Predictive Coding and Control

Abstract

This paper deals with feedback control over a single fixed-rate channel using predictive coding at the transmitter side. The central thrust is to demonstrate that optimal control based on predictive coding plus fixed memoryless quantization at the transmitter, designed to improve the efficiency of the channel usage and exemplified (or perhaps extremized) by the transmission of the quantized innovations signal, in general requires the construction of the joint density of both the plant and predictor states at the receiver side and inherits a plant stability requirement, which is examined. The Bayesian filter is developed. This recursive filter's state density is used to compute the optimal feedback control. This is in contrast to the less complicated propagation solely of the predictor state, which would suffice in the linear quadratic optimal control problem-a feature that is elucidated. A linear non-quadratic optimal control example is provided to illustrate the approach and its benefits over control based on the recovered predictor state density or control without predictive coding. In each of these competing cases, a lower complexity receiver architecture is possible but at the expense of closed-loop control performance.

Real Time Coding and Estimation of Linear Discrete Time System Over Networks

“…In such cases, it should be pointed out that the optimal codingestimation policy cannot be written in the separated form as presented for the single observation case, for details, see e.g., [17]. On the other hand, the derived results in this work make it interesting to consider the extension of this framework to closed-loop networked control systems where the objective is to identify the performance of control under communication constraints, see for instance [5], [8], [36]. Due to the nonlinear and uncertain characteristics of most of the practical networked systems, see e.g., [6], [7], [37], the design and performance analysis of the coding-estimation and control systems in such cases will be also under consideration in future.…”

Adversarial Radar Inference: Inverse Tracking, Identifying Cognition, and Designing Smart Interference

“…There are strong parallels between inverse filtering and Bayesian social learning [10], [22], [21], [20]; the key difference is that social learning aims to estimate the underlying state given noisy posteriors, whereas our aim is to estimate the posterior given noisy measurements of the posterior and the underlying state. Recently, [19] used cascaded Kalman filters for LQG control over communication channels.…”

An Integrative Perspective to LQ and $\ell _\infty$ Control for Delayed and Quantized Systems

“…For the latter, the stability conditions are known for linear systems with quantization or data rate constraints [18]- [20], and performance bounds are given in [5]- [8], [21]- [27]. The design and performance of systems with fixed and random delays are recently investigated in [28], [29], and performance bounds are recently obtained in [30]. The relation between the optimal cost and the causal rate-distortion function is studied in [8], [31]- [38].…”