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.

In the present study, we investigate kernel density estimation (KDE) and its application to the Gumbel probability distribution. We introduce the basic concepts of reliability analysis and estimation in ordinary and Bayesian settings. The robustness of top three kernels used in KDE with respect to three different optimal bandwidths is presented. The parametric, Bayesian, and empirical Bayes estimates of the reliability, failure rate, and cumulative failure rate functions under the Gumbel failure model are derived and compared with the kernel density estimates. We also introduce the concept of target time subject to obtaining a specified reliability. A comparison of the Bayes estimates of the Gumbel reliability function under six different priors, including kernel density prior, is performed. A comparison of the maximum likelihood (ML) and Bayes estimates of the target time under desired reliability using the Jeffrey's non-informative prior and square error loss function is studied. In order to determine which of the two different loss functions provides a better estimate of the location parameter for the Gumbel probability distribution, we study the performance of four criteria, including the non-parametric kernel density criterion. Finally, we apply both KDE and the Gumbel probability distribution in modeling the annual extreme stream flow of the Hillsborough River, FL. We use the jackknife procedure to improve ML parameter estimates. We model quantile and return period functions both parametrically and using KDE, and show that KDE provides a better fit in the tails.