<p> The abort mission refers to the mission where the landing vehicle needs to terminate the landing mission when an anomaly happens and be safely guided to the desired orbit. Missions involving crew on board demands for a robust and efficient abort strategy. This thesis focuses on solving the time-optimal abort guidance (TOAG) problem in real-time via the feature-based learning method. First, according to the optimal control theory, the features are identified to represent the optimal solutions of TOAG using a few parameters. After that, a sufficiently large dataset of time-optimal abort trajectories is generated offline by solving the TOAG problems with different initial conditions. Then the features are extracted for all generated cases. To find the implicit relationships between the initial conditions and identified features, neural networks are constructed to map the relationships based on the generated dataset. A successfully trained neural network can generate solution in real time for a reasonable initial condition. Finally, experimental flight tests are conducted to demonstrate the onboard computation capability and effectiveness of the proposed method. </p>

本文以最適控制理論證明，獎勵再生能源產出之政策，應以再生能源淨能源產出做為獎勵的基礎，而非現行以再生能源總能源產出做為獎勵基礎之模式。這裡的淨能源產出，指的是再生能源廠商生產出之再生能源，減去生產再生能源時所用的能源投入。本文首先將社會最適情況下的總能源產出分別與以淨能源產出和總能源產出為獎勵政策基礎之價格與數量政策下之總能源產出作比較，提出獎勵再生能源產出的政策，需以淨能源產出做為獎勵的基礎，而非現行以總能源產出作為基礎的政策，接著，在以淨能源產出為基礎的政策下，探討環境外部性與防治成本以及研究發展的議題。 / By the optimal control theory, this paper proves that policies on encouraging the production of renewable energy should be based on its net output or net energy instead of on its gross output or gross energy. Here net energy is defined as the surplus of renewable energy output minus energy input from its production. This paper first compares the optimal gross output of the renewable energy under the social optimal condition with the gross outputs under the price-based policy instrument and the quantity-based policy instrument based on net energy output and gross energy output, respectively, suggesting that policy instruments used to encourage the production of renewable energy should be based on its net output instead of on its gross output. Finally, it probes the cases of environmental externality and R&D based on the net output of renewable energy.

Este trabalho aborda um método de otimização dinâmica baseado em modelos bioeconômicos estabelecidos na teoria do controle ótimo, que visa modelar o resultado econômico-financeiro relacionado à atividade de extração dos recursos naturais, de modo que a otimização do resultado financeiro seja controlada por uma extração sustentável desse recurso. Mais especificamente, consideramos a exploração de madeira florestal restrita a uma série de vínculos econômicos e operacionais, bem como à dinâmica de crescimento natural da floresta. Avaliando o uso efetivo dessa metodologia aplicada ao planejamento das concessões florestais e procurando contribuir com o debate a respeito da viabilidade da forma de gestão florestal baseada em concessões florestais no Brasil. / This work addresses a dynamic optimization method based on bioeconomics models established in optimal control theory, which aims to model the economic-financial result related to the activity of extraction of natural resources, so that the optimization of the financial result is controlled by a sustainable extraction of this resources. More specifically, we consider the exploration of forest wood restricted to a series of economic and operational linkages, as well as the dynamics of natural forest growth. Assessing the effective use of this methodology applied to the planning of forest concessions and seeking to contribute to the debate about the viability of forest management form based on forest concessions in Brazil.

Este trabalho aborda um método de otimização dinâmica baseado em modelos bioeconômicos estabelecidos na teoria do controle ótimo, que visa modelar o resultado econômico-financeiro relacionado à atividade de extração dos recursos naturais, de modo que a otimização do resultado financeiro seja controlada por uma extração sustentável desse recurso. Mais especificamente, consideramos a exploração de madeira florestal restrita a uma série de vínculos econômicos e operacionais, bem como à dinâmica de crescimento natural da floresta. Avaliando o uso efetivo dessa metodologia aplicada ao planejamento das concessões florestais e procurando contribuir com o debate a respeito da viabilidade da forma de gestão florestal baseada em concessões florestais no Brasil. / This work addresses a dynamic optimization method based on bioeconomics models established in optimal control theory, which aims to model the economic-financial result related to the activity of extraction of natural resources, so that the optimization of the financial result is controlled by a sustainable extraction of this resources. More specifically, we consider the exploration of forest wood restricted to a series of economic and operational linkages, as well as the dynamics of natural forest growth. Assessing the effective use of this methodology applied to the planning of forest concessions and seeking to contribute to the debate about the viability of forest management form based on forest concessions in Brazil.

