Fault Tolerant Stabilizability of Multi-Hop Control Networks

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

“…As derived in [20] the dynamics of a MCN N can be modeled as in Figure 3, where each block is a discrete-time SISO LTI system with sampling time equal to the frame duration, characterized by the transfer functions G R (z), P (z) and G O (z). Throughout the paper, given a transfer function F (z), we will denote by N F and D F respectively its numerator and denominator.…”

“…where M (z) is the polynomial whose roots are the stable poles of P (z). Since P (z) is derived by discretizing a continuous-time transfer function, the degree r + deg(M (z)) of the denominator is equal to n. As illustrated in [20], the transfer function of the controllability graph G R (z) can be expressed as follows:…”

“…The mathematical framework defined in [21] is compositional, namely it is possible to exploit compositional operators of automata to design scalable scheduling and routing for multiple control loops closed on the same multi-hop communication network. In [20], we extended the MCN definition to model redundancy in data communication (i.e. sending sensing and actuation data through multiple paths), with the aim of rendering the system fault tolerant with respect to link failures and robust with respect to packet losses.…”

“…sending sensing and actuation data through multiple paths), with the aim of rendering the system fault tolerant with respect to link failures and robust with respect to packet losses. In [17] a MCN is defined as an autonomous system where the wireless network itself acts as a fully decentralized controller, and differs from the model we use in [20] and in this paper, where the wireless network transfers sensing and actuation data between a plant and a centralized controller. Moreover, in our model we explicitly take into account the effect of the scheduling ordering of the node transmissions in the sensing and actuation data relay, which provides more information when modeling the transient response of the system.…”

“…Since we assume that the data transfer is performed using multiple paths and merging redundant data by linear combination, the communication networks will be characterized by LTI SISO dynamics that depend on the network configuration (topology, scheduling and routing). In [20] we showed that, no matter how complex is the topology of the network, it is always possible to design a controller and a network configuration (scheduling and routing) that guarantees asymptotic stability of the networked closed loop system. In this paper we 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.…”