Daniel E. Quevedo

Audio quantization from a receding horizon control perspective

By introducing psycho-acoustical aspects, the audio quantization problem is translated into a finite horizon optimal control problem with a finite input constraint set. An explicit solution is obtained. Its receding horizon implementation gives rise to the receding horizon quantizer (RHQ). The RHQ corresponds to a closed loop, which embeds the widely-adopted noise shaping quantizer in a broader framework and allows for enhanced performance. Furthermore, suboptimal algorithms are described and their behaviour illustrated by means of an example.

Minimizing down-link traffic in networked control systems via optimal control techniques

This paper presents a control strategy for multivariable plants where controller and actuators are connected via a digital data-rate limited channel. In order to minimize bandwidth utilization, a communication constraint is imposed, which restricts all data transmitted to belong to a finite set and only permits one plant input to be addressed at a time. We develop a new scheme, which aims at optimizing quadratic performance under the above communication constraint. A key aspect of this contribution is the implementation of the control scheme to a real laboratory-scale system.

Optimal coding for bit-rate limited networked control systems in the presence of data loss

This paper studies networked control of SISO LTI plant models, where the communication channel is subject to both quantization and data dropouts. Using a standard signal-to-noise ratio constrained white noise model for quantization, we derive coder-decoder pairs that minimize the impact of channel artifacts on closed loop performance. In addition, we provide a simple necessary and sufficient condition that guarantees the stability of the considered networked control system architecture.

Multistep Detector for Linear ISI-Channels Incorporating Degrees of Belief in Past Estimates

This paper formulates the channel equalization problem in the framework of constrained maximum-likelihood estimation. This allows us to highlight key issues including the need to summarize past data and to apply a finite alphabet constraint over a sliding optimization window. The approach adopted here leads to embellishments of the usual (nonadaptive) decision-feedback equalizer and its multistep extensions. It includes a provision for degrees of belief in past estimates, which addresses the problem of error propagation.

Design issues arising in a networked control system architecture

We consider a networked control system architecture, where a centralized controller is connected to a set of actuators via a data-rate limited digital channel. The presence of the communication channel forces all data transmitted to be quantized and limits only one actuator to be addressed at a given time. Within this context, we present a networked controller aimed at optimizing performance and which incorporates coding. Furthermore, we propose a design procedure for the coder. The methodology allows one to trade-off channel utilization versus robustness with respect to transmission errors.

Multi-step optimal quantization in oversampled filter banks

Using concepts from the receding horizon control framework, we propose an approach to quantization in oversampled filter banks. The key idea is to pose the quantization problem as a multi-step optimization problem, where the decision variables are restricted to belong to a finite set. It is shown that the resulting architecture yields enhanced performance when compared to the well-known noise shaping coder. In particular, the quantizer proposed can be tuned with stability concepts in mind.

Moving horizon Monte Carlo state estimation for linear systems with output quantization

This paper develops a novel scheme for state estimation of discrete-time linear time-invariant systems with output quantization. The method combines concepts from Monte Carlo sampling and moving horizon estimation. The effectiveness of the scheme is illustrated via a simulation example.

Conditions for optimality of scalar feedback quantization

This paper presents novel results on scalar feedback quantization (SFQ) with uniform quantizers. We focus on general SFQ configurations where reconstruction is via a linear combination of frame vectors. Using a deterministic approach, we derive two necessary and sufficient conditions for SFQ to be optimal, i.e., to produce, for every input, a quantized sequence that is a global minimizer of the 2-norm of the reconstruction error. The first optimality condition is related to the design of the feedback quantizer, and can always be achieved. The second condition depends only on the reconstruction vectors, and is given explicitly in terms of the Gram matrix of the reconstruction frame. As a by-product, we also show that the the first condition alone characterizes scalar feedback quantizers that yield the smallest MSE, when one models quantization noise as uncorrelated, identically distributed random variables.

Quantization and Sampling of Not Necessarily Band-Limited Signals

This paper presents novel results on the joint problem of sampling and quantization of non bandlimited signals. Existing literature typically focuses either on sampling in the absence of quantization, or, conversely, studies quantization for already sampled signals. Our emphasis here is on the issues that arise al the intersection of these two design problems. We argue that the joint problem can be formulated and solved to any desired level of accuracy, using moving horizon optimization methods. We present several examples which show that consideration of the combined sampling and quantization problem gives important performance gains, relative to strategies which dont specifically address the interaction between these two problems

An application of receding horizon control to estimation with quantized coefficients

A methodology for designing optimal finite impulse response estimators with quantized coefficients is proposed. The problem of minimizing the covariance of the estimation error is translated into a constrained quadratic regulator problem, where the inputs need to be chosen from a finite set. Solving it has a computational complexity which is exponential in the filter impulse response length. To overcome the associated computational burden, we propose an approximate algorithm using receding horizon ideas borrowed from the model predictive control framework. This approach can be independently motivated without utilizing the control analogy. We present a closed form expression for the exact solution to the problem. An example illustrates the trade-off that arises between computational time and performance.