Abstract
This paper studies the mean square stabilization problem of multi-input discrete-time systems with multiplicative noise constraints. The channel resources are fixed and cannot be arbitrarily allocated, and the channel is modeled as multiplicative noise. The main purpose is to discuss the relationship between the minimum channel capacity of each subchannel and the system topological entropy by using majorization theory. The basic idea is to investigate the stabilization from the perspective of the supply and demand balance. Specifically, for communication resources, each system input is regarded as the demand side and the channel is considered as the supplier. The supply resources of the channel are characterized according to the channel capacity, and stabilization of networked control systems requires a balance between the supply and demand of the communication resources. Since the channel resources are not configurable, one can satisfy the supplier’s requirements by adjusting the demand side (a certain transmission mechanism). We provide a sufficient condition and a necessary condition to stabilize networked control systems. Finally, numerical examples verify the conclusions.
Highlights
Networked control systems (NCSs) are feedback control systems in which the systems and the controllers communicate over a shared network
(3) We provide a sufficient condition and a necessary condition to stabilize networked control systems, and these majorization-type conditions establish the relationship between the minimum channel capacity of each subchannel and the system topological entropy
PROBLEM FORMULATION When the network resources cannot be arbitrarily allocated, how can networked discrete-time system stabilization based on the multiplicative channel be realized? The purpose of this paper is two-fold: (1) to co-design the coding/controller for networked stabilization and (2) to discuss the relationship between the minimum channel capacity required for networked stabilization and the system topological entropy
Summary
Networked control systems (NCSs) are feedback control systems in which the systems and the controllers communicate over a shared network. The minimum total capacity required for multi-input networked stabilization can be characterized by the open-loop system topological entropy Another solution is to fix each channel resource and discuss the problem of the networked stabilization from the perspective of communication theory for the multi-input and multi-output transmission mechanism. By virtue of scheduling/control co-design, a sufficient condition is obtained for the overall quality of service of channels required for stabilization given in terms of twice the topological entropy of the plant This is a different perspective from which to research the networked control system stabilization problem. The primary contributions of this paper are as follows: (1) When the channel resources are fixed and cannot be arbitrarily allocated, the paper discusses the problem of mean square stabilization of multi-input discrete-time systems with multiplicative noise constraints; to the best of our knowledge, this problem has never been investigated before. Channel/controller joint design adjusts the supply to satisfy the demand, whereas coding/controller joint design adjusts the demand according to the supply
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