Abstract
This paper studies mean square stabilization for multi-input discrete-time systems over a general fading channel, and the channel is modeled as a cascade of multiplicative noise and white Gaussian additive noise. The main objective is to determine the minimum mean capacity required to enable stabilization. The basic idea of our method is to consider stabilization from the viewpoint of a supply/demand balance. Specifically, for communication resources, each system control input is viewed as the demand side, while the channel is viewed as the supply side, and the supply resource of the channel is characterized by the mean square capacity of each channel. Stabilization of the networked control system requires the balance of supply and demand. Based on whether the channel resources are configurable, two different methods for balancing the supply and the demand are discussed. If the channel resources are configurable, the demand side can be satisfied by adjusting the supply side (channel resources); otherwise, the demand side (a certain transceiver design mechanism) can be adjusted to meet the requirements of the supplier. For both cases, sufficient and necessary conditions for stabilizing discrete-time networked control systems are given.
Highlights
Networked control systems (NCSs) are feedback control systems in which the system and controller communicate through a shared network
Mean square stabilization under input channel information constraints is a basic problem for NCSs
Using a logarithmic quantizer to quantize the input signal, the authors in [9] discussed the state feedback mean square stabilization problem for a single-input system, and based on the Lyapunov method, the coarsest quantization density required for quadratic stabilization was obtained, where the requirement can be expressed in terms of the Mahler measure of a plant, i.e., the product of unstable poles
Summary
Networked control systems (NCSs) are feedback control systems in which the system and controller communicate through a shared network. With the additional design freedom of channel resource allocation, it has been proven that the minimum total capacity required for stabilizing a multi-input networked system can be characterized by the topological entropy of an open-loop system. We present a necessary condition and a sufficient condition for stabilizing NCSs using majorization theory, and the obtained conclusions indicate that the minimum network requirement for stabilizing an NCS is closely related to the Mahler measure of cyclic decomposition subsystems Both the channel/controller joint design and the coder/controller joint design problems can be regarded as a balance of the supply and demand of communication resources. The channel/controller joint design adjusts the supply to meet the demand, while the transceiver/controller joint design takes the opposite approach; that is, the adjustment is carried out to satisfy the supply
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