In this thesis we investigate how the properties of chordal graphs can be used to exploit sparsity in several optimisation problems that arise in control theory. In particular, we focus on analysis and synthesis problems that involve semidefinite constraints and can be formulated as semidefinite programming (SDP) problems. Using a relationship between chordal graphs and sparse semidefinite matrices, we decompose the semidefinite constraints in the associated SDP problems into multiple, smaller semidefinite constraints along with some additional equality constraints. The benefit of this approach is that for sparse dynamical systems we can solve significantly larger analysis and synthesis problems than is possible using traditional dense methods. We begin by considering the properties of chordal graphs and their connection to sparse positive semidefinite matrices. We then turn our attention to the problem of constructing Lyapunov functions for linear time-invariant (LTI) systems. From this starting point, we derive methods of exploiting chordal sparsity in other analysis problems found in control theory. In particular, this approach is applied to the problem of bounding the input-output properties of systems via the KYP lemma for both continuous and discrete-time systems. We then consider how the properties of chordal graphs can be exploited in the SDPs that arise in static state feedback controller synthesis problems for LTI systems. We show that the sparse inverse property of the maximum determinant completion of a partial positive matrix can be used to design controllers with a pre-specified sparsity pattern. We then consider how to exploit chordal sparsity when designing a static state feedback controller to minimise the H-infinity norm of an LTI system. Next we shift from linear systems to nonlinear systems and develop a chordal sparsity approach to scalable stability analysis of systems with polynomial dynamics using the Sums of Squares (SOS) technique. We develop a method of exploiting chordal sparsity that avoids the computationally costly step of forming the coefficient matrix in the SOS problem. We then apply this method to the problem of constructing Lyapunov functions for systems with correlatively sparse polynomial vector fields. Finally, we conclude by discussing some directions for future research.

Groundwater contamination is a very serious problem as it leads to the depletion of water resources. Seawater intrusion is a special category of groundwater contamination that threatens the health and possibly lives of many people living in coastal areas. The focus of this work is to develop a numerical model to study seawater intrusion and its effects on groundwater quality and develop a control method to effectively control seawater intrusion. Two major approaches are used in this study: the first approach is the development of a finite element model to simulate seawater intrusion; the second is the development of a simulation-optimization model to study the control of seawater intrusion in coastal aquifers using different management scenarios. The simulation-optimization model is based on the integration of a genetic algorithm optimization technique with the transient density-dependent finite element model developed in this research. The finite element model considers the coupled flow of air and water and solute transport in saturated and unsaturated soils. The governing differential equations include two mass balance equations of water and air phases and the energy balance equation for heat transfer, together with a balance equation for miscible solute transport. The nonlinear governing differential equations are solved using the finite element method in the space domain and a finite difference scheme in the time domain. A two dimensional finite element model is developed to solve the governing equations and provide values of solute concentration, pore water pressure, pore air pressure and temperature at different points within the region at different times. The mathematical formulation and numerical implementation of the model are presented. The numerical model is validated by application to standard examples from literature followed by application to a number of case studies involving seawater intrusion problems. The results show good agreement with previous results reported in the literature. The model is then used to predict seawater intrusion for a number of real world case studies. The developed model is capable of predicting, with a good accuracy, the intrusion of seawater in coastal aquifers. In the second approach, a simulation-optimization model is developed to study the control of seawater intrusion using three management scenarios: abstraction of brackish water, recharge of fresh water and combination of abstraction and recharge. The objectives of these management scenarios include minimizing the total costs for construction and operation, minimizing salt concentrations in the aquifer and determining the optimal depths, locations and abstraction/recharge rates for the wells. Also, a new methodology is presented to control seawater intrusion in coastal aquifers. In the proposed methodology ADR (abstraction, desalination and recharge), seawater intrusion is controlled by abstracting brackish water, desalinating it using a small scale reverse osmosis plant and recharging to the aquifer. The simulation-optimization model is applied to a number of case studies. The efficiencies of three different scenarios are examined and compared. Results show that all the three scenarios could be effective in controlling seawater intrusion. However, ADR methodology can result in the lowest cost and salt concentration in aquifers and maximum movement of the transition zone towards the sea. The results also show that for the case studies considered in this work, the amount of abstracted and treated water is about three times the amount required for recharge; therefore the remaining treated water can be used directly for different proposes. The application of ADR methodology is shown to be more efficient and more practical, since it is a cost-effective method to control seawater intrusion in coastal aquifers. This technology can be used for sustainable development of water resources in coastal areas where it provides a new source of treated water. The developed method is regard as an effective tool to control seawater intrusion in coastal aquifers and can be applied in areas where there is a risk of seawater intrusion. Finally, the developed FE model is applied to study the effects of likely climate change and sea level rise on seawater intrusion in coastal aquifers. The results show that the developed model is capable of predicting the movement of the transition zone considering the effects of sea level rise and over-abstraction. The results also indicate that the change of water level in the sea side has a significant effect on the position of the transition zone especially if the effect of sea level rise is combined with the effect of increasing abstraction from the aquifer.

Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Tsiotras, Panagiotis; Committee Member: Calise, Anthony J.; Committee Member: Egerstedt, Magnus; Committee Member: Prasad, J. V. R.; Committee Member: Russell, Ryan P.; Committee Member: Zhou, Hao-Min.

Energy saving and fuel consumption reduction techniques are among the principal interests for both academic institutions and industries, in particular, system optimization and hybridization. This paper presents a new hydraulic hybrid system layout for mobile machinery implemented on a middle size excavator. The hybridization procedure took advantage of a dynamic programming (DP) algorithm, which was also utilized for the hybrid components dimensioning and control strategy definition. A dedicated experimental activity on test bench was performed on the main components of the energy recovery system (ERS). The JCMAS working cycle was considered as the reference test for a fuel consumption comparison between the standard and the hybrid excavator. A fuel saving up to 8% on the JCMAS cycle, and up to 11% during the digging cycle, has been allowed by the proposed hybrid system.

Les approches physico-chimiques étant insuffisantes pour évaluer l'impact de la pollution sur les écosystèmes , de nombreux bioessais, variant de par le niveau d'organisation représenté, ont été développés. Parmi ces essais on trouve les essais en microcosme aquatique de laboratoire qui sont un compromis entre les essais monospécifiques standards de laboratoire, méthodes couramment employées mais très simplifiées et peu représentatives sur le plan écologique et les essais en mésocosme extérieurs, plus représentatifs mais coûteux, lourds à mettre en œuvre, moins réplicables et plus difficiles à interpréter. Dans ce travail, nous nous sommes plus particulièrement intéressés à l'essai initialement développé par Clément et Cadier (1998). Cet outil permet d'évaluer l'effet de substances ou de matrices potentiellement contaminées sur un écosystème artificiel composé d'eau et de sédiment, dans lesquels sont introduites simultanément 5 espèces aquatiques d'eau douce usuellement employées dans des essais de toxicité mono-spécifiques : l'algue Pseudokirchneriella subcapitata, la lentille d'eau Lemna minor, la daphnie Daphnia magna, l'amphipode Hyalella azteca et l'insecte Chironomus riparius. Cet essai en microcosme a été utilisé dans de nombreux projets depuis sa conception mais sa variabilité demeurait la principale limite malgré les améliorations successives. Le principal objectif de ce travail était donc d'optimiser l'essai. La principale amélioration testée a été le renouvellement continu de l'eau du système, qui a permis de stabiliser les paramètres physico-chimiques de la colonne d'eau des microcosmes et la densité algale, et ainsi d'améliorer le développement des organismes et la réplicabilité de l'essai. Le cadmium a été utilisé comme contaminant modèle afin d'évaluer les développements méthodologiques proposés. La diminution de la variabilité en présence de renouvellement d'eau augmente la capacité à détecter des effets sublétaux sur les organismes pélagiques avec les tests statistiques classiques. Le développement d'un cadre de modélisation dynamique a permis de comparer la sensibilité des daphnies au cadmium dans des expériences aux profils d'exposition différents. / The physico-chemical approaches are insufficient to assess the impact of pollution on ecosystems. Thus many bioassays, varying in the level of organization represented, have been developed, as laboratory aquatic microcosm tests. These tests are a compromise between single-species tests, which are standard laboratory methods commonly used but highly simplified and not very ecologically representative, and outdoor mesocosm tests, which are more representative but more expensive, heavy to implement, less replicable and more difficult to interpret. In this work, we focused on the bioassay originally developed by Clément and Cadier (1998). This tool allows to evaluate the effect of substances or potentially contaminated matrices on an artificial ecosystem consisting of water and sediment in which are introduced simultaneously five freshwater aquatic species commonly used in monospecific toxicity testing : the algea Pseudokirchneriella subcapitata, the duckweed Lemna minor, the daphnia Daphnia magna, the amphipod Hyalella azteca and the insect Chironomus riparius. This test was used in many projects since its conception but its variability remains the main limitation despite successive improvements. The main objective of this study was to optimize the test. The main improvement was continuous renewal of the water system, which helped to stabilize the physico-chemical parameters of the water column and algal density, and thus improve the development of organisms and replicability of the test. Cadmium was used as a model contaminant to evaluate the proposed methodological developments. The decrease in variability in flowthrough microcosms increases the ability to detect sublethal effects on pelagic organisms with conventional statistical tests. The development of a dynamic modeling framework was used to compare the sensitivity of Daphnia to cadmium in experiments with different exposure pattern.