Distributed optimal control problems with transient convection dominated diffusion convection reaction equations are considered. The problem is discretized in space by using three types of discontinuous Galerkin (DG) method: symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), incomplete interior penalty Galerkin (IIPG). For time discretization, Crank-Nicolson and backward Euler methods are used. The discretize-then-optimize approach is used to obtain the finite dimensional problem. For one-dimensional unconstrained problem, Newton-Conjugate Gradient method with Armijo line-search. For two-dimensional control constrained problem, active-set method is applied. A priori error estimates are derived for full discretized optimal control problem. Numerical results for one and two-dimensional distributed optimal control problems for diffusion convection equations with boundary layers confirm the predicted orders derived by a priori error estimates.

Many real-life applications such as the shape optimization of technological devices, the identification of parameters in environmental processes and flow control problems lead to optimization problems governed by systems of convection diusion partial dierential equations (PDEs). When convection dominates diusion, the solutions of these PDEs typically exhibit layers on small regions where the solution has large gradients. Hence, it requires special numerical techniques, which take into account the structure of the convection. The integration of discretization and optimization is important for the overall eciency of the solution process. Discontinuous Galerkin (DG) methods became recently as an alternative to the finite dierence, finite volume and continuous finite element methods for solving wave dominated problems like convection diusion equations since they possess higher accuracy. This thesis will focus on analysis and application of DG methods for linear-quadratic convection dominated optimal control problems. Because of the inconsistencies of the standard stabilized methods such as streamline upwind Petrov Galerkin (SUPG) on convection diusion optimal control problems, the discretize-then-optimize and the optimize-then-discretize do not commute. However, the upwind symmetric interior penalty Galerkin (SIPG) method leads to the same discrete optimality systems. The other DG methods such as nonsymmetric interior penalty Galerkin (NIPG) and incomplete interior penalty Galerkin (IIPG) method also yield the same discrete optimality systems when penalization constant is taken large enough. We will study a posteriori error estimates of the upwind SIPG method for the distributed unconstrained and control constrained optimal control problems. In convection dominated optimal control problems with boundary and/or interior layers, the oscillations are propagated downwind and upwind direction in the interior domain, due the opposite sign of convection terms in state and adjoint equations. Hence, we will use residual based a posteriori error estimators to reduce these oscillations around the boundary and/or interior layers. Finally, theoretical analysis will be confirmed by several numerical examples with and without control constraints

This thesis presents a technique termed Blended Shared Control, whereby a human operator's commands are merged with the commands of an electronic agent in real time to control a manipulator. A four degree-of-freedom hydraulic excavator is used as an application example, and two types of models are presented: a fully dynamic model incorporating the actuator and linkage systems suitable for high-fidelity user studies, and a reduced-order velocity-constrained kinematic model amenable for real-time optimization. Intended operator tasks are estimated with a recursive algorithm; the task is optimized in real time; and a command perturbation is computed which, when summed with the operator command, results in a lower task completion time. Experimental results compare Blended Shared Control to other types of controllers including manual control and haptic feedback. Trials indicate that Blended Shared Control decreases task completion time when compared to manual operation.

The objective of this dissertation is to provide a framework for constructing a transitional behavior, connecting any two trajectories from a set with a particular characteristic, in such a way that the transition is as inconspicuous as possible. By this we mean that the connection is such that the characteristic behavior persists during the transition. These special classes include stationary solutions, limit cycles etc. We call this framework the Gluskabi raccordation. This problem is motivated from physical applications where it is often desired to steer a system from one stationary solution or periodic orbit to another in a ̒smooth̕ way. Examples include motion control in robotics, chemical process control and quasi-stationary processes in thermodynamics, etc. Before discussing the Gluskabi raccordations of periodic behaviors, we first study several periodic phenomena. Specifically, we study the self- propulsion of a number of legless, toy creatures based on differential friction under periodic excitations. This friction model is based on viscous friction which is predominant in a wet environment. We investigate the effects of periodic and optimal periodic control on locomotion. Subsequently, we consider a control problem of a stochastic system, under the basic constraint that the feedback control signal and the observations from the system cannot use the communication channel simultaneously. Hence, two modes of operation result: an observation mode and a control mode. We seek an optimal periodic regime in a statistical steady state by switching between the observation and the control mode. For this, the duty cycle and the optimal gains for the controller and observer in either mode are determined. We then investigate the simplest special case of the Gluskabi raccordation, namely the quasi-stationary optimal control problem. This forces us to revisit the classical terminal controller. We analyze the performance index as the control horizon increases to infinity. This problem gives a good example where the limiting operation and integration do not commute. Such a misinterpretation can lead to an apparent paradox. We use symmetrical components (the parity operator) to shed light on the correct solution. The main part of thesis is the Gluskabi raccordation problem. We first use several simple examples to introduce the general framework. We then consider the signal Gluskabi raccordation or the Gluskabi raccordation without a dynamical system. Specifically, we present the quasi-periodic raccordation where we seek the maximally ̒smooth̕ transitions between two periodic signals. We provide two methods, the direct and indirect method, to construct these transitions. Detailed algorithms for generating the raccordations based on the direct method are also provided. Next, we extend the signal Gluskabi raccordation to the dynamic case by considering the dynamical system as a hard constraint. The behavioral modeling of dynamical system pioneered by Willems provides the right language for this generalization. All algorithms of the signal Gluskabi raccordation are extended accordingly to produce these ̒smooth̕ transition behaviors.

