<p>In this work we examine a state constrained resource allocation model a with finite time horizon. Therefore, we use the necessary conditions of the Pontrjagin's Maximum Principle to find candidates for the solution and verify them later on using the sufficient conditions given by the duality concept of Klötzler. Moreover, we proof that the solution of the corresponding infinite horizon model does not fulfill the overtaking criterion of Weizsäcker.</p>

In this work we examine a state constrained resource allocation model a with finite time horizon. Therefore, we use the necessary conditions of the Pontrjagin's Maximum Principle to find candidates for the solution and verify them later on using the sufficient conditions given by the duality concept of Klötzler. Moreover, we proof that the solution of the corresponding infinite horizon model does not fulfill the overtaking criterion of Weizsäcker.

This work provides first and second-order expressions to approximate neighboring solutions to the m-point boundary value problem. Multi-point problems arise in optimal control because of interior constraints or switching dynamics. Many problems have this form, and so this work fills a void in the study of extremal fields and neighboring optimal control of constrained systems. Only first and second-order terms are written down, but the approach is systematic and higher order expressions can be found similarly. The constraints and their parameters define an extremal field because any solution to the problem must satisfy the constraints. The approach is to build a Taylor series using constraint differentials, state differentials, and state variations. The differential is key to these developments, and it is a unifying element in the optimization of points, optimal control, and neighboring optimal control. The method is demonstrated on several types of problems including lunar descent, which has nonlinear dynamics, bounded thrust, and free final time. The control structure is bang-off-bang, and the method successfully approximates the unknown initial conditions, switch times, and final time. Compared to indirect shooting, computation time decreases by about three orders of magnitude.

This thesis investigates the optimal use of intervention strategies to mitigate the spread of infectious diseases. Three main problems are addressed: (i) The optimal use vaccination and isolation resources under the assumption that these resources are limited. Specifically we address the problem of minimizing the outbreak size and we determine the optimal vaccination-only, isolation-only and mixed vaccination-isolation strategies. (ii) The optimal use of a single antiviral drug to minimize the total outbreak size, under the assumption that treatment causes de novo resistance. (iii) The optimal use of two antiviral drugs to minimize the total infectious burden. Specifically we address the situation where there are two different strains and each strain is effectively treated by only one drug. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2011-01-25 19:59:17.263

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität zu Bonn, 1984. / Includes bibliographical references (p. 189-194).

No description available.

The aim of this thesis is to present a structural model for a wind turbine and its supporting pylon, to analyze and simulate attendant vibration phenomena and to suggest and simulate an appropriate control procedure. A wind turbine can be described as an elastic system consisting of distributed parameter, beam and rod type, elements coupled to a rotating lumped mass generator/turbine component at one end. We allow for both lateral and torsional movements of the beam. Solution methods for related vibration and control problems are suggested and analyzed. Results of computations for sample problems are presented. Applications of control of structural vibrations in wind energy units using proof mass type actuators as part of the tip mass are also analyzed. / Master of Science

