A Novelty in Blahut-Arimoto Type Algorithms: Optimal Control Over Noisy Communication Channels

Abstract

A probability-theoretic problem under information constraints for the concept of optimal control over a noisymemoryless channel is considered. For our Observer-Controller block, i.e., the lossy joint-source-channel-coding (JSCC) scheme, after providing the relative mathematical expressions, we propose a Blahut-Arimoto-type algorithm − which is, to the best of our knowledge, for the first time. The algorithm efficiently finds the probability-mass-functions (PMFs) required for min. This problem is an N P−hard and non-convex multi-objective optimisation (MOO) one, were the objective functions are respectively the distortion function dim Null I( Ŝ; S → ∞ and the memorylesschannel capacity dim Null I(X; X → 0. Our novel algorithm applies an Alternating optimisation method. Subsequently, a robust version of the algorithm is discussed with regard to the perturbed PMFs − parameter uncertainties in general.The aforementioned robustness is actualised by exploiting the simultaneous-perturbation-stochastic-approximation (SPSA). The principles of detectability-and-stabilisability as well as synchronisability are explored, in addition to providing the simulationsby which the efficiency of our work is shown. We also calculate the total complexity of our proposed algorithms respectively as O T K M 0 K log K and O T K M 0 K log K + 0.33K . Our methodology is generic which can be applied to other fields of studies which are optimisation-driven.

A Game Theoretical Analysis on the Gray-Wyner System and Generalised Common Information

“…13 For more details and about the rotations of the probabilities relating to each other see e.g. [2] − where an Alternating optimisation method was proposed.…”

“…Two terms control and information are interchangeable [1], [2], [3], [4], [5]. The information-theoretic bounds achieved through simultaneous resource use have a lot of priorities compared with the recent random access strategies.…”

“…A. Literature review 1) Information-theory & control-theory: From an information-theoretic control-theoretic point of view, in joint control and network design, the application is control [2], [3], [4], [5]. In this fashion, some brilliant activities have been performed.…”

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“…Some of the most successful data-driven techniques will be highlighted as follows citing both classical and fresh papers that actually apply them: Iterative Feedback Tuning (IFT) (Hjalmarsson, 2002;Jung et al, 2020), Modelfree Adaptive Control (Hou & Wang, 2013;Yu et al, 2020), Simultaneous Perturbation Stochastic Approximation (Spall & Cristion, 1998;Zamanipour, 2020), Correlation-based Tuning (Karimi et al, 2004;Sato, 2020), Frequency Domain Tuning (Kammer et al, 2000;da Silva Moreira et al, 2018), Iterative Regression Tuning (Halmevaara & Hyötyniemi, 2006), and adaptive online IFT (McDaid et al, 2012). While these data-driven techniques actually carry out the iterative experiment-based update of controller parameters, non-iterative techniques are also popular as Model-Free Control (MFC) (Fliess & Join, 2009, Virtual Reference Feedback Tuning (Campi et al, 2002;Formentin et al, 2019); Active Disturbance Rejection Control (Gao, 2006;Roman et al, 2020), data-driven predictive control (Kadali et al, 2003;Lucchini et al, 2020), unfalsified control (Safonov & Tsao, 1997;Jiang et al, 2016) and Data-Driven Inversion Based Control (Novara et al, 2015;Galluppi et al, 2019).…”

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“…This kind of optimisation problem can be solved by the alternating direction method of multipliers: See e.g [27],[28],[29]…”