Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

Integrando multiagentes em ambientes 3D: um serious game para estimulação cognitiva

Sistemas Multiagentes estão recebendo cada vez mais a atenção de pesquisadores e desenvolvedores de jogos virtuais. O uso de agentes permite controlar o desempenho do usuário, adaptando a interface e alterando automaticamente o nível de dificuldade das tarefas. Este trabalho descreve uma estratégia de integração de sistemas multiagentes e ambientes virtuais tridimensionais e exemplifica a viabilidade dessa integração através do desenvolvimento de um jogo com características de Serious game. Este jogo visa estimular as funções cognitivas, tais como atenção e memória e é voltado para pessoas portadoras de diferentes distúrbios neuropsiquiátricos. A construção do jogo foi apoiada em um processo de desenvolvimento composto por várias etapas: estudos teóricos sobre as áreas envolvidas, estudo de tecnologias capazes de apoiar essa integração, levantamento de requisitos com especialistas, implementação e avaliação com especialistas. O produto final foi avaliado por especialistas da área médica, que consideraram os resultados como positivos.

A Game-Theoreteic Analysis of Minority Language Use in Multilingual Societies

This chapter studies multilingual democratic societies with highly developed economies. These societies are assumed to have two languages with official status: language A, spoken by every individual, and language B, spoken by the bilingual minority. We emphasize that language rights are important, but the survival of the minority language B depends mainly on the actual use bilinguals make of B. The purpose of the present chapter is to study some of the factors affecting the bilingual speakers language choice behaviour. Our view is that languages with their speech communities compete for speakers just as fi rms compete for market share. Thus, the con ict among the minority languages in these societies does not take the rough expressions such as those studied in Desmet et al. (2012). Here the con flict is more subtle. We model highly plausible language choice situations by means of choice procedures and non-cooperative games, each with different types of information. We then study the determinants of the bilinguals ' strategic behaviour with regard to language. We observe that the bilinguals' use of B is shaped, essentially, by linguistic conventions and social norms that are developed in situations of language contact.