Bei der Kristallzüchtung insbesondere von Halbleitern hat die Form des freien Randes (dem Interface zwischen fester und flüssiger Phase) einen starken Einfluss auf die Qualität des Kristalls. Die Dissertation befasst sich mit der Optimalsteuerung der Form und des Verlaufs des freien Randes. Als Vorlage für die in der Arbeit betrachteten Modellkonfigurationen dient das VGF-Verfahren (Vertical Gradient Freeze). Der Erstarrungsprozess wird durch ein Zweiphasen-Stefan-Problem mit durch Konvektion und Lorentzkräfte getriebener Strömung beschrieben. Der freie Rand wird als Graph formuliert. Das Kontrollziel besteht in der Ansteuerung eines gewünschten Verlaufs des freien Randes. Als Kontrollgrößen dient die Temperatur auf der Wand des Schmelztiegels und/oder wandnahe oder verteilte Lorentzkräfte. Das Kontrollziel wird durch Minimierung eines geeigneten Kosten-Funktionals erreicht. Das daraus resultierende Minimierungsproblem wird mit einem Adjungierten-Ansatz gelöst. Anhand numerischer Experimente mit Aluminium und Gallium-Arsenid Schmelzen wird gezeigt, das das vorgestellte Verfahren gut funktioniert.

Waterflooding is a common type of oil recovery techniques where water is pumped into the reservoir for increased productivity. Reservoir states change with time, as such, different injection and production settings will be required to lead the process to optimal operation which is actually a dynamic optimization problem. This could be solved through optimal control techniques which traditionally can only provide an open-loop solution. However, this solution is not appropriate for reservoir production due to numerous uncertain properties involved. Models that are updated through the current industrial practice of ‘history matching’ may fail to predict reality correctly and therefore, solutions based on history-matched models may be suboptimal or non-optimal at all. Due to its ability in counteracting the effects uncertainties, direct feedback control has been proposed recently for optimal waterflooding operations. In this work, two feedback approaches were developed for waterflooding process optimization. The first approach is based on the principle of receding horizon control (RHC) while the second is a new dynamic optimization method developed from the technique of self-optimizing control (SOC). For the SOC methodology, appropriate controlled variables (CVs) as combinations of measurement histories and manipulated variables are first derived through regression based on simulation data obtained from a nominal model. Then the optimal feedback control law was represented as a linear function of measurement histories from the CVs obtained. Based on simulation studies, the RHC approach was found to be very sensitive to uncertainties when the nominal model differed significantly from the conceived real reservoir. The SOC methodology on the other hand, was shown to achieve an operational profit with only 2% worse than the true optimal control, but 30% better than the open-loop optimal control under the same uncertainties. The simplicity of the developed SOC approach coupled with its robustness to handle uncertainties proved its potentials to real industrial applications.

