Search

Consider a discrete-time, linear time-invariant process, two sensors and one controller. The process state is observed in the presence of noise by the sensors, which are connected to the controller via links that feature erasure. If a link transmits successfully then a finite-dimensional vector of real numbers is conveyed from the sensor to the controller. If an erasure event occurs, then any information conveyed over the link is lost. This paper addresses the problem of designing the maps that specify the processing at the controller and at the sensors to minimize a quadratic cost function. When the information is lost over the links either in an independent and identically distributed (i.i.d.) or in a (time-homogeneous) Markovian fashion, we derive necessary and sufficient conditions for the existence of maps such that the process is stabilized in the bounded second moment sense. We also solve the optimal design problem in the presence of delayed noiseless acknowledgment signals at the sensors from the controller for an arbitrary packet drop pattern. We provide explicit recursive schemes to implement our solution. We also indicate how our approach can be extended to situations when more than two sensors are available and when the sensors can cooperate. The analysis also carries over to the case when each point-to-point erasure link connecting the sensors and the controller is replaced by a network of erasure links. Index Terms--Control over communication channels, distributed estimation, linear time-invariant, networked control systems, sensor networks.

Hysteresis hinders the effective use of smart materials in sensors and actuators. This paper addresses recursive identification and adaptive inverse control of hysteresis in smart material actuators, where hysteresis is modeled by a Preisach operator with a piecewise uniform density function. Two classes of identification schemes are proposed and compared, one based on the hysteresis output, the other based on the time-difference of the output. Conditions for parameter convergence are presented in terms of the input to the Preisach operator. An adaptive inverse control scheme is developed by updating the Preisach operator (and thus its inverse) with the output-based identification method. The asymptotic tracking property of this scheme is established, and for periodic reference trajectories, the parameter convergence behavior is characterized. Practical issues in the implementation of the adaptive identification and inverse control methods are also investigated. Simulation and experimental results based on a magnetostrictive actuator are provided to illustrate the proposed approach. Index Terms--Adaptive control, hysteresis, identification, inversion, Preisach operator, smart materials.

This paper addresses data-aided (DA) synchronization, in which the reference parameter acquisition is aided by a training sequence known to the receiver. The Cramer-Rao lower bound (CRB) for the DA timing and/or carrier phase recovery is presented. For DA parameter estimation, the CRB typically varies with the training sequence. This indicates that different training sequences offer fundamentally different performance. In the literature, the widely cited closed-form CRB for timing and carrier phase recovery was derived under the assumption that the training sequence is independent and identically distributed (i.i.d.) and sufficiently long. In this paper, we derive a closed-form CRB for timing and carrier phase recovery with respect to an arbitrary training sequence and pulse shaping function for the over and under sampling cases. It turns out that the CRB is a weighted summation of the aperiodic correlation of the training sequence and the weighting factor is determined by the pulse shaping filter. Therefore, this paper reveals the fundamental link between a training sequence and its corresponding performance limit. Index Terms--Cramer-Rao bound (CRB), data-aided (DA) synchronization, phase estimation, timing, synchronizations.

Many issues in signal processing involve the inverses of Toeplitz matrices. One widely used technique is to replace Toeplitz matrices with their associated circulant matrices, based on the well-known fact that Toeplitz matrices asymptotically converge to their associated circulant matrices in the weak sense. This often leads to considerable simplification. However, it is well known that such a weak convergence cannot be strengthened into strong convergence. It is this fact that severely limits the usefulness of the close relation between Toeplitz matrices and circulant matrices. Observing that communication receiver design often needs to seek optimality in regard to a data sequence transmitted within finite duration, we define the finite-term strong convergence regarding two families of matrices. We present a condition under which the inverses of a Toeplitz matrix converges in the strong sense to a circulant matrix for finite-term quadratic forms. This builds a critical link in the application of the convergence theorems for the inverses of Toeplitz matrices since the weak convergence generally finds its usefulness in issues associated with minimum mean squared error and the finite-term strong convergence is useful in issues associated with the maximum-likelihood or maximum a posteriori principles. Index Terms--Circulant matrix, maximum a posteriori, maximum likelihood, strong convergence, Toeplitz matrix.