The selective infrared (IR) excitation of molecular vibrations is a powerful tool to control the photoreactivity prior to electronic excitation in the ultraviolet / visible (UV/Vis) light regime ("vibrationally mediated chemistry"). For adsorbates on surfaces it has been theoretically predicted that IR preexcitation will lead to higher UV/Vis photodesorption yields and larger cross sections for other photoreactions. In a recent experiment, IR-mediated desorption of molecular hydrogen from a Si(111) surface on which atomic hydrogen and deuterium were co-adsorbed was achieved, following a vibrational mechanism as indicated by the isotope-selectivity. In the present work, selective vibrational IR excitation of adsorbate molecules, treated as multi-dimensional oscillators on dissipative surfaces, has been simulated within the framework of open-system density matrix theory. Not only potential-mediated, inter-mode coupling poses an obstacle to selective excitation but also the coupling of the adsorbate ("system") modes to the electronic and phononic degrees of freedom of the surface ("bath") does. Vibrational relaxation thereby takes place, depending on the availabilty of energetically fitting electron-hole (e/h) pairs and/or phonons (lattice vibrations) in the surface, on time-scales ranging from milliseconds to several hundreds of femtoseconds. On metal surfaces, where the relaxation process of the adsorbate via the e/h pair mechanism dominates, vibrational lifetimes are usually shorter than on insulator or semiconductor surfaces, in the range of picoseconds, being also the timescale of the IR pulses used here. Further inhibiting factors for selectivity can be the harmonicity of a mode and weak dipole activities ("dark modes") rendering vibrational excitation with moderate field intensities difficult. In addition to simple analytical pulses, optimal control theory (OCT) has been employed here to generate a suitable electric field to populate the target state/mode maximally. The complex OCT fields were analyzed by Husimi transformation, resolving the control field in time and energy. The adsorbate/surface systems investigated were CO/Cu(100), H/Si(100) and 2H/Ru(0001). These systems proved to be suitable models to study the above mentioned effects. Further, effects of temperature, pure dephasing (elastic scattering processes), pulse duration and dimensionality (up to four degrees of freedom) were studied. It was possible to selectively excite single vibrational modes, often even state-selective. Special processes like hot-band excitation, vibrationally mediated desorption and the excitation of "dark modes" were simulated. Finally, a novel OCT algorithm in density matrix representation has been developed which allows for time-dependent target operators and thus enables to control the excitation mechanism instead of only the final state. The algorithm is based on a combination of global (iterative) and local (non-iterative) OCT schemes, such that short, globally controlled time-intervals are coupled locally in time. Its numerical performance and accuracy were tested and verified and it was successfully applied to stabilize a two-state linear-combination and to enforce a successive "ladder climbing" in a rather harmonic system, where monochromatic, analytical pulses simultaneously excited several states, leading to a population loss in the target state. / Die selektive Anregung von Molekülschwingungen mittels Infrarotlicht (IR) ist vorteilhaft, um die Wirkungsquerschnitte nachfolgender photochemischer oder photophysikalischer Prozesse zu steigern, welche durch Elektronenanregung mittels ultraviolettem (UV) bzw. sichtbarem (Vis) Licht ausgelöst werden. Für Adsorbatmoleküle auf Oberflächen wurden theoretische Vorhersagen getroffen, dass eine kombinierte (IR plus UV)-Strategie ("schwingungsvermittelte Chemie") die Ausbeute bei Photodesorption und anderen Photoreaktionen deutlich zu erhöhen vermag. Kürzlich wurde im Experiment gezeigt, dass eine rein IR-vermittelte Desorption möglich ist, welche über einen schwingungsangeregten Mechanismus erfolgt. Hierbei wurde molekularer Wasserstoff von einer Si(111)-Oberfläche desorbiert, an der atomarer Wasserstoff und atomares Deuterium gebunden waren. Eine thermische Anregung, die zum Bindungsbruch führt, konnte hierbei wegen der Isotopenselektivität ausgeschlossen werden. In der vorliegenden Arbeit wurde die selektive IR-Schwingungsanregung von Adsorbaten, die als multidimensionale Oszillatoren auf dissipativen Oberflächen behandelt wurden, mit Hilfe der Dichtematrixtheorie für offene Systeme simuliert. Nicht nur die potentialvermittelte Kopplung zwischen den einzelnen Moden ist ein Hindernis für selektive Anregung, sondern auch die Kopplung der Moden des Adsorbats ("Systems") an elektronische und phononische Freiheitsgrade des Substrats ("Bades"). Die Schwingungsrelaxation verläuft hierbei auf Zeitskalen, die von Millisekunden bis hin zu wenigen hundert Femtosekunden reichen, je nach Verfügbarkeit energetisch geeigneter Elektron-Loch-Paar-Anregungen bzw. Phononen (Gitterschwingungen) in der Oberfläche. Auf Metalloberflächen, bei denen die Schwingungrelaxation des Adsorbats zumeist von einem Elektronen-Loch-Paar-Mechanismus dominiert wird, sind die Schwingungslebensdauern normalerweise kürzer als auf Isolator- oder Halbleiteroberflächen und betragen einige Picosekunden, ebenso wie die Zeitskala der hier gewählten IR-Pulse. Weitere Faktoren, die die selektive Anregung behindern können sind die Harmonizität einer Mode und die geringe Dipolaktivität sogenannter "dunkler Moden", die eine Anregung mit moderat intensiven Feldern erschweren. Zusätzlich zu einfachen analytischen Pulsen wurden Felder mittels Optimaler Kontrolltheorie (OCT) erzeugt, um eine(n) Zielzustand/-mode maximal zu populieren. Komplexe OCT Pulse wurden mit Hilfe der Husimi-Transformation analysiert, welche das Kontrollfeld im Zeit- und Energieraum aufzulösen vermag. Die in dieser Arbeit untersuchten Adsorbat/Oberflächen-Systeme waren CO/Cu(100), H/Si(100) und 2H/Ru(0001), die sich als passende Modelle erwiesen, um oben genannte Faktoren zu untersuchen. Desweiteren wurden die Auswirkungen von Temperatur, reiner Dephasierung (elastische Streuprozesse), Dauer des IR-Pulses und Systemdimensionalit"at (Behandlung von bis zu vier Freiheitsgraden) studiert. Einzelne Schwingungsmoden konnten angeregt werden, in vielen Fällen sogar zustandsselektiv. Spezielle Prozesse wie die Anregung "heißer Banden", Desorption via alleiniger Schwingungsanregung und die Anregung "dunkler Moden" wurden simuliert. Schließlich wurde ein neuer OCT-Algorithmus in Dichtematrixdarstellung entwickelt, der es erlaubt, zeitabhängige Zieloperatoren einzuführen, um nicht nur Kontrolle über den Endzustand einer Anregung, sondern auch über den Anregungsmechanismus zu erlangen. Der Algorithmus basiert auf einer Kombination von globaler (iterativer) und lokaler (nicht-iterativer) optimaler Kontrollschemata in der Art, dass kurze, global kontrollierte Intervalle zeitlich lokal miteinander gekoppelt werden. Nach numerischen Tests wurde der Algorithmus erfolgreich angewandt, um eine Linearkombination aus zwei Zuständen zu stabilisieren, sowie um eine schrittweise "Leiteranregung" in einem harmonischen System zu forcieren, bei dem monochromatische, analytische Pulse mehrere Zustände zugleich anregen und somit einen Populationsverlust im angestrebten Zielzustand zur Folge haben.

The remarkable evolution of wireless networks into the next generation to provide ubiquitous and seamless broadband applications has recently triggered the emergence of Wireless Mesh Networks (WMNs). The WMNs comprise stationary Wireless Mesh Routers (WMRs) forming Wireless Backbone Mesh Networks (WBMNs) and mobile Wireless Mesh Clients (WMCs) forming the WMN access. While WMCs are limited in function and radio resources, the WMRs are expected to support heavy duty applications : that is, WMRs have gateway and bridge functions to integrate WMNs with other networks such as the Internet, cellular, IEEE 802.11, IEEE 802.15, IEEE 802.16, sensor networks, et cetera. Consequently, WMRs are constructed from fast switching radios or multiple radio devices operating on multiple frequency channels. WMRs are expected to be self-organized, self-configured and constitute a reliable and robust WBMN which needs to sustain high traffic volumes and long "online" time. However, meeting such stringent service expectations requires the development of decentralized dynamic transmission power control (DTPC) approaches. This thesis addresses the DTPC problem for both single and multiple channel WBMNs. For single channel networks, the problem is formulated as the minimization of both the link-centric and network-centric convex cost function. In order to solve this issue, multiple access transmission aware (MATA) models and algorithms are proposed. For multi-radio multi-channel (MRMC) WBMNs, the network is modelled as sets of unified channel graphs (UCGs), each consisting of interconnected active network users communicating on the same frequency channel. For each UCG set, the minimization of stochastic quadratic cost functions are developed subject to the dynamic Link State Information (LSI) equations from all UCGs. An energy-efficient multi-radio unification protocol (PMMUP) is then suggested at the Link-Layer (LL). Predictive estimation algorithms based on this protocol are proposed to solve such objective functions. To address transmission energy and packet instabilities, and interference across multiple channels, singularly-perturbed weakly-coupled (SPWC) control problems are formulated. In order to solve the SPWC transmission power control problem, a generalized higher-order recursive algorithm (HORA) that obtains the Riccati Stabilizing Solutions to the control problem is developed. The performance behaviours of the proposed models and algorithms are evaluated both analytically and through computer simulations. Several simulations are performed on a large number of randomly generated topologies. Simulation and analytical results confirm the efficacy of the proposed algorithms compared to the most recently studied techniques

In this thesis novel feedback attitude control algorithms and attitude estimation algorithms are developed for a three-axis stabilised spacecraft attitude control system. The spacecraft models considered include a rigid-body spacecraft equipped with (i) external control torque devices, and (ii) a redundant reaction wheel configuration. The attitude sensor suite comprises a three-axis magnetometer and three-axis rate gyroscope assembly. The quaternion parameters (also called Euler symmetric parameters), which globally avoid singularities but are subject to a unity-norm constraint, are selected as the primary attitude coordinates. There are four novel contributions presented in this thesis. The first novel contribution is the development of a robust control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix, actuator magnitude constraints, bounded persistent external disturbances, and state estimation error. The novel component of this algorithm is the incorporation of state estimation error into the stability analysis. The proposed control law contains a parameter which is dynamically adjusted to ensure global asymptotic stability of the overall closedloop system, in the presence of these specific system non-idealities. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The control design approach also ensures minimum angular path maneuvers, since the attitude quaternion parameters are not unique. The second novel contribution is the development of a robust direct adaptive control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix. The novel aspect of this algorithm is the incorporation of a composite parameter update strategy, which ensures global exponential convergence of the closed-loop system. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The exponential convergence results provided by this control strategy require persistently exciting reference trajectory commands. The control design approach also ensures minimum angular path maneuvers. The third novel contribution is the development of an optimal control strategy for spacecraft attitude maneuvers, based on a rigid body spacecraft model including a redundant reaction wheel assembly. The novel component of this strategy is the proposal of a performance index which represents the total electrical energy consumed by the reaction wheel over the maneuver interval. Pontraygin's minimum principle is applied to formulate the necessary conditions for optimality, in which the control torques are subject to timevarying magnitude constraints. The presence of singular sub-arcs in the statespace and their associated singular controls are investigated using Kelley's necessary condition. The two-point boundary-value problem (TPBVP) is formulated using Pontrayagin's minimum principle. The fourth novel contribution is an attitude estimation algorithm which estimates the spacecraft attitude parameters and sensor bias parameters from three-axis magnetometer and three-axis rate gyroscope measurement data. The novel aspect of this algorithm is the assumption that the state filtering probability density function (PDF) is Gaussian distributed. This Gaussian PDF assumption is also applied to the magnetometer measurement model. Propagation of the filtering PDF between sensor measurements is performed using the Fokker-Planck equation, and Bayes theorem incorporates measurement update information. The use of direction cosine matrix elements as the attitude coordinates avoids any singularity issues associated with the measurement update and estimation error covariance representation.

