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The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale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

Understanding Micro- and Macro-Mechanics of Soil Liquefaction: A Necessary Step for Field-Scale Assessment

Liquefaction is a devastating instability associated with saturated, loose, and cohesionless soils. It poses a significant risk to distributed infrastructure systems that are vital for the security, economy, safety, health, and welfare of societies. In order to make our cities resilient to the effects of liquefaction, it is important to be able to identify areas that are most susceptible. Some of the prevalent methodologies employed to identify susceptible areas include conventional slope stability analysis and the use of so-called liquefaction charts. However, these methodologies have some limitations, which motivate our research objectives. In this dissertation, we investigate the mechanics of origin of liquefaction in a laboratory test using grain-scale simulations, which helps (i) understand why certain soils liquefy under certain conditions, and (ii) identify a necessary precursor for onset of flow liquefaction. Furthermore, we investigate the mechanics of liquefaction charts using a continuum plasticity model; this can help in modeling the surface hazards of liquefaction following an earthquake. Finally, we also investigate the microscopic definition of soil shear wave velocity, a soil property that is used as an index to quantify liquefaction resistance of soil. We show that anisotropy in fabric, or grain arrangement can be correlated with anisotropy in shear wave velocity. This has the potential to quantify the effects of sample disturbance when a soil specimen is extracted from the field. In conclusion, by developing a more fundamental understanding of soil liquefaction, this dissertation takes necessary steps for a more physical assessment of liquefaction susceptibility at the field-scale.

Electronic properties of graphene grain boundaries

Grain boundaries and defect lines in graphene are intensively studied for their novel electronic and magnetic properties. However, there is not a complete comprehension of the appearance of localized states along these defects. Graphene grain boundaries are herein seen as the outcome of matching two semi-infinite graphene sheets with different edges. We classify the energy spectra of grain boundaries into three different types, directly related to the combination of the four basic classes of spectra of graphene edges. From the specific geometry of the grains, we are able to obtain the band structure and the number of localized states close to the Fermi energy. This provides a new understanding of states localized at grain boundaries, showing that they are derived from the edge states of graphene. Such knowledge is crucial for the ultimate tailoring of electronic and optoelectronic applications.

The juvenile salmonid populations of the River Lune catchment, 1981 to 1985

The aim of this study was to assess the status of the juvenile salmonid populations of the River Lune and its tributaries. There was special emphasis on juvenile salmon stocks in view of the implementation of a net limitation order in 1980. The number of licensed instruments were reduced as follows: (1) Drift, hang or whammel nets - from 12 to 10 (2) Draft or seine nets - from 3 to 1 (3) Heave or haaf nets - from 4 6 to 2 6 For the purpose of this report, the River Lune system has been divided into 13 subcatchments and these are examined with a view to detecting any trends in the data such as subcatchment productivity, partitioning between salmon and trout nursery streams, and whether the restrictions on salmon fishing had any discernible effects on juvenile salmon productivity. The effect of flow and instream obstructions on salmonid densities are also investigated as these have been shown to be important factors affecting abundance. Throughout the study period a programme of enhancement stocking took place primarily with salmon ova and fry. The possible impact of this on the results of the surveys has been assessed. The distribution and abundance of juvenile salmon was found to be relatively consistent in each of the 13 subcatchments studied over the 1981-1985 period.

A survey of river habitats on the River Lune

A survey of the River Lune using River Habitat Survey (RHS) was carried out at 103 sections in February/March 99, to which were added 37 sites surveyed between 1994 -1996. Summary statistics were produced on the distribution and extent of flow features (e.g. riffles, pools, rapids etc.), substrate types, tree and associated features and bank profiles. Information on land-use and management was also included in the analyses. A Habitat Modification Score (HMS) describing the level of habitat modification was derived for each site and compared to the whole reference network and to rivers of similar types in Britain. The HMS shows that more than 70% of the sites on the catchment are predominantly unmodified and very few sites are significantly modified. Highly modified sites are concentrated in the urban areas and on the tributaries.

Report on the analysis of salmon scale samples returned by anglers on the Rivers Ribble and Hodder

Fisheries technical staff from the North West Central Area of the National Rivers Authority (NRA) currently provide a service for the ageing of salmon scales from fish caught by anglers on the Rivers Ribble and Hodder in order to gather information on the biological characteristics of the salmon population on the River Ribble system in terms of weight, freshwater age and sea age. At the beginning of each fishing season, scale envelopes are distributed by the NRA to angling clubs and some individual anglers. Scales taken from salmon caught on the rivers are returned to the NRA Central Area Office by the anglers, or more often, by NRA bailiffs. The age of each fish caught is then determined by the identification and counting of annuli for both the river and sea zones on the scale. Information is provided by the angler on the scale packet concerning the length and weight of the fish caught, and the date, location and method of capture. Both this information and the age of the fish is recorded on a database. These data can be used to investigate the distribution, and exploitation patterns of the different age classes of the salmon stock within the river system. This report is principally concerned with the scale samples received in 1994, although comparison is also made with samples from 1993 and 1992. References to data will all relate to that received in 1994 unless an alternate year is stated.

River Lune processes. A study of change in the River Lune catchment and recommendations for flood defence management

There has been a perception of increasing river channel instability in north west rivers and the River Lune in particular in recent decades. This has been attributed variously to: (a) long-term trends in precipitation-runoff regime; (b) changes in land-use such as moor-draining and sub-soil draining such that the river is more flashy than previously, and (c) a change in the magnitude-frequency relationships of flow such that high discharges are occurring with increased frequency. Resources are available in the form of rainfall and runoff records, archived information on channel planform, land use statistics and local engineering experience which have not been jointly and fully evaluated. Effective interpretation of the nature of channel change through time with respect to this resource may enhance the Environment Agency's ability to manage the river channel efficiently in the future and will aid the development of effective policy. The results of this study will for the first time, provide robust guidance with respect to long-term channel adjustment and the appropriate management options. The research provides suggestions as to how policy might be developed taking account of other pertinent factors.

An analysis of salmon rod catch data from castle fisheries, River Derwent, 1923-1989.

The aim of this study was to investigate the historical catch record from the Castle Fishery on the River Derwent over the period 1923 - 1989, to determine if changes had taken place in the composition of the catch and to examine the influence of flow on the performance of the fishery. The River Derwent is situated in West Cumbria, North West England. It flows from its source on Scafell Pike (NGR NY 229 089) westwards discharging into the Irish sea at Workington, a distance of 52 km. Over its length it receives water from an additional 214 km of stream, 5 large lakes and approximately 30 small tarns. The catchment drains a total area of 663 km2. The study concludes that through the time period there was considerable variation in catch between years. The trend was for the catch to increase steadily over the period 1923 - 1958, declining rapidly in 1959, after which catches increased steadily reaching a peak in the mid-sixties, before declining towards the end of the decade. During the seventies and eighties catches remained relatively stable at between 300 - 600 salmon per year until 1988 when over 2000 salmon were reported caught, the greatest number in any year over the study period.

Computational study of the vortex path variation with the VG height

An extensive range of conventional, vane-type, passive vortex generators (VGs) are in use for successful applications of flow separation control. In most cases, the VG height is designed with the same thickness as the local boundary layer at the VG position. However, in some applications, these conventional VGs may produce excess residual drag. The so-called low-profile VGs can reduce the parasitic drag associated to this kind of passive control devices. As suggested by many authors, low-profile VGs can provide enough momentum transfer over a region several times their own height for effective flow-separation control with much lower drag. The main objective of this work is to study the variation of the path and the development of the primary vortex generated by a rectangular VG mounted on a flat plate with five different device heights h = delta, h(1) = 0.8 delta, h(2) = 0.6 delta, h(3) = 0.4 delta and h(4) = 0.2 delta, where delta is the local boundary layer thickness. For this purpose, computational simulations have been carried out at Reynolds number Re = 1350 based on the height of the conventional VG h = 0.25m with the angle of attack of the vane to the oncoming flow beta = 18.5 degrees. The results show that the VG scaling significantly affects the vortex trajectory and the peak vorticity generated by the primary vortex.

Otolith morphometrics and population structure of Pacific sardine (Sardinops sagax) along the west coast of North America

The broad distribution of Pacific sardine (Sardinops sagax) along the Pacif ic coast of North America makes it difficult for fisheries managers to identify regional stocks of this dominant small pelagic species. An investigation of morphometric characteristics of otoliths of Pacific sardine across most of their range revealed regional differences in populations. In a survey of over 2000 otoliths, all ages (with an emphasis on age-1 recruits) were compared. Principal components analysis, multivariate analysis of variance, and a novel method derived from regression and residuals calculations, termed perimeter-weight profiles (PWPs), revealed otolith similarities and differences. The results of the different approaches to statistical comparisons did not always agree. Sardine otoliths from Mexican waters were generally lighter and more lobate than those from U.S. and Canadian populations. Age-1 otoliths from northern California in 2006–07 tended to be heavier and smoother than those from other areas, including year-class cohorts from southern California. Comparisons of age-groups and year-classes of northern California otoliths with the use of the PWP models indicated signif icant trends in year-to-year patterns. In conjunction with other established indices of population structure, otolith PWPs are a useful tool for identifying local and regional stocks of Pacific sardine and may help distinguish populations of other fish species as well.

