Control And Stabilization Of Networked Control Systems Under Communication Constraints

In modern industrial systems, sensors, controllers and actuators are often connected over a network medium. Such closed-loop control systems are called networked control systems (NCSs). Compared with the traditional control systems, NCSs include many ad-vantages, such as resource sharing, simple installation and maintenance, reduced weight, high reliability, etc. However, inserting network into control systems will also introduce new challenges for the analysis and design of control systems, such as packet dropout, packet disordering, network-induced time delay, communication constraints, etc. The ex-isting results mainly focus on feedback control problems for NCSs with time delay and packet dropout. However, feedback control problems for NCSs under communication constraints are not still taken into full consideration.This thesis, on the basis of previous works of others, investigates feedback control problems for NCSs under communication constraints, and presents the inherent trade-off between control and communication costs, and gives a new method on networked control under communication constraints by employing information theory as a power-ful conceptual aid. The minimum data rate for mean square stabilization of NCSs over a bandwidth-limited, packet dropout communication channel is presented by employing an adaptive differential coding strategy and a predictive control policy. Furthermore, the robust stabilization problem for parameter uncertain systems with limited data rate is addressed. A time-varying recursive allocation (TVRA) algorithm is proposed to solve the modal decomposition and data rate allocation problems. Sufficient conditions for ro-bust stabilization of parameter uncertain systems are derived. The linear quadratic (LQ) control problem for NCSs under data rate limitations is addressed. An explicit formula on the tradeoff between the LQ cost and the data rate of the feedback channel is pro-posed. Finally, the quantized output feedback control problem for single-input single-output (SISO) linear systems with limited data rate is addressed. The details of this thesis are as follows.Chapters1-2first summarize and analyze the development and main research meth- ods in networked control systems. Preliminaries about the considered problems are also given.Chapter3investigates stabilization problems for linear time-invariant control sys-tems, where the sensors and controllers are geographically separated and connected via noisy, bandwidth-limited digital communication channels. The packet dropout process of the channel is modeled as a time-homogeneous Markov process. An adaptive differential coding strategy and a predictive control policy are implemented to achieve the minimum data rate of the channel for mean square stabilization of the unstable plant. In particu-lar, it is shown that, for the system without disturbances, a sufficient condition on mean square stabilization is that the data rate is more than the lower bound given in our results; however, for the system with disturbances, the sufficient condition decomposes into two terms:a condition on the data rate and a condition on the transition probabilities of the Markov chain. An illustrative example is given to demonstrate the effectiveness of the proposed method.Chapter4investigates the robust stabilization problem for parameter uncertain sys-tems with limited data rate. A time-varying recursive allocation (TVRA) algorithm is proposed to solve the modal decomposition and data-rate allocation problems that have to be faced for a multi-dimensional uncertain system. Sufficient conditions for robust sta-bilization of the feedback loop are derived. A positive critical lower bound of data rates is presented, below which there exists no quantization, coding and control scheme to sta-bilize the unstable parameter uncertain plant. Simulation results show the validity of the proposed scheme.Chapter5investigates linear quadratic (LQ) control problems for stochastic linear discrete-time systems, where the sensors and controllers are geographically separated and connected via noiseless, bandwidth-limited digital communication channels. The plant states are quantized, encoded by an adaptive differential coding strategy. A full knowledge LQ cost under data rate limitations is presented in our results. Sufficient conditions on a lower bound of data rates for stabilization are derived. An explicit formula on the tradeoff between the LQ cost and the data rate of the channel is proposed. An illustrative example is given to demonstrate the effectiveness of the proposed method.Chapter6addresses the quantized output feedback control problem for single-input single-output (SISO) linear systems with quantized measurements of the plant output, where the sensors and controllers are connected via errorless digital channels carrying a finite number of bits per unit time. The main idea here is to present a lower bound of data rates, above which there exists a quantization, coding and control scheme to guar-antee both stabilization and a prescribed control performance of the unstable plant. A quantization and coding scheme, which is based on the distribution of measurements and the dynamics of the plant, is proposed. The proof techniques rely on both information-theoretic and control-theoretic tools. An illustrative example is given to demonstrate the effectiveness of the proposed scheme.Finally, the results of the dissertation are summarized and further research topics are pointed out.