This work is motivated by several modern applications involving social networks, crowds, and markets. Our work focuses on the theme of designing effective incentive strategies for these applications. Viral marketing is receiving much attention by practicing marketers and researchers alike. While not a new idea, it has come to the forefront because of multiple effects – products have become more complex, making buyers to increasingly rely on opinions of their peers; consumers have evolved to distrust advertising; and Web2.0 has revolutionized the way people can connect, communicate and share. With power shifting to consumers, it has become important for companies to devise effective viral marketing strategies. Incentives are also a critical aspect of crowd sourcing tasks and play a crucial role in attracting, motivating and sustaining participation. The thesis addresses the following problems. (i) Optimal Control of Information Epidemics: We address two problems concerning information propagation in a population: a) how to maximize the spread of a given message in the population within the stipulated time and b) how to create a given level of buzz- measured by the fraction of the population engaged in conversation on a topic of interest- at a specified time horizon. (ii) Optimal Control Strategies for Social Influence (SI) Marketing: We investigate four SI strategies, namely, recommendation programs, referral programs, consumer reviews and campaigns on on-line forums. The campaign is assumed to be of finite duration, and the objective is to maximize profit, the (un-discounted) revenue minus the expenditure on the SI strategy under consideration, over the campaign duration. For each SI strategy, we focus on its timing, i.e., determining at what times to execute it. We address two important questions pertaining to them: a) how to execute a given SI strategy optimally? and b) having executed it so, what gains does it lead to? (iii) Optimal Mix of Incentive Strategies on Social Networks: The reach of a product in a pop- ulation can be influenced by offering (a) direct incentives to influence the buying behavior of potential buyers and (b) referral rewards to exploit the impact of social influence in inducing a purchasing decision. The company is interested in an optimal mix of these incentive programs. We report results on structure of optimal strategies for the company with significant practical implications. (iv) Truthful Tractable Mechanisms with Applications to Crowd sourcing: We focus on crowd- sourcing applications that involve specialized tasks for which the planner hardly has any idea about crowdworkers’ costs, for example, tagging geographical regions with air pollution levels or severity level of Ebola like disease. The mechanisms have to be robust to untruthful bidding from the crowdworkers. In our work, we propose tractable allocation algorithms that are monotone, leading to design of truthful mechanisms that can be successfully deployed in such applications.

