Modeling And Control Of Networked Control Systems Based On Hidden Markov Models

A networked control system (NCS) is a distributed feedback control system whose data is exchanged via a real-time communication network. Compared with conventional point-to-point control systems, the NCS has enormous advantages including reduced system wiring, simplified system expansion and maintenance, and improved system flexibility and reliability. However, due to the limited network bandwidth, there are inevitably network-induced delays when the data is transmitted in the network. Moreover, the delays are random since they are governed by many stochastic factors (e.g., network load, nodes competition, network congestion). All these factors can be collected to be defined as the network states which reflect the network status and determine the randomness of delays. In the NCS, the delays degrade the system performance and even cause the system instability. So, the studies of modeling methods for the delays are critical issues in the NCS. Under such a background, this thesis introduces the discrete-time hidden Markov model (DTHMM) to model the network delays, which is based on the mechanism that the network delays are governed by the network states. Furthermore, the modeling and control methods for the NCS with short delays in the forward network (denoted as forward delays) are studied. The main contents are as follows:1. Network-induced delays are modeled as a discrete-time hidden Markov model (DTHMM), and the forward delay in the current sampling period is predicted based on the DTHMM. First, the delays are quantized by using the uniform quantization method and the K-means clustering quantization method respectively. Then, the delays are modeled as a DTHMM, where the hidden Markov chain consists of the network states and the visible observation process consists of the quantized sequence of delays. The missing-data expectation maximization algorithm is used to train the DTHMM and derive the optimal estimation of the DTHMM parameters. Finally, the Viterbi algorithm is used to estimate the network state sequence corresponding to the quantized sequence of delays. Based on the estimated network state sequence and the derived DTHMM parameters, the forward delay in the current sampling period is predicted. Under the method of uniform quantization, the prediction is taken from the midpoint of the subinterval in which the forward delay falls, while under the method of K-means clustering quantization, the prediction is taken from the centroid of the cluster to which the forward delay belongs.2. Based on the DTHMM delay model, a state-feedback controller is designed to compensate for the effect of the delays on the NCS. First, the NCS is modeled as a typical discrete-time Markovian jump linear system (MJLS) according to the Markovian characteristics of the network states. Then, the sufficient conditions for the stochastic stability of the NCS are obtained by using the stochastic stability theory in the MJLS, and the state-feedback controller for the NCS with full state feedback is designed based on these sufficient conditions. Furthermore, the controller design problem is solved via the linear matrix inequality approach by using the Schur complement lemma. Since the prediction of the forward delay in the current sampling period is considered in the controller design, the effect of the delay on the NCS is compensated directly. Finally, simulation experiments are done to verify the validity of the state-feedback controller.3. Under some certain performance criteria, an optimal controller is designed for the NCS based on the DTHMM delay model. The effect of the delay on the NCS is better compensated by the optimal controller than by the state-feedback controller. First, the NCS is modeled as an augmented state system, where the augmented state consists of the plant state in the current sampling period and the control law in the previous sampling period. Then, the optimal controller under certain performance criteria is designed based on Bellman's dynamic programming principle. The optimal controller guarantees the exponential mean square stability of the NCS. Since the prediction of the forward delay in the current sampling period is considered in the optimal controller design, the effect of the delay on the NCS is compensated directly. Compared with the state-feedback controller, the optimal controller renders the NCS better performance. Finally, simulation experiments are done to verify the validity and superiority of the optimal controller.4. Based on TrueTime 1.5, a simulation platform named NCS-SP is designed for the NCS to work in Matlab/Simulink environment. The kernel block of TrueTime 1.5 is used to design the network nodes (e.g., sensor, controller, actuator, interference unit) on the NCS-SP. The network block of TrueTime 1.5 is used to design the network between the controller and the actuator on the NCS-SP. The state-space block of Simulink is used to design the plant (i.e. damped compound pendulum). The modeling and predictive methods for the network delays and the modeling and control methods for the NCS given in this thesis are all validated on the NCS-SP. Moreover, some contrastive simulation experiments are done to demonstrate the superiority of the K-means clustering quantization to the uniform quantization and the superiority of the optimal controller to the state-feedback controller.