Computer-based control systems are widely used in vehicle applications (e.g., aircraft, marine and automobile). The earlier forms of control systems were typified by a central computer connected to sub-systems using hard-wired point-to-point communication links. However, such systems suffered from several major drawbacks: (i) fault-tolerance problems, (ii) maintenance and cabling costs, and (iii) excessive cable weight. These problems were minimised by using master-slave networks with distributed control architecture. However, using such networks raises the question of fault-tolerance and integrity of the communication system. In view of this, efforts have been made to employ the architecture provided by the IEEE 802.4 Token Bus for real time control applications although the performance of the Token Bus is not adequate for applications where fast response times are required.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis studies control systems with communication constraints. Such constraints arise due to the fact that practical control systems often use non-transparent communication links, i.e., links subject to data-rate constraints, random data-dropouts or random delays. Traditional control theory cannot deal with such constraints and the need for new tools and insights arises. We study two problems: control with average data-rate constraints and control over analog erasure channels with i.i.d. dropout profiles. When focusing on average data-rate constraints, it is natural to ask whether information theoretic ideas may assist the study of networked control systems. In this thesis we show that it is possible to use fundamental information theoretic concepts to arrive at a framework that allows one to tackle performance related control problems. In doing so, we show that there exists an exact link between control systems subject to average data-rate limits, and control systems which are closed over additive i.i.d. noise channels subject to a signal-to-noise ratio constraint. On the other hand, in the case of control systems subject to i.i.d. data-dropouts, we show that there exists a second-order moments equivalence between a linear feedback system which is interconnected over an analog erasure channel, and the same system when it is interconnected over an additive i.i.d. noise channel subject to a signal-to-noise ratio constraint. From the results foreshadowed above, it follows that the study of control systems closed over signal-to-noise ratio constrained additive i.i.d. noise channels is a task of relevance to many networked control problems. Moreover, the interplay between signal-to-noise ratio constraints and control objectives is an interesting issue in its own right. This thesis starts with such a study. Then, we use the resultant insights to address performance issues in control systems subject to either average data-rate constraints or i.i.d. data-dropouts. Our approach shows that, once key equivalences are exposed, standard control intuition and synthesis machinery can be used to tackle networked control problems in an exact manner. It also sheds light into fundamental results in the literature and gives (partial) answers to several previously open questions. We believe that the insights in this thesis are of fundamental importance and, to the best of the author's knowledge, novel.

A control system in which sensors, actuators, and controllers are interconnected over a communication network is called a networked control system (NCS). Enhanced computational capabilities and bandwidths in the networking technology enabled researchers to develop NCSs to implement distributed control schemes. This dissertation presents a framework for the modeling, design, stability analysis, control, and bandwidth allocation of real-time control over networks. This framework covers key research issues regarding control over networks and can be the guidelines of NCS design. A single actuator ball magnetic-levitation (maglev) system is implemented as a test bed for the real-time control over networks to illustrate and verify the theoretical results of this dissertation. Experimentally verifying the feasibility of Internet-based real-time control is another main objective of this dissertation. First, this dissertation proposes a novel NCS model in which the effects of the networkinduced time delay, data-packet loss, and out-of-order data transmission are all considered. Second, two simple algorithms based on model-estimator and predictor- and timeout-scheme are proposed to compensate for the network-induced time delay and packet loss simultaneously. These algorithms are verified experimentally by the ball maglev test bed. System stability analyses of original and compensated systems are presented. Then, a novel co-design consideration related to real-time control and network communication is also proposed. The working range of the sampling frequency is determined by the analysis of the system stability and network parameters such as time delay, data rate, and data-packet size. The NCS design chart developed in this dissertation can be a useful guideline for choosing the network and control parameters in the design of an NCS. Using a real-time operating system for real-time control over networks is also proposed as one of the main contributions of this dissertation. After a real-time NCS is successfully implemented, advanced control theories such as robust control, optimal control, and adaptive control are applied and formulated to improve the quality of control (QoC) of NCSs. Finally, an optimal dynamic bandwidth management method is proposed to solve the optimal network scheduling and bandwidth allocation problem when NCSs are connected to the same network and are sharing the network resource.

