Control and estimation with limited data rate and packet loss
Date of Issue2011
School of Electrical and Electronic Engineering
With the rapid advances in information processing, communication and sensing technologies, networked control systems(NCSs) have gained substantial research interest due to their broad applications. The incorporation of resource limited communication networks in the feedback loop induces new challenges in system analysis and synthesis. One of the main challenges in NCSs is on the quantized feedback control under limited data rate. It is well established that there exists a minimum average data rate above which a discrete LTI system can be stabilized. To exploit the capacity of logarithmic quantization, we show that a finite-level logarithmic quantizer suffices to approach the minimum average data rate for stabilizing a discrete LTI system under two basic network configurations. While in a practical networked system, the issues of packet loss and limited data rate generally co-exist. Data rate theorem for mean square stabilization of an LTI system over lossy digital channels is studied, which reveals the joint effect of quantization and packet loss on the mean square stabilizability. More specifically, the additional data rates required to counter the effect of packet loss are explicitly quantified for single input systems under i.i.d. packet loss, and for scalar systems under Markovian packet loss. Sufficient data rate conditions are also provided for general discrete LTI systems. Then, we proceed to analyze the effect of limited data rate and packet loss on filtering performance. Under limited data rate constraints, a multi-level quantized innovations Kalman filter is proposed to estimate the state of linear stochastic systems. The quantized filter has the same complexity as the standard Kalman filter and exhibits a comparable estimation performance under quantization with a moderate number of bits. With Markovian packet losses, the problem on mean stability of the estimation error covariance matrices of Kalman filter is quite challenging. Based on the realization of the packet loss process, two stability notions, namely stability in stopping times and stability in sampling times, are introduced to examine the behavior of the estimation error covariances.
DRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation