Optimal Control of Heterogeneous Systems

Цветомир Цачев - В настоящия доклад се прави преглед на някои резултати от областта на оптималното управление на непрекъснатите хетерогенни системи, публикувани в периодичната научна литература в последните години. Една динамична система се нарича хетерогенна, ако всеки от нейните елементи има собствена динамиката. Тук разглеждаме оптимално управление на системи, чиято хетерогенност се описва с едномерен или двумерен параметър – на всяка стойност на параметъра отговаря съответен елемент на системата. Хетерогенните динамични системи се използват за моделиране на процеси в икономиката, епидемиологията, биологията, опазване на обществената сигурност (ограничаване на използването на наркотици) и др. Тук разглеждаме модел на оптимално инвестиране в образование на макроикономическо ниво [11], на ограничаване на последствията от разпространението на СПИН [9], на пазар на права за въглеродни емисии [3, 4] и на оптимален макроикономически растеж при повишаване на нивото на върховите технологии [1]. Ключови думи: оптимално управление, непрекъснати хетерогенни динамични системи, приложения в икономиката и епидемиолегията

Inverse four-wave mixing and self-parametric amplification in optical fibre

An important group of nonlinear processes in optical fibre involve the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and those arising from self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect—self-parametric amplification—which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. Self-parametric amplification and the observed stable nonlinear spectral propagation with a random temporal waveform can find applications in optical communications and high-power fibre lasers with nonlinear intracavity dynamics.

Polarization dynamics of bound state solitons in a carbon nanotubes mode locked erbium doped fiber laser

Optical solitons are important in the modern photonics. Passively mode locked erbium doped fiber lasers provide a neat platform to study soliton dynamics. Soliton interaction dynamics is important for various applications and has quite different manifestations, including e.g. such as bound state solitons [1], soliton rains [2]. Soliton interactions have been observed with different mode locking approaches such as figure-of-eight [3] and nonlinear polarization rotation [4]. Carbon nanotubes (CNT) have recently been widely applied as an efficient saturable absorber for passively mode locked fiber lasers. We have recently studied the polarization dynamics in a CNT mode locked vector soliton erbium doped fiber laser [5]. So far, the polarization dynamics of bound state solitons have yet to be investigated. In this report, we present a wide range of polarization dynamics of bound state solitons generated in a CNT mode locked erbium doped fiber laser. The fiber laser consists of ∼ 2 m highly doped erbium fiber (Liekki Er80-8/125) as the gain medium, an optical isolator to ensure unidirectional oscillation anda 980 nm laser diode is used to pump the gain through the 1550/980 nm wavelength division multiplexer. A fused 10:90 coupler is used to couple 10 % of the light out of the laser cavity and two in-line polarization controllers (NewPort) are used to control the birefringence of the cavity and polarization of the pump light respectively. The total cavity length is ∼ 7.8 m indicating a 25.7 MHz fundamental repetition rate. © 2013 IEEE.

Real-time high-resolution heterodyne-based measurements of spectral dynamics in fibre lasers

Conventional tools for measurement of laser spectra (e.g. optical spectrum analysers) capture data averaged over a considerable time period. However, the generation spectrum of many laser types may involve spectral dynamics whose relatively fast time scale is determined by their cavity round trip period, calling for instrumentation featuring both high temporal and spectral resolution. Such real-time spectral characterisation becomes particularly challenging if the laser pulses are long, or they have continuous or quasi-continuous wave radiation components. Here we combine optical heterodyning with a technique of spatiooral intensity measurements that allows the characterisation of such complex sources. Fast, round-trip-resolved spectral dynamics of cavity-based systems in real-time are obtained, with temporal resolution of one cavity round trip and frequency resolution defined by its inverse (85 ns and 24 MHz respectively are demonstrated). We also show how under certain conditions for quasi-continuous wave sources, the spectral resolution could be further increased by a factor of 100 by direct extraction of phase information from the heterodyned dynamics or by using double time scales within the spectrogram approach.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

The commercial bark harvest of the African cherry (Prunus africana) on Mount Oku, Cameroon: Effects on traditional uses and population dynamics

Bark extracts of the African cherry (Prunus africana) are used to treat benign prostatic hyperplasia. This study examined the effects of commercial bark harvest on population dynamics in the Kilum-Ijim Forest Preserve on Mount Oku, Cameroon and on traditional uses. P. africana is valued for its timber and as fuel although its greatest value is as a traditional medicine for human and animal ailments. Harvest has depleted the resource and has eroded traditional forest protection practices. I constructed matrix models to examine the effects of bark harvest on population structure and on population dynamics in harvested and unharvested populations. Harvesting simulations examined the effect on the population growth rate (λ) with differing levels of mortality of harvest-sized and large trees and differing harvest frequencies. Size class frequencies for the entire forest decreased in a reverse j-shaped curve, indicating adequate recruitment in the absence of harvest. Individual plots showed differences from the overall forest data, suggesting effects of natural and man-made perturbations, particularly due to bark harvest. One plot (harvested in the 1980s) showed a temporal difference in λ and fluctuated around one, due to alternating high and low fruiting years; other unharvested plots showed smaller temporal differences. Harvested plots (harvested illegally in 1997) had values of λ less than one and showed small temporal differences. The control plot also showed λ less than one, due to poor recruitment in the closed canopy forest. The value of λ for the combined data was 0.9931 suggesting a slightly declining population. The elasticity matrix for the combined data indicated the population growth rate was most sensitive to the survival of the large reproductive trees (42.5% of the elasticity). In perturbation analyses, reducing the survival of the large trees caused the largest reductions in λ. Simulations involving harvesting frequency indicated λ returns to pre-harvest conditions if trees are re-harvested after 10–15 years, but only if the large trees are left unharvested. Management scenarios suggest harvest can be sustainable if seedlings and small saplings are planted in the forest and actively managed, although large-scale plantations may be the only feasible option to meet market demand. ^

Ecological genetics of Melaleuca quinquenervia (Myrtaceae): Population variation in Florida and its influence on performance of the biological control agent Oxyops vitiosa (Coleoptera: Curculionidae)

Melaleuca quinquenervia (Cav.) Blake (Myrtaceae) was imported into Florida from Australia over a century ago as a landscape plant. A favorable climate and periodic wildfires helped M. quinquenervia thrive; it now occupies about 200,000 hectares in southern Florida. A biological control (i.e., biocontrol) program against M. quinquenervia has been initiated, but not all biocontrol releases are successful. Some scientists have argued that poor biocontrol agent success may relate to genetic differences among populations of invasive weeds. I tested this premise by determining (1) the number and origins of M. quinquenervia introductions into Florida, (2) whether multiple introduction events resulted in the partitioning of Florida's M. quinquenervia populations into discrete biotypes, and (3) whether Oxyops vitiosa, an Australia snout beetle imported to control this weed, might discriminate among putative M. quinquenervia biotypes. Careful scrutiny of early horticultural catalogs and USDA plant introduction records suggested at least six distinct introduction events. Allozyme analyses indicated that the pattern of these introductions, and the subsequent redistribution of progeny, has resulted in geographic structuring of the populations in southern Florida. For example, trees on Florida's Gulf Coast had a greater effective number of alleles and exhibited greater heterozygosity than trees on the Atlantic Coast. Essential oil yields from M. quinquenervia leaves followed a similar trend; Gulf Coast trees yielded nearly twice as much oil as Atlantic Coast trees when both were grown in a common garden. These differences were partially explained by the predominance of a chemical phenotype (chemotype) very rich in the sesquiterpene (E)-nerolidol in M. quinquenervia trees from the Gulf Coast, but rich in a mixture of the monoterpene 1,8-cineole and the sesquiterpene viridiflorol in trees from the Atlantic Coast. Performance of O. vitiosa differed dramatically in laboratory studies depending on the chemotype of the foliage they were fed. Larval survivorship was four-fold greater on the (E)-nerolidol chemotype. Growth was also greater, with adult O. vitiosa gaining nearly 50% more biomass on the (E)-nerolidol plants than on the second chemotype. The results of this study thus confirmed the premise that plant genotype can affect the population dynamics of insects released as weed biocontrols. ^

Local biomass control on the composition and reactivity of particulate organic matter in aquatic environments

Freshwater ecosystems have been recognized as important components of the global carbon cycle, and the flux of organic matter (OM) from freshwater to marine environments can significantly affect estuarine and coastal productivity. The focus of this study was the assessment of carbon dynamics in two aquatic environments, namely the Florida Everglades and small prairie streams in Kansas, with the aim of characterizing the biogeochemistry of OM. In the Everglades, particulate OM (POM) is mostly found as a layer of flocculent material (floc). While floc is believed to be the main energy source driving trophic dynamics in this oligotrophic wetland, not much is known about its biogeochemistry. The objective of this study was to determine the origin/sources of OM in floc using biomarkers and pigment-based chemotaxonomy to assess specific biomass contributions to this material, on a spatial (freshwater marshes vs. mangrove fringe) and seasonal (wet vs. dry) scales. It was found that floc OM is derived from the local vegetation (mainly algal components and macrophyte litter) and its composition is controlled by seasonal drivers of hydrology and local biomass productivity. Photo-reactivity experiments showed that light exposure on floc resulted in photo-dissolution of POC with the generation of significant amounts of both dissolved OM (DOM) and nutrients (N & P), potentially influencing nutrient dynamics in this ecosystem. The bio-reactivity experiments determined as the amount and rate of CO2 evolution during incubation were found to vary on seasonal and spatial scales and were highly influenced by phosphorus limitation. Not much is known on OM dynamics in small headwater streams. The objective of this study was to determine carbon dynamics in sediments from intermittent prairie streams, characterized by different vegetation cover for their watershed (C4 grasses) vs. riparian zone (C3 plants). In this study sedimentary OM was characterized using a biomarker and compound specific carbon stable isotope approach. It was found that the biomarker composition of these sediments is dominated by higher plant inputs from the riparian zone, although inputs from adjacent prairie grasses were also apparent. Conflicting to some extent with the River Continuum Concept, sediments of the upper reaches contained more degraded OM, while the lower reaches were enriched in fresh material deriving from higher plants and plankton sources as a result of hydrological regimes and particle sorting.

Hydrological Conditions Control P Loading and Aquatic Metabolism in an Oligotrophic, Subtropical Estuary

Using high-resolution measures of aquatic ecosystem metabolism and water quality, we investigated the importance of hydrological inputs of phosphorus (P) on ecosystem dynamics in the oligotrophic, P-limited coastal Everglades. Due to low nutrient status and relatively large inputs of terrestrial organic matter, we hypothesized that the ponds in this region would be strongly net heterotrophic and that pond gross primary production (GPP) and respiration (R) would be the greatest during the “dry,” euhaline estuarine season that coincides with increased P availability. Results indicated that metabolism rates were consistently associated with elevated upstream total phosphorus and salinity concentrations. Pulses in aquatic metabolism rates were coupled to the timing of P supply from groundwater upwelling as well as a potential suite of hydrobiogeochemical interactions. We provide evidence that freshwater discharge has observable impacts on aquatic ecosystem function in the oligotrophic estuaries of the Florida Everglades by controlling the availability of P to the ecosystem. Future water management decisions in South Florida must include the impact of changes in water delivery on downstream estuaries.

Regional processes in mangrove ecosystems: spatial scaling relationships, biomass, and turnover rates following catastrophic disturbance

Physiological processes and local-scale structural dynamics of mangroves are relatively well studied. Regional-scale processes, however, are not as well understood. Here we provide long-term data on trends in structure and forest turnover at a large scale, following hurricane damage in mangrove ecosystems of South Florida, U.S.A. Twelve mangrove vegetation plots were monitored at periodic intervals, between October 1992 and March 2005. Mangrove forests of this region are defined by a −1.5 scaling relationship between mean stem diameter and stem density, mirroring self-thinning theory for mono-specific stands. This relationship is reflected in tree size frequency scaling exponents which, through time, have exhibited trends toward a community average that is indicative of full spatial resource utilization. These trends, together with an asymptotic standing biomass accumulation, indicate that coastal mangrove ecosystems do adhere to size-structured organizing principles as described for upland tree communities. Regenerative dynamics are different between areas inside and outside of the primary wind-path of Hurricane Andrew which occurred in 1992. Forest dynamic turnover rates, however, are steady through time. This suggests that ecological, more-so than structural factors, control forest productivity. In agreement, the relative mean rate of biomass growth exhibits an inverse relationship with the seasonal range of porewater salinities. The ecosystem average in forest scaling relationships may provide a useful investigative tool of mangrove community biomass relationships, as well as offer a robust indicator of general ecosystem health for use in mangrove forest ecosystem management and restoration.