Liquid desiccant air conditioning (LDAC) has received much attention in recent years. This is mainly because LDAC systems are able to control latent loads in a more energy efficient way than conventional air conditioning systems. Although many research studies have been conducted on LDAC technologies, the following gaps in the scientific literature are addressed in this thesis: (1) carryover of desiccant droplets in air streams, (2) direct comparisons between different configurations of LDAC systems, (3) fundamentals of capacity matching in heat-pump LDAC systems, (4) optimal-control strategies for heat-pump LDAC systems, and (5) importance of transients in evaluating the performance of a LDAC system. Items (1) to (4) are addressed using TRNSYS simulations, and item (5) is addressed using data collected from a field test. The use of liquid-to-air membrane energy exchangers (LAMEEs) as dehumidifiers and regenerators in LDAC systems eliminate the desiccant droplets carryover problem in air streams. This is because LAMEE separate the air and solution streams using semi-permeable membranes, which allow the transfer of heat and moisture but do not allow the transfer of the liquid desiccant. A preliminary configuration for a membrane LDAC system, which uses LAMEEs as the dehumidifier and regenerator, is proposed and investigated under fixed operating conditions in this thesis. The influences of key design and operating parameters on the heat and mass transfer performances of the membrane LDAC system are evaluated. Results show that the membrane LDAC technology is able to effectively remove latent loads in applications that the humidity to be controlled. A comprehensive evaluation is conducted in this thesis for the thermal, economic and environmental performances of several configurations of membrane LDAC systems. The solution cooling load is covered using a cooling heat pump in all systems studied, while the solution heating load is covered using one of the following five different heating systems: (1) a gas boiler, (2) a heating heat pump, (3) a solar thermal system with gas boiler backup, (4) a solar thermal system with heat pump backup, and (5) the condenser of the solution cooling heating pump. Each of the membrane LDAC systems studied is evaluated with/without an energy recovery ventilator (ERV) installed in the air handling system. The influence of operating the ERV under balanced/unbalanced operating conditions is studied. It is found that the most economic membrane LDAC system is the one which uses the evaporator and condenser of the same heat pump to cover the solution cooling and heating loads, respectively (i.e. heat-pump membrane LDAC system). No clear guidance was found in the literature for sizing the evaporator and condenser in a heat-pump LDAC system to simultaneously meet the solution cooling and heating loads. When the heating and cooling provided by the heat pump exactly match the heating and cooling requirements of the solution, the system is “capacity matched”. A parametric study is conducted on a heat-pump membrane LDAC system to identify the influence of key operating and design parameters on achieving capacity matching. It is concluded that the solution inlet temperatures to the dehumidifier and regenerator are the most influential parameters on the moisture removal rate, capacity matching and coefficient of performance (COP). Three control strategies are developed for heat-pump membrane LDAC systems, where these strategies meet the latent loads and achieve one of the following three objectives: (1) meet the sensible loads, (2) achieve capacity matching, or (3) optimize the COP. Results show that the COP of a heat-pump LDAC system can be doubled by selecting the right combination of solution inlet temperatures to the regenerator and dehumidifier. The importance of transients in evaluating the performance of a LDAC system is addressed in the thesis using a data collected from a field test on a solar LDAC system. It is found that the sensible, latent and total cooling energy, and the total primary energy consumption of the LDAC system are changed by less than 10% during an entire test day when transients are considered. Thus, it can be concluded that steady-state models are reliable to evaluate the energy performances of LDAC systems.

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This thesis addresses flight control of the perch landing maneuver for micro-aerial vehicles. A longitudinal flight model is constructed for a pigeon-sized aircraft. In addition to a standard elevator control surface, wing-rotation also considered as a non-standard actuator for increasing low-speed aerodynamic braking. Optimal state and control trajectories for the perch landing maneuver are computed using commercial software. A neighboring optimal control law is then developed and implemented in a set of flight simulations. Simulations are run with both a quasisteady and an unsteady aerodynamic model. The effectiveness of wing rotation and of the neighboring optimal control law is discussed, as is the importance of unsteady aerodynamics during the maneuver. Wing rotation was found to be minimally effective in this case, but it showed potential to be more effective in further research. The unsteady aerodynamic model has significant influence over the success or failure of the maneuver.

This thesis addresses optimal control problems with elasticity for large deformations. A hyperelastic model with a polyconvex energy density is employed to describe the elastic behavior of a body. The two approaches to derive the nonlinear partial differential equation, a balance of forces and an energy minimization, are compared. Besides the conventional volume and boundary loads, two novel internal loads are presented. Furthermore, curvilinear coordinates and a hierarchical plate model can be incorporated into the formulation of the elastic forward problem. The forward problem can be solved with Newton\\\'s method, though a globalization technique should be used to avoid divergence of Newton\\\'s method. The repeated solution of the Newton system is done by a CG or MinRes method with a multigrid V-cycle as a preconditioner. The optimal control problem consists of the displacement (as the state) and a load (as the control). Besides the standard tracking-type objective, alternative objective functionals are presented for problems where a reasonable desired state cannot be provided. Two methods are proposed to solve the optimal control problem: an all-at-once approach by a Lagrange-Newton method and a reduced formulation by a quasi-Newton method with an inverse limited-memory BFGS update. The algorithms for the solution of the forward problem and the optimal control problem are implemented in the finite-element software FEniCS, with the geometrical multigrid extension FMG. Numerical experiments are performed to demonstrate the mesh independence of the algorithms and both optimization methods.