The following is an exploration into the optimal guidance and control of gun-launched guided projectiles. Unlike their early counterparts, modern-day gun-launched projectiles are capable of considerable accuracy. This ability is enabled through the use of control surfaces, such as fins or wings, which allow the projectile to maneuver towards a target. These aerodynamic features are part of a control system which lets the projectile achieve some effect at the target. With the advent of very high velocity guns, such as the Navy's electromagnetic railgun, these systems are a necessary part of the projectile design. This research focuses on a control scheme that uses the projectile's angle of attack as the single control in the development of an optimal control methodology that maximizes impact velocity, which is directly related to the amount of damage in icted on the target. This novel approach, which utilizes a reference trajectory as a seed for an iterative optimization scheme, results in an optimal control history for a projectile. The investigation is geared towards examining how poor an approximation of the true optimal solution that reference trajectory can be and still lead to the determination of an optimal control history. Several different types of trajectories are examined for their applicability as a reference trajectory. Although the use of aerodynamic control surfaces enables control of the projectile, there is a potential down side. With steady development of guns with longer ranges and higher launch velocities, it becomes increasingly likely that a projectile will y into a region of the atmosphere (and beyond) in which there is not sufficient air ow over the control surfaces to maintain projectile control. This research is extended to include a minimum dynamic pressure constraint in the problem; the imposition of such a constraint is not examined in the literature. Several methods of adding the constraint are discussed and a number of cases with varying dynamic pressure limits are evaluated. As a result of this research, a robust methodology exists to quickly obtain an optimal control history, with or without constraints, based on a rough reference trajectory as input. This methodology finds its applicability not only for gun-launched weapons, but also for missiles and hypersonic vehicles. / Doctor of Philosophy / As the name implies, optimal control problems involve determining a control history for a system that optimizes some aspect of the system's behavior. In aerospace applications, optimal control problems often involve finding a control history that minimizes time of ight, uses the least amount of fuel, maximizes final velocity, or meets some constraint imposed by the designer or user. For very simple problems, this optimal control history can be analytically derived; for more practical problems, such as the ones considered here, numerical methods are required to determine a solution. This research focuses on the optimal control problem of a gun-launched guided projectile. Guided projectiles have the potential to be significantly more accurate than their unguided counterparts; this improvement is achieved through the use of a control mechanism. For this research, the projectile is modeled using a single control approach, namely using the angle of attack as the only control for the projectile. The angle of attack is the angle formed between the direction the projectile is pointing and the direction it is moving (i.e., between the main body axis and the velocity vector of the projectile). An approach is then developed to determine an optimal angle of attack history that maximizes the projectile's final impact velocity. While this problem has been extensively examined by other researchers, the current approach results in the analytical determination of the costate estimates that eliminates the need to iterate on their solutions. Subsequently, a minimum dynamic pressure constraint is added to the problem. While extensive investigation has been conducted in the examination of a maximum dynamic pressure constraint for aerospace applications, the imposition of a minimum represents a novel body of work. For an aerodynamically controlled projectile, (i.e., one controlled with movable surfaces that interact with the air stream), dropping below a minimum dynamic pressure may result in loss of sufficient control. As such, developing a control history that accommodates this constraint and prevents the loss of aerodynamic control is critical to the ongoing development of very long range, gun-launched guided projectiles. This new methodology is applied with the minimum dynamic pressure constraint imposed and the resulting optimal control histories are then examined. In addition, the possibility of implementing other constraints is also discussed.

A new software tool was needed for flight planning of a high altitude, low speed unmanned aerial vehicle which would be flying in winds close to the actual airspeed of the vehicle. An energy modeled NLP formulation was used to obtain results for a variety of missions and wind profiles. The energy constraint derived included terms due to the wind field and the performance index was a weighted combination of the amount of fuel used and the final time. With no emphasis on time and with no winds the vehicle was found to fly at maximum lift to drag velocity, V_md. When flying in tail winds the velocity was less than V_md, while flying in head winds the velocity was higher than Vmd. A family of solutions was found with varying times of flight and varying fuel amounts consumed which will aid the operator in choosing a flight plan depending on a desired landing time. At certain parts of the flight, the turning terms in the energy constraint equation were found to be significant. An analysis of a simpler vertical plane cruise optimal control problem was used to explain some of the characteristics of the vertical plane NLP results. / Master of Science

Demonstrating strength and agility on virtual and real humanoids has been an important goal in computer graphics and robotics. However, developing physics- based controllers for various agile motor skills requires a tremendous amount of prior knowledge and manual labor due to complex mechanisms of the motor skills. The focus of the dissertation is to develop a set of computational tools to expedite the design process of physics-based controllers that can execute a variety of agile motor skills on virtual and real humanoids. Instead of designing directly controllers real humanoids, this dissertation takes an approach that develops appropriate theories and models in virtual simulation and systematically transfers the solutions to hardware systems. The algorithms and frameworks in this dissertation span various topics from spe- cific physics-based controllers to general learning frameworks. We first present an online algorithm for controlling falling and landing motions of virtual characters. The proposed algorithm is effective and efficient enough to generate falling motions for a wide range of arbitrary initial conditions in real-time. Next, we present a robust falling strategy for real humanoids that can manage a wide range of perturbations by planning the optimal contact sequences. We then introduce an iterative learning framework to easily design various agile motions, which is inspired by human learn- ing techniques. The proposed framework is followed by novel algorithms to efficiently optimize control parameters for the target tasks, especially when they have many constraints or parameterized goals. Finally, we introduce an iterative approach for exporting simulation-optimized control policies to hardware of robots to reduce the number of hardware experiments, that accompany expensive costs and labors.