Optimal LQG Control Across a Packet-Dropping Link

We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design

Mean Square Capacity of Power Constrained Fading Channels with Causal Encoders and Decoders

This paper is concerned with the mean square stabilization problem of discrete-time LTI systems over a power constrained fading channel. Different from existing research works, the channel considered in this paper suffers from both fading and additive noises. We allow any form of causal channel encoders/decoders, unlike linear encoders/decoders commonly studied in the literature. Sufficient conditions and necessary conditions for the mean square stabilizability are given in terms of channel parameters such as transmission power and fading and additive noise statistics in relation to the unstable eigenvalues of the open-loop system matrix. The corresponding mean square capacity of the power constrained fading channel under causal encoders/decoders is given. It is proved that this mean square capacity is smaller than the corresponding Shannon channel capacity. In the end, numerical examples are presented, which demonstrate that the causal encoders/decoders render less restrictive stabilizability conditions than those under linear encoders/decoders studied in the existing works.Comment: Accepted by the 54th IEEE Conference on Decision and Contro

Stability of the replica symmetric solution for the information conveyed by by a neural network

The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts of noise. The region of instability depends on the contribution of the threshold and the sparseness: for distributed pattern distributions, the unstable region extends to higher noise variances than for very sparse distributions, for which it is almost nonexistant.Comment: 19 pages, LaTeX, 5 figures. Also available at http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E Minor change

Composite CDMA - A statistical mechanics analysis

Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it provides robustness and flexibility in utilising multi-access channels, whilst not making significant sacrifices in terms of transmission power. Random codes are generated from some ensemble, here we consider the possibility of combining two standard paradigms, sparsely and densely spread codes, in a single composite code ensemble. The composite code analysis includes a replica symmetric calculation of performance in the large system limit, and investigation of finite systems through a composite belief propagation algorithm. A variety of codes are examined with a focus on the high multi-access interference regime. In both the large size limit and finite systems we demonstrate scenarios in which the composite code has typical performance exceeding sparse and dense codes at equivalent signal to noise ratio.Comment: 23 pages, 11 figures, Sigma Phi 2008 conference submission - submitted to J.Stat.Mec

Data Transmission Over Networks for Estimation and Control

We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal linear-quadratic-Gaussian (LQG) controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network