On the effect of quantization on performance at high rates

We study the effect of quantization on the performance of a scalar dynamical system in the high rate regime. We evaluate the LQ cost for two commonly used quantizers: uniform and logarithmic and provide a lower bound on performance of any centroid-based quantizer based on entropy arguments. We also consider the case when the channel drops data packets stochastically

Stabilization over power-constrained parallel Gaussian channels

This technical note is concerned with state-feedback stabilization of multi-input systems over parallel Gaussian channels subject to a total power constraint. Both continuous-time and discrete-time systems are treated under the framework of H2 control, and necessary/sufficient conditions for stabilizability are established in terms of inequalities involving unstable plant poles, transmitted power, and noise variances. These results are further used to clarify the relationship between channel capacity and stabilizability. Compared to single-input systems, a range of technical issues arise. In particular, in the multi-input case, the optimal controller has a separation structure, and the lower bound on channel capacity for some discrete-time systems is unachievable by linear time-invariant (LTI) encoders/decoder

Kalman Filtering Over a Packet-Dropping Network: A Probabilistic Perspective

We consider the problem of state estimation of a discrete time process over a packet-dropping network. Previous work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k ≤ M], i.e., the probability that P_k is bounded by a given M. We consider two scenarios in the paper. In the first scenario, when the sensor sends its measurement data to the remote estimator via a packet-dropping network, we derive lower and upper bounds on Pr[P_k ≤ M]. In the second scenario, when the sensor preprocesses the measurement data and sends its local state estimate to the estimator, we show that the previously derived lower and upper bounds are equal to each other, hence we are able to provide a closed form expression for Pr[P_k ≤ M]. We also recover the results in the literature when using Pr[P_k ≤ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper

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