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The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and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.

Does rating shopping exist in spanish securitization issues?

[EN] Debt issue credit ratings can lead to conflicts of interest as the issuer itself is entrusted with contracting and compensating the rating agency. Into the bargain, the credit rating agency may be involved in designing the issues that the same agency subsequently rates. Credit rating agencies thus could have incentives to rate issues advantageously. Given the economic importance of this issue, in this paper we have proposed to analyze this phenomenon, known as rating shopping in academic literature, for Spanish market securitization issues for the period of time comprehensive from January 1993 to December 2011. In sum 3,665 published ratings are been analysed, for an issued nominal amount of 791,090 million Euros. The results show an association between the credit rating agency contracted and the mean rating awarded. Significant differences are observed in the ratings associated to the contracting manager (or special purpose vehicle SPV- manager firm), to the number of ratings or to the type of collateral. Furthermore, a pattern compatible with rating shopping was observed for some types of collateral: abnormally high market shares associated with certain agencies awarding unusually generous ratings. However, this phenomenon is not seen to be widespread on the rating market associated to Spanish securitization issues.

A working guide to the assessment, implementation and post project monitoring of fisheries habitat improvement schemes in South Cumbria

Due to changes in land use over the last century, the physical nature of many streams and rivers in the British Isles has probably changed. In some cases this change may be large for example as a result of flood defence schemes and is easily observed, whilst in other cases altered land use, farming, forestry or urbanization may have resulted in more subtle changes to river features. This working guide draws together a way of assessing habitat in any stream or river and determine sites or reaches on the assessed watercourse that may benefit from habitat improvement schemes. It will determine a method of measuring existing habitat in a broad sense, whilst referring to R and D studies currently being undertaken in this area. A method of prioritising any proposed habitat restoration work will be suggested. The limitations of fisheries improvement schemes in terms of cross functional acceptance (flood defence and conservation) will be examined along with suggested proposals for some example watercourses. The need for pre and post enhancement monitoring will be discussed as will the requirement for maintenance programs on schemes. Finally methods for determining the cost benefits of small schemes will be examined, compared to other currently used enhancement strategies. This will allow small scale revenue schemes to be used to back up pre project cost benefit analysis as required in future capital submissions.

Building TRACE (translations censored) theatre corpus: some methodological questions on text selection

Editores:Micaela Muñoz-Calvo; Carmen Buesa-Gómez

River Wyre salmon and sea trout spawning habitat restoration / creation project. Gravel enhancement schemes.

As part of an overall desire to maintain and improve the migratory salmonid population in the River Wyre, a project was commissioned to investigate remedial action which may improve and enhance spawning success and lead to an eventual improvement in the status of adult stocks. The report, titled "River Wyre Salmon and Sea Trout Spawning Habitat Restoration/Creation Project", concluded that usable spawning gravels appeared to be in short supply in the River Wyre catchment and may be the limiting factor influencing the returning adult stock, as juvenile nursery habitat was not found to be limiting. This report looks at gravel enhancement schemes to improve River Wyre salmon and sea trout spawning habitat restoration. It examines methods for gravel enhancement schemes: mechanical cleaning and construction of gravel addition structures. Includes sites figures of sites identified for enhancement.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

Sportsmanship rating scale in tennis competition with young players

World Conference on Psychology and Sociology 2012