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A networked control system (NCS) is a control system where sensors, actuators, and controllers are interconnected over a communication network. This dissertation presents a framework for modeling, stability analysis, optimal control, and bandwidth allocation of the NCS. A ball magnetic-levitation (maglev) system, four DC motor speed-control systems, and a wireless autonomous robotic wheelchair are employed as test beds to illustrate and verify the theoretical results of this dissertation. This dissertation first proposes an output feedback method to stabilize and control the NCSs. The random time delays in the controller-to-actuator and sensor-to-controller links are modeled with two time-homogeneous Markov chains while the packet losses are treated with Dirac delta functions. An asymptotic mean-square stability criterion is established to compensate for the network-induced random time delays and packet losses in the NCS. Then, an algorithm to implement the asymptotic mean-square stability criterion is presented. Experimental results illustrate effectiveness of the proposed output feedback method compared to conventional controllers. The proposed output feedback controller could reduce the errors of the NCS by 13% and 30–40% for the cases without and with data packet losses, respectively. The optimal bandwidth allocation and scheduling of the NCS with nonlinear-programming techniques is also presented in the dissertation. The bandwidth utilization (BU) of each client is defined in terms of its sampling frequency. Two nonlinear approximations, exponential and quadratic approximations, are formulated to describe the system performance governed by discrete-time integral absolute error (DIAE) versus sampling frequency. The optimal sampling frequencies are obtained by solving the approximations with Karush-Kuhn-Tucker (KKT) conditions. Simulation and experimental results are given to verify the effectiveness of the proposed approximations and the bandwidth allocation and scheduling algorithms. In simulations and experiments, the two approximations could maximize the total BU of the NCS up to about 98% of the total available network bandwidth.

This thesis is concerned with the analysis of the control design to the nonlinear networked control systems (NCSs). Ignoring the network connection and cascading actuators, the plant and sensors together, a sampled-data system is obtained. The stabilization problem of nonlinear sampled-data systems is considered under the low measurement rate constraint. Dual-rate control schemes based on the emulation design and discrete-time design approaches respectively are proposed that utilize a numerical integration model to approximately predict the current state of the plant. It is shown that using the dual-rate control schemes, input-to-state stability property will be preserved for the closed loop sampled-data system in a practical sense. On the other hand, the networked realization of nonlinear control systems is studied and a model-based control scheme is addressed as a solution to reduce the network traffic and resultantly, to attain a higher performance. The NCSs are modeled as continuous-time systems and sampled-data systems, respectively. Under the proposed control scheme, a tradeoff between satisfactory control performance and reduction of network traffic can be achieved. It is shown that by using the estimated values, generated by the plant model, instead of true values of the plant, a significant saving in the required bandwidth is achieved and this makes possible stabilization of the plant even under slow network conditions.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis studies control systems with communication constraints. Such constraints arise due to the fact that practical control systems often use non-transparent communication links, i.e., links subject to data-rate constraints, random data-dropouts or random delays. Traditional control theory cannot deal with such constraints and the need for new tools and insights arises. We study two problems: control with average data-rate constraints and control over analog erasure channels with i.i.d. dropout profiles. When focusing on average data-rate constraints, it is natural to ask whether information theoretic ideas may assist the study of networked control systems. In this thesis we show that it is possible to use fundamental information theoretic concepts to arrive at a framework that allows one to tackle performance related control problems. In doing so, we show that there exists an exact link between control systems subject to average data-rate limits, and control systems which are closed over additive i.i.d. noise channels subject to a signal-to-noise ratio constraint. On the other hand, in the case of control systems subject to i.i.d. data-dropouts, we show that there exists a second-order moments equivalence between a linear feedback system which is interconnected over an analog erasure channel, and the same system when it is interconnected over an additive i.i.d. noise channel subject to a signal-to-noise ratio constraint. From the results foreshadowed above, it follows that the study of control systems closed over signal-to-noise ratio constrained additive i.i.d. noise channels is a task of relevance to many networked control problems. Moreover, the interplay between signal-to-noise ratio constraints and control objectives is an interesting issue in its own right. This thesis starts with such a study. Then, we use the resultant insights to address performance issues in control systems subject to either average data-rate constraints or i.i.d. data-dropouts. Our approach shows that, once key equivalences are exposed, standard control intuition and synthesis machinery can be used to tackle networked control problems in an exact manner. It also sheds light into fundamental results in the literature and gives (partial) answers to several previously open questions. We believe that the insights in this thesis are of fundamental importance and, to the best of the author's knowledge, novel.