Quantum optimal control theory is applied to find optimal pulses for controlling the motion of an ion and a molecule for two different applications. Those optimal pulses enable the control of the dynamics of the system by driving the atom or the molecule from an initial state to desired states.The evolution equations obtained by means of the quantum optimal control theory are resolved iteratively using a monotonic convergent algorithm. A number of simulation parameters are varied in order to get the optimal pulses including the duration of the pulses, the time step of the time grid, a penalty factor that limits the maximal intensity of the fields, and a guess pulse which is used to start the optimal control.The optimal pulses obtained for each application are analyzed by Fourier transform, and also by looking at the time evolution of the populations that they generate in the system.The first application is the preparation of specific vibrational states of acetylene that are usually not reachable from the ground state, and that would remain unpopulated by usual spectroscopy. Relevant state energies and transition dipole moments are extracted from the experimental literature and especially from the global acetylene Hamiltonian conferring an uncommon precision to the control simulation. The control starts from the ground state. The target states belongs to the polyad Ns=1, Nr=5 of acetylene which includes two vibrational dark states and one vibrational bright state. First, the simulation is performed with the Schrödinger equation and in a second step, with the Liouville--von Neumann equation, as mixed states are prepared. Indeed, the control starts from a Boltzmann distribution of population in the rotational levels of the vibrational ground state chosen in order to simulate an experimental condition. But the distribution is truncated to limit the computational effort. One of the dark states appears to be a potential target for a realistic experimental investigation because the average population of the Rabi oscillation remains high and decoherence is expected to be weak. The optimal pulses obtained have a high fidelity, have a spectrum with well-resolved peak frequencies, and their experimental feasibility seems achievable within the current abilities of experimental laboratories.The second application is to propose an experimental realization of a microscopic physical device able to simulate quantum dynamics. The idea is to use the motional states of a Cd^+ ion trapped in an anharmonic potential to realize a quantum dynamics simulator of a single-particle Schrödinger equation. In this way, the motional states store the information and the optimal pulse manipulates this information to realize operations. In the present case, the simulated dynamics was the propagation of a wave packet in a harmonic potential. Starting from an initial quantum state, the pulse acts on the system to modify the motional states of the ion in such a way that the final superposition of motional states corresponds to the results of the dynamics. This simulation is performed with the Liouville--von Neumann equation and also with the Lindblad equation as dissipation is included to test the robustness of the pulse against perturbations of the potential. The optimal pulses that are obtained have a high fidelity which shows that the ion trap system has correctly realized the quantum dynamics simulation. The optimal pulses are valid for any initial condition if the potential of the simulation or the mass of the propagated wave packet is unchanged. / La théorie du contrôle optimal quantique est utilisée pour trouver des impulsions optimales permettant de contrôler la dynamique d'un atome et d'une molécule les menant d'un état initial à un état final. Les équations d'évolution obtenues grâce au contrôle optimal limitent l'intensité maximale de l'impulsion et sont résolues itérativement grâce à l'algorithme de Zhu--Rabitz. Le contrôle optimal est utilisé pour réaliser deux objectifs. Le premier est la préparation d'états vibrationnels de l'acétylène qui sont généralement inaccessibles par transition au départ de l'état vibrationnel fondamental. Ces états, appelés états sombres, sont les états cibles de la simulation. Ils appartiennent à la polyade Ns=1, Nr=5 de l'acétylène qui en contient deux ainsi qu'un état, dit brillant, qui lui est accessible depuis l'état fondamental. Les énergies des états du système et les moments de transitions dipolaires sont déterminés à partir d'un Hamiltonien très précis qui confère une précision inhabituelle à la simulation. Un des états sombres apparaît être un candidat potentiel pour une réalisation expérimentale car la population moyenne de cet état reste élevée après l'application de l'impulsion.Les niveaux rotationnels des états vibrationnels sont également pris en compte.Les impulsions optimales obtenues ont une fidélité élevée et leur spectre en fréquence présente des pics résolus.Le deuxième objectif est de proposer la réalisation expérimentale d'un dispositif microscopique capable de simuler une dynamique quantique. Ce travail montre qu'on peut utiliser les états de mouvement d'un ion de Cd^+ piégé dans un potentiel anharmonique pour réaliser la propagation d'un paquet d'onde dans un potentiel harmonique. Ce dispositif stocke l'information de la dynamique simulée grâce aux états de mouvements et l'impulsion optimale manipule l'information pour réaliser les propagations. En effet, démarrant d'un état quantique initial, l'impulsion agit sur le système en modifiant les états de mouvements de l'ion de telle sorte que la superposition finale des états de mouvements corresponde aux résultats de la dynamique. De la dissipation est incluse pour tester la robustesse de l'impulsion face à des perturbations du potentiel anharmonique. Les impulsions optimales obtenues ont une fidélité élevée ce qui montre que le système a correctement réalisé la simulation de dynamique quantique. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

