Filtering and control of networked systems over unreliable channels

• Main Author: Xiao, Nan
• Other Authors: Xie Lihua
• Format: Theses and Dissertations
• Language: English
• Published: 2011
• Subjects: DRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation::Control engineering
• Online Access: https://hdl.handle.net/10356/46461
• Institution: Nanyang Technological University

Networked control systems have attracted recurring research interests from the control community due to their wide applications in intelligent transportation, industrial automation, advanced manufacturing, and national defense. This thesis summarizes research results on filtering and control of networked systems over unreliable channels with emphasis on two typical channel models: lossy channel model and fading channel model. In the first place, it is assumed that a lossy network is placed in the networked system, where the packet-loss process is driven by a Markov chain. We start by considering the Kalman filtering of a linear time-invariant plant over a lossy channel with bounded Markovian packet dropouts. If the observability index of the plant is one, then the peak error covariance matrix of a remote Kalman filter is always bounded from above in the mean sense. For plants with observability index greater than one, a sufficient condition is provided for the stability of the peak error covariance matrix in the mean sense, which is specified in terms of the dynamics of the plant and the transition probability of the Markov chain that describes the packet-loss process. The quantized stabilization over a lossy channel is then studied by modeling the networked system into a Markov jump linear system. Given a measure of quantization coarseness, it is shown that a logarithmic quantizer and a linear state feedback are optimal for the mean square quadratic stabilization of a single-input Markov jump linear system. The optimal co-design of quantizer and controller are addressed via a linear matrix inequality approach. A recursive algorithm is presented to estimate the unknown mode process of the underlying Markov chain at the controller side. Next, we suppose that a fading network is put into the networked system, and the channel fading is modeled by a white sequence. We begin with studying the Kalman filtering of a linear time-invariant plant across fading channels. Necessary and sufficient conditions for the stability of the mean error covariance matrix of the remote Kalman filter are derived in terms of the unstable poles of the plant. Lower and upper bounds for the mean error covariance matrix are provided in the form of a modified Lyapunov iteration and a modified Riccati iteration, respectively. The mean square stabilization of networked systems over fading channels is then addressed. For the case of state feedback, the minimal overall mean square capacity of the network for mean square stabilizability is given in terms of the Mahler measure of the plant under the parallel transmission strategy and the assumption on capacity allocation. Under the serial transmission strategy, the minimal capacity for stabilizability in general can only be computed by optimization. For the case of dynamic output feedback, a tight lower bound on the capacity requirement for stabilization of single-input single-output plants is given in terms of the anti-stable poles, nonminimum phase zeros and relative degree of the plant. Sufficient and necessary conditions are also derived for stabilization of triangularly decoupled multi-input multi-output plants. The effect of channel processing, channel feedback, and channel input power bound is further analyzed. We show that the channel feedback plays a key role in reducing the network requirement for stabilizability caused by the nonminimum phase zeros and high relative degree of the plant, and the network requirement for stabilizability becomes more stringent when a power bound is applied on the channel input. A suboptimal algorithm is proposed for performance design of networked systems over fading channels. Finally, the results on control of discrete-time networked systems over fading channels are extended to the continuous-time case.