Optimal co-design of control, scheduling and routing in multi-hop control networks

TL;DR

This paper addresses the joint design of control and network parameters in multi-hop control networks to ensure stability and optimize transient performance, despite the NP-hard nature of the problem.

Contribution

It formulates the co-design problem as a polynomial optimization and identifies conditions under which it becomes a convex problem, enabling practical solutions.

Findings

Optimization problem is NP-hard in general.

Sufficient conditions are provided for convexity.

Network topology and scheduling conditions enable polynomial-time solutions.

Abstract

A Multi-hop Control Network consists of a plant where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. Given a SISO LTI plant, we will address the problem of co-designing a digital controller and the network parameters (scheduling and routing) in order to guarantee stability and maximize a performance metric on the transient response to a step input, with constraints on the control effort, on the output overshoot and on the bandwidth of the communication channel. We show that the above optimization problem is a polynomial optimization problem, which is generally NP-hard. We provide sufficient conditions on the network topology, scheduling and routing such that it is computationally feasible, namely such that it reduces to a convex optimization problem.