Top down control in a relatively pristine seagrass ecosystem

The loss of large-bodied herbivores and/or top predators has been associated with large-scale changes in terrestrial, freshwater, and marine ecosystems around the world. Understanding the consequences of these declines has been hampered by a lack of studies in relatively pristine systems. To fill this gap, I investigated the dynamics of the relatively pristine seagrass ecosystem of Shark Bay, Australia. I began by examining the seagrass species distributions, stoichiometry, and patterns of nutrient limitation across the whole of Shark Bay. Large areas were N-limited, P-limited, or limited by factors other than nutrients. Phosphorus-limitation was centered in areas of restricted water exchange with the ocean. Nutrient content of seagrasses varied seasonally, but the strength of seasonal responses were species-specific. Using a cafeteria-style experiment, I found that fast-growing seagrass species, which had higher nutrient content experienced higher rates of herbivory than slow-growing species that are dominant in the bay but have low nutrient content. Although removal rates correlated well with nutrient content at a broad scale, within fast-growing species removal rates were not closely tied to N or P content. Using a combination of stable isotope analysis and animal borne video, I found that green turtles (Chelonia mydas)—one of the most abundant large-bodied herbivores in Shark Bay—appear to assimilate little energy from seagrasses at the population level. There was, however, evidence of individual specialization in turtle diets with some individuals foraging largely on seagrasses and others feeding primarily on macroalgae and gelatinous macroplankton. Finally, I used exclusion cages, to examine whether predation-sensitive habitat shifts by megagrazers (green turtles, dugongs) transmitted a behavior-mediated trophic cascade (BMTC) between sharks and seagrasses. In general, data were consistent with predictions of a behavior-mediated trophic cascade. Megaherbivore impacts on seagrasses were large only in the microhabitat where megaherbivores congregate to reduce predation risk. My study highlights the importance of large herbivores in structuring seagrass communities and, more generally, suggests that roving top predators likely are important in structuring communities—and possibly ecosystems—through non-consumptive pathways.

Three essays on market depth in futures markets

Liquidity is an important market characteristic for participants in every financial market. One of the three components of liquidity is market depth. Prior literature lacks a comprehensive analysis of depth in U.S. futures markets due to past limitations on the availability of data. However, recent innovations in data collection and dissemination provide new opportunities to investigate the depth dimension of liquidity. In this dissertation, the Chicago Mercantile Exchange (CME) Group proprietary database on depth is employed to study the dynamics of depth in the U.S. futures markets. This database allows for the analysis of depth along the entire limit order book rather than just at the first level. The first essay examines the characteristics of depth within the context of the five-deep limit order book. Results show that a large amount of depth is present in the book beyond the best level. Furthermore, the findings show that the characteristics of five-deep depth between day and night trading vary and that depth is unequal across levels within the limit order book. The second essay examines the link between the five-deep market depth and the bid-ask spread. The results suggest an inverse relation between the spread and the depth after adjusting for control factors. The third essay explores transitory volatility in relation to depth in the limit order book. Evidence supports the relation between an increase in volatility and a subsequent decrease in market depth. Overall, the results of this dissertation are consistent with limit order traders actively managing depth along the limit order book in electronic U.S. futures markets.

Application of biomarkers and compound specific stable isotopes for the assessment of hydrology as a driver of organic matter dynamics in the Everglades ecosystem