<p>Numerical trajectory optimization is helpful not only for mission planning but also design</p> <p>space exploration and quantifying vehicle performance. Direct methods for solving the opti-</p> <p>mal control problems, which first discretize the problem before applying necessary conditions</p> <p>of optimality, dominate the field of trajectory optimization because they are easier for the</p> <p>user to set up and are less reliant on a forming a good initial guess. On the other hand,</p> <p>many consider indirect methods, which apply the necessary conditions of optimality prior to</p> <p>discretization, too difficult to use for practical applications. Indirect methods though provide</p> <p>very high quality solutions, easily accessible sensitivity information, and faster convergence</p> <p>given a sufficiently good guess. Those strengths make indirect methods especially well-suited</p> <p>for generating large data sets for system analysis and worth revisiting.</p> <p>Recent advancements in the application of indirect methods have already mitigated many</p> <p>of the often cited issues. Automatic derivation of the necessary conditions with computer</p> <p>algebra systems have eliminated the manual step which was time-intensive and error-prone.</p> <p>Furthermore, regularization techniques have reduced problems which traditionally needed</p> <p>many phases and complex staging, like those with inequality path constraints, to a signifi-</p> <p>cantly easier to handle single arc. Finally, continuation methods can circumvent the small</p> <p>radius of convergence of indirect methods by gradually changing the problem and use previ-</p> <p>ously found solutions for guesses.</p> <p>The new optimal control problem solver Giuseppe incorporates and builds upon these</p> <p>advancements to make indirect methods more accessible and easily used. It seeks to enable</p> <p>greater research and creative approaches to problem solving by being more flexible and</p> <p>extensible than previous solvers. The solver accomplishes this by implementing a modular</p> <p>design with well-defined internal interfaces. Moreover, it allows the user easy access to and</p> <p>manipulation of component objects and functions to be use in the way best suited to solve</p> <p>a problem.</p> <p>A new technique simplifies and automates what was the predominate roadblock to using</p> <p>continuation, the generation of an initial guess for the seed solution. Reliable generation of</p> <p>a guess sufficient for convergence still usually required advanced knowledge optimal contrtheory or sometimes incorporation of an entirely separate optimization method. With the</p> <p>new method, a user only needs to supply initial states, a control profile, and a time-span</p> <p>over which to integrate. The guess generator then produces a guess for the “primal” problem</p> <p>through propagation of the initial value problem. It then estimates the “dual” (adjoint)</p> <p>variables by the Gauss-Newton method for solving the nonlinear least-squares problem. The</p> <p>decoupled approach prevents poorly guessed dual variables from altering the relatively easily</p> <p>guess primal variables. As a result, this method is simpler to use, faster to iterate, and much</p> <p>more reliable than previous guess generation techniques.</p> <p>Leveraging the continuation process also allows for greater insight into the solution space</p> <p>as there is only a small marginal cost to producing an additional nearby solutions. As a</p> <p>result, a user can quickly generate large families of solutions by sweeping parameters and</p> <p>modifying constraints. These families provide much greater insight in the general problem</p> <p>and underlying system than is obtainable with singular point solutions. One can extend</p> <p>these analyses to high-dimensional spaces through construction of compound continuation</p> <p>strategies expressible by directed trees.</p> <p>Lastly, a study into common convergence explicates their causes and recommends mitiga-</p> <p>tion strategies. In this area, the continuation process also serves an important role. Adaptive</p> <p>step-size routines usually suffice to handle common sensitivity issues and scaling constraints</p> <p>is simpler and out-performs scaling parameters directly. Issues arise when a cost functional</p> <p>becomes insensitive to the control, which a small control cost mitigates. The best perfor-</p> <p>mance of the solver requires proper sizing of the smoothing parameters used in regularization</p> <p>methods. An asymptotic increase in the magnitude of adjoint variables indicate approaching</p> <p>a feasibility boundary of the solution space.</p> <p>These techniques for indirect methods greatly facilitate their use and enable the gen-</p> <p>eration of large libraries of high-quality optimal trajectories for complex problems. In the</p> <p>future, these libraries can give a detailed account of vehicle performance throughout its flight</p> <p>envelope, feed higher-level system analyses, or inform real-time control applications.</p>