transitions through information exchange. The final goal is to formulate the global optimization problem that maximizes the quality-of-control for multi-loop and multi-hop scenarios and to derive tractable and scalable local policies. We aim to validate our theoretical findings in a practical, proof-of-concept experiment with multiple robots sharing a multi-hop wireless network.