Networked control systems (NCSs) are known as distributed control systems (DCSs) which are based on traditional feedback control systems but closed via a real-time communication channel. In an NCS, the control and feedback signals are exchanged among the system’s components in the form of information packages through the communication channel. The research of NCSs is important from the application perspective due to the significant advantages over the traditional point-to-point control. However, the insertion of the communication links would also bring challenges and constraints such as the network-induced delays, the missing packets, and the inter symbol interference (ISI) into the system design. In order to tackle these issues and move a step further toward industry applications, two important design problems are investigated in the control areas: Tracking Control (Chapter 2–Chapter 5) and Signal Estimation (Chapter 6–Chapter8). With the fact that more than 90% of control loops in industry are controlled by proportional-integral-derivative (PID) controllers, the first work in this thesis aims to propose the design algorithm on PID controllers for NCSs. Such a design will not require the change or update of the existing industrial hardware, and it will enjoy the advantages of the NCSs. The second motivation is that, due to the network-induced constraints, there is no any existing work on tuning the PID gains for a general NCS with a state-space model. In Chapter 2, the PID tracking control for multi-variable NCSs subject to time-varying delays and packet dropouts is exploited. The H_infty control is employed to attenuate the load disturbance and the measurement noise. In Chapter 3, the probabilistic delay model is used to design the delay-scheduling tracking controllers for NCSs. The tracking control strategy consists of two parts: (1) the feedforward control can enhance the transient response, and (2) the feedback control is the digital PID control. In order to compensate for the delays on both communication links, the predictive control scheme is adopted. To make full use of the delay information, it is better to use the Markov chain to model the network-induced delays and the missing packets. A common assumption on the Markov chain model in the literature is that the probability transition matrix is precisely known. However, the assumption may not hold any more when the delay is time-varying in a large set and the statistics information on the delays is inadequate. In Chapter 4, it is assumed that the transition matrices are with partially unknown elements. An observer-based robust energy-to-peak tracking controller is designed for the NCSs. In Chapter 5, the step tracking control problem for the nonlinear NCSs is in- vestigated. The nonlinear plant is represented by Takagi-Sugeno (T-S) fuzzy linear model. The control strategy is a modified PI control. With an augmentation technique, the tracking controller design problem is converted into an H_infty optimization problem. The controller parameters can be obtained by solving non-iterative linear matrix inequality conditions. The state estimation problem for networked systems is explored in Chapter 6. At the sensor node, the phenomenon of multiple intermittent measurements is considered for a harsh sensing environment. It is assumed that the network-induced delay is time- varying within a bounded interval. To deal with the delayed external input and the non-delayed external input, a weighted H_infty performance is defined. A Lyapunov- based method is employed to deal with the estimator design problem. When the delay is not large, the system with delayed state can be transformed into delay-free systems. By using the probabilistic delay model and the augmentation, the H_infty filter design algorithm is proposed for networked systems in Chapter 7. Considering the phenomenon of ISI, the signals transmitted over the communication link would distort, that is, the output of the communication link is not the same with the input to the communication link. If the phenomenon occurs in the NCSs, it is desired to reconstruct the signal. In Chapter 8, a robust equalizer design algorithm is proposed to reconstruct the input signal, being robust against the measurement noise and the parameter variations. Finally, the conclusions of the dissertation are summarized and future research topics are presented. / Graduate

The main focus of the thesis is to derive stability criteria for networked control system (NCS) models featuring imperfections such as time-varying and constant delays, quantization, packet dropouts, and non-uniform sampling intervals. The main method of proof is based on matrix algebra, as opposed to methods using Lyapunov functions or integral quadratic constraints (IQC). This work puts a particular focus on handling systems with a single integrator. This framework is elaborated in different specific directions as motivated by practical realizations of NCSs, as well as through numerical examples. A novel proof of the discrete time multivariate circle criterion and the Tsypkin criterion for systems including a single integrator is presented, as well as a stability criterion for linear systems with a single integrator subject to variable sampling periods and sector-bounded nonlinear feedback. Four stability criteria for different classes of systems subject to packet loss and time-varying delay are given. Stability criteria for a closed loop system switching between a set of linear time-invariant systems (LTIs) are proved. This result is applied to a single-link NCS with feedback subject to packet loss. Finally, necessary and sufficient conditions for delay-independent stability of an LTI system subject to nonlinear feedback are derived.

Stochastic system identification is of great interest in the areas of control and communication. In stochastic system identification, a model of a dynamic system is determined based on given inputs and received outputs from the system, where stochastic uncertainties are also involved. The scope of the report is to consider continuous-time models used within control and communication and to estimate the model parameters from sampled data with high accuracy in a computational efficient way. Continuous-time models of systems controlled in a networked environment, stochastic closed-loop systems, and wireless channels are considered. The parameters of a transfer function based model for the process in a networked control system are first estimated by a covariance function based approach, relying upon the second order statistical properties of the output signal. Some other approaches for estimating the parameters of continuous-time models for processes in networked environments are also considered. Further, the parameters of continuous-time autoregressive exogenous models are estimated from closed-loop filtered data, where the controllers in the closed-loop are of proportional and proportional integral type, and where the closed-loop also contains a time-delay. Moreover, a stochastic differential equation is derived for Jakes's wireless channel model, describing the dynamics of a scattered electric field with the moving receiver incorporating a Doppler shift. / <p>Article I was still in manuscript form at the time of the defense.</p>