Compositional Modeling and Analysis of Multi-Hop Control Networks

Abstract

Abstract-We propose a mathematical framework for modeling and analyzing multi-hop control networks designed for systems consisting of multiple control loops closed over a multi-hop (wireless) communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system, providing an explicit translation of multi-hop control networks to switched systems. We propose formal models for analyzing robustness of multi-hop control networks, where data is exchanged through a multi-hop communication network subject to disruptions. When communication disruptions are long, compared to the speed of the control system, we propose to model them as permanent link failures. We show that the complexity of analyzing such failures is NP-hard, and discuss a way to overcome this limitation for practical cases using compositional analysis. For typical packet transmission errors, we propose a transient error model where links fail for one time slot independently of the past and of other links. We provide sufficient conditions for almost sure stability in presence of transient link failures, and give efficient decision procedures. We deal with errors that have random time span and show that, under some conditions, the permanent failure model can be used as a reliable abstraction. Our approach is compositional, namely it addresses the problem of designing scalable scheduling and routing policies for multiple control loops closed on the same multi-hop control network. We describe how the translation of multi-hop control networks to switched systems can be automated, and use it to solve control and networking co-design challenges in some representative examples, and to propose a scheduling solution in a mineral floatation control problem that can be implemented on a time triggered communication protocols for wireless networks.Index Terms-Compositional analysis, multi-hop sensor and actuator networks, networked control.

Periodic Model Predictive Control of Multi-Hop Control Networks

“…is the discrete time, and This definition is based on that in [4], [14]. In [4], the controller is given by a linear system. In [14], the controller is given by a kind of optimizer.…”

“…In such networks, communications between nodes are achieved through multi-hop paths. Furthermore, a control system over a multi-hop wireless network is called a multi-hop control network (MHCN) [4]. In [4], its formal model has been proposed, and several properties have been analyzed.…”

“…Furthermore, a control system over a multi-hop wireless network is called a multi-hop control network (MHCN) [4]. In [4], its formal model has been proposed, and several properties have been analyzed. In [7], [10], fault tolerant control has been studied.…”

“…Since a linear system is derived for each candidate of paths, a given MHCN can be modeled by a switched linear system. Also in [4], a switched linear system is used as a model of MHCNs. In the models in [4], [14], a directed graph appeared in an MHCN is modeled, but in the proposed method, time sequence of the state for a fixed path is modeled off-line.…”

“…Also in [4], a switched linear system is used as a model of MHCNs. In the models in [4], [14], a directed graph appeared in an MHCN is modeled, but in the proposed method, time sequence of the state for a fixed path is modeled off-line. Hence, the proposed model is compatible with the finite-time optimal control problem and MPC.…”