The Everglades is a sub-tropical coastal wetland characterized among others by its hydrological features and deposits of peat. Formation and preservation of organic matter in soils and sediments in this wetland ecosystem is critical for its sustainability and hydrological processes are important divers in the origin, transport and fate of organic matter. With this in mind, organic matter dynamics in the greater Florida Everglades was studied though various organic geochemistry techniques, especially biomarkers, bulk and compound specific δ13C and δD isotope analysis. The main objectives were focused on how different hydrological regimes in this ecosystem control organic matter dynamics, such as the mobilization of particulate organic matter (POM) in freshwater marshes and estuaries, and how organic geochemistry techniques can be applied to reconstruct Everglades paleo-hydrology. For this purpose organic matter in typical vegetation, floc, surface soils, soil cores, and estuarine suspended particulates were characterized in samples selected along hydrological gradients in the Water Conservation Area 3, Shark River Slough and Taylor Slough. ^ This research focused on three general themes: (1) Assessment of the environmental dynamics and source-specific particulate organic carbon export in a mangrove-dominated estuary. (2) Assessment of the origin, transport and fate of organic matter in freshwater marsh. (3) Assessment of historical changes in hydrological conditions in the Everglades (paleo-hydrology) though biomarkes and compound specific isotope analyses. This study reports the first estimate of particulate organic carbon loss from mangrove ecosystems in the Everglades, provides evidence for particulate organic matter transport with regards to the formation of ridge and slough landscapes in the Everglades, and demonstrates the applicability of the combined biomarker and compound-specific stable isotope approach as a means to generate paleohydrological data in wetlands. The data suggests that: (1) Carbon loss from mangrove estuaries is roughly split 50/50 between dissolved and particulate carbon; (2) hydrological remobilization of particulate organic matter from slough to ridge environments may play an important role in the maintenance of the Everglades freshwater landscape; and (3) Historical changes in hydrology have resulted in significant vegetation shifts from historical slough type vegetation to present ridge type vegetation. ^

Self-tuning algorithm for dsp-based motion control in cnc applications

This thesis describes the development of an adaptive control algorithm for Computerized Numerical Control (CNC) machines implemented in a multi-axis motion control board based on the TMS320C31 DSP chip. The adaptive process involves two stages: Plant Modeling and Inverse Control Application. The first stage builds a non-recursive model of the CNC system (plant) using the Least-Mean-Square (LMS) algorithm. The second stage consists of the definition of a recursive structure (the controller) that implements an inverse model of the plant by using the coefficients of the model in an algorithm called Forward-Time Calculation (FTC). In this way, when the inverse controller is implemented in series with the plant, it will pre-compensate for the modification that the original plant introduces in the input signal. The performance of this solution was verified at three different levels: Software simulation, implementation in a set of isolated motor-encoder pairs and implementation in a real CNC machine. The use of the adaptive inverse controller effectively improved the step response of the system in all three levels. In the simulation, an ideal response was obtained. In the motor-encoder test, the rise time was reduced by as much as 80%, without overshoot, in some cases. Even with the larger mass of the actual CNC machine, decrease of the rise time and elimination of the overshoot were obtained in most cases. These results lead to the conclusion that the adaptive inverse controller is a viable approach to position control in CNC machinery.

Fuzzy Modeling and Control Based Virtual Machine Resource Management

Virtual machines (VMs) are powerful platforms for building agile datacenters and emerging cloud systems. However, resource management for a VM-based system is still a challenging task. First, the complexity of application workloads as well as the interference among competing workloads makes it difficult to understand their VMs’ resource demands for meeting their Quality of Service (QoS) targets; Second, the dynamics in the applications and system makes it also difficult to maintain the desired QoS target while the environment changes; Third, the transparency of virtualization presents a hurdle for guest-layer application and host-layer VM scheduler to cooperate and improve application QoS and system efficiency. This dissertation proposes to address the above challenges through fuzzy modeling and control theory based VM resource management. First, a fuzzy-logic-based nonlinear modeling approach is proposed to accurately capture a VM’s complex demands of multiple types of resources automatically online based on the observed workload and resource usages. Second, to enable fast adaption for resource management, the fuzzy modeling approach is integrated with a predictive-control-based controller to form a new Fuzzy Modeling Predictive Control (FMPC) approach which can quickly track the applications’ QoS targets and optimize the resource allocations under dynamic changes in the system. Finally, to address the limitations of black-box-based resource management solutions, a cross-layer optimization approach is proposed to enable cooperation between a VM’s host and guest layers and further improve the application QoS and resource usage efficiency. The above proposed approaches are prototyped and evaluated on a Xen-based virtualized system and evaluated with representative benchmarks including TPC-H, RUBiS, and TerraFly. The results demonstrate that the fuzzy-modeling-based approach improves the accuracy in resource prediction by up to 31.4% compared to conventional regression approaches. The FMPC approach substantially outperforms the traditional linear-model-based predictive control approach in meeting application QoS targets for an oversubscribed system. It is able to manage dynamic VM resource allocations and migrations for over 100 concurrent VMs across multiple hosts with good efficiency. Finally, the cross-layer optimization approach further improves the performance of a virtualized application by up to 40% when the resources are contended by dynamic workloads.