Variation in movement patterns of red drum (Sciaenops ocellatus) inferred from conventional tagging and ultrasonic telemetry

We used 25 years of conventional tagging data (n= 6173 recoveries) and 3 years of ultrasonic telemetry data (n=105 transmitters deployed) to examine movement rates and directional preferences of four age classes of red drum (Sciaenops ocellatus) in estuarine and coastal waters of North Carolina. Movement rates of conventionally tagged red drum were dependent on the age, region, and season of tagging. Age-1 and age-2 red drum tagged along the coast generally moved along the coast, whereas fish tagged in oligohaline waters far from the coast were primarily recovered in coastal regions in fall months. Adult (age-4+) red drum moved from overwintering grounds on the continental shelf through inlets into Pamlico Sound in spring and summer months and departed in fall. Few tagged red drum were recovered in adjacent states (0.6% of all recoveries); however, some adult red drum migrated seasonally from overwintering grounds in coastal North Carolina northward to Virginia in spring, returning in fall. Age-2 transmitter-tracked red drum displayed seasonal emigration from a small tributary, but upstream and downstream movements within the tributary were correlated with fluctuating salinity regimes and not season. Large-scale conventional tagging and ultrasonic telemetry programs can provide valuable insights into the complex movement patterns of estuarine fish.

Abundance, condition, and diet of juvenile Pacific ocean perch (Sebastes alutus) in the Aleutian Islands

T he relative value of pelagic habitat for three size classes of juvenile Pacific ocean perch (Sebastes alutus) was investigated by comparing their abundance and condition in two areas of the Aleutian Islands. Diet, zooplankton biomass, and water column temperatures were examined as potential factors affecting observed differences. Juvenile Pacific ocean perch abundance and condition, and zooplankton biomass varied significantly between areas, whereas juvenile Pacific ocean perch diet varied only by size class. Observed differences in fish condition may have been due to the quantity or quality of pelagic prey items consumed. For the delineation of essential demersal fish habitat, important ecological features of the pelagic habitat must therefore be considered.

Degeneration of postovulatory follicles in the Iberian sardine Sardina pilchardus: structural changes and factors affecting resorption

Inaccuracy in the aging of postovulatory follicles (POFs) and in estimating the effect of temperature on the resorption rate of POFs may introduce bias in the determination of the daily spawning age classes with the daily egg production method (DEPM). To explore the above two bias problems with f ield-collected European pilchard (Sardina pilchardus, known regionally as the Iberian sardine), a method was developed in which the time elapsed from spawning (POF age) was estimated from the size of POFs (i.e., from the cross-sectional area in histological sections). The potential effect of the preservative type and embedding material on POF size and the effect of ambient water temperature on POF resorption rate are taken into account with this method. A highly significant loglinear relationship was found between POF area and age; POF area shrank by approximately 50% per day. POFs were also shown to shrink faster at higher temperatures (approximately 3% per degree), but this temperature effect is unlikely to be an important source of bias in the assignment of females to daily spawning classes. The embedding material was also shown to influence the size of POFs, the latter being significantly larger in resin than in paraffin sections. In conclusion, the size of POFs provides an indirect, reliable estimation of the time elapsed from spawning and may thus be used to test both the validity of POF staging criteria for identifying daily classes of spawners and the effect of other factors (such as temperature and laboratory processing) in applications of the DEPM to S. pilchardus and other fish species.

Estimating consumption rates of juvenile sandbar sharks (Carcharhinus plumbeus) in Chesapeake Bay, Virginia, using a bioenergetics model*

Using a bioenergetics model, we estimated daily ration and seasonal prey consumption rates for six age classes of juvenile sandbar sharks (Carcharhinus plumbeus) in the lower Chesapeake Bay summer nursery area. The model, incorporating habitat and species-specific data on growth rates, metabolic rate, diet composition, water temperature (range 16.8−27.9°C), and population structure, predicted mean daily rations between 2.17 ±0.03 (age-0) and 1.30 ±0.02 (age-5) % body mass/day. These daily rations are higher than earlier predictions for sandbar sharks but are comparable to those for ecologically similar shark species. The total nursery population of sandbar sharks was predicted to consume ~124,000 kg of prey during their 4.5 month stay in the Chesapeake Bay nursery. The predicted consumption rates support the conclusion that juvenile sandbar sharks exert a lesser top-down effect on the Chesapeake Bay ecosystem than do teleost piscivores and hu