UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

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Subject: search.filters.subject.optimal control

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    Direct Nonlinear Trajectory Optimization and State Estimation for a Tethered Underwater Energy Harvesting Kite
    (2022) Bhattacharjee, Debapriya; Fathy, Hosam K.; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This dissertation addresses the coupled challenges of state estimation and trajectory optimization for a marine hydro-kinetic energy harvesting kite. The optimization objective is to maximize the kite's average mechanical power output. This work is motivated by the potential of ``pumping-mode" tethered kites to provide attractive levelized costs of electricity, especially when cross-current motion is exploited to maximize energy harvesting. In ``pumping-mode" kites, the kite is tethered to platform carrying a motor/generator, and electricity generation is achieved by reeling the kite out and in at high and low tether tension levels, respectively. Marine hydro-kinetic (MHK) systems are heavily influenced by wind energy systems. In both contexts, for instance, tethered kites can be used for electricity generation instead of stationary turbines. Similar to airborne wind energy (AWE) systems, the power production capacities of MHK kites are heavily influenced by their flight trajectories. While trajectory optimization is a well-established research area for AWE systems, it is a nascent but growing field for MHK kites. Moreover, although both AWE and MHK kites have the potential to benefit from trajectory optimization, the lessons learned from AWE systems might not be directly applicable to MHK kites, since MHK systems are often close to neutral buoyancy whereas AWE systems are not. Finally, there is little work in the literature that co-optimizes the spooling and cross-current trajectories of a pumping-mode MHK kite. The first contribution of this dissertation is to explore the simultaneous optimization of the cross-current trajectory and the spooling motion of a pumping-mode kite using direct transcription. While the results highlight the degree to which simultaneous optimization can be beneficial for these systems, they also motivate the need for a solution approach that satisfies the constraints imposed by the kite dynamics exactly, as opposed to approximately. This leads to the second contribution of this dissertation, namely, finding an analytic solution to the inverse dynamics of the MHK kite, i.e., mapping a desired combination of kite position, velocity, and acceleration onto the corresponding actuation inputs. The dissertation then proceeds to its third contribution, namely, solving the kite trajectory optimization problem based on the above exact solution of the kite's inverse dynamics. The resulting simulation provides more realistic optimization results. However, all of the above work focuses on the special case where the free-stream fluid velocity is known and spatio-temporally constant. This motivates the fourth and final contribution of this dissertation, namely, the development of an unscented Kalman filter for simultaneously estimating both the kite's state and the free-stream fluid velocity. One interesting outcome of the estimation study is the finding that simple unscented Kalman filtering is not able to estimate the fluid velocity accurately without the direct measurement of the attitude of the kite.
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    COGNITIVE CONTROL, EVOLUTIONARY GAMES, AND LIE ALGEBRAS
    (2019) Raju, Vidya; P. S., Krishnaprasad; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In recent years, pursuit-based feedback control laws have helped realize complex spatio-temporal behaviors of robot collectives by utilizing relative information (e.g. optic flow) of the target with respect to the pursuer. For instance, these algorithms can enable a team of Unmanned Aerial Vehicles (UAVs) perform search, rescue and surveillance. However, such platforms are far from being completely autonomous and frequently require human intervention to reset the goals for the mission midstream, to be accomplished by choosing one from a pool of control laws. While this can ensure achievement of very specific goals over a short duration, such as reaching a search location and performing motions to cover an annular region around it, there is a need to autonomously generate high level goals especially in the face of adverse or unexpected events. This requires using sensory information gathered from the environment in which the agents operate to decide the next course of action. The broad aim of this thesis is to establish a mathematical framework to enable a collective of robotic agents, each with a finite set of actions to choose from, arrive at a cognitive decision that is justified by aggregated evidence. We motivate the use of models from evolutionary game theory, particularly the replicator dynamics, to model the evolution of the probabilities associated with choosing each action. We take inspiration from neuroscience for realizing context-dependent decision making by means of a three-layer cognitive hierarchy operating at multiple timescales. We show how evolutionary game theory offers a natural framework to model this hierarchy. In particular, replicator dynamics associated to fitness maps capture the evolution of a finite number of population fractions or probabilities that grow depending on the fitness or reward obtained for each population type. In the present setting, we interpret the types as synonymous with strategies implemented by feedback laws and the decision of an autonomous agent as represented by probabilities over its strategies. This formulation can be used to realize a combination of available control laws that will enable the agent to achieve its goal. In the bottom layer are the dynamics of an agent which responds to external stimuli from the physical environment at a fast timescale by a combination of its feedback laws. In the intermediate layer is the replicator dynamics evolving in a comparatively slower timescale, in which the decision making that goes behind choosing the feedback law in the lower layer is updated using knowledge of the fitness of each strategy. In the top layer evolving at the slowest timescale, we consider replicator control systems specified by control laws that seek to realize context dependence (cognition) at the higher level. The contributions of this thesis are in all three layers of the cognitive hierarchy, explained through a top-down approach. We first consider the top layer by extending the replicator dynamics to a replicator control system whose controls vary the fitness of strategies in a time-dependent manner. We show a Lie algebraic structure in the space of fitness maps. We exploit this mathematical structure in the dynamics to modulate the fitness so that an arbitrary final set of probabilities can be attained from an initial state. In the process, we determine the associated controllability conditions. In the intermediate layer, we highlight an optimizing property of the replicator dynamics by showing that it satisfies first order necessary conditions for optimality for an appropriate cost function. In the bottom layer, we consider the interpretations of mixed strategies in the agent's physical world. An instance of dyadic pursuit in which the pursuer aims to capture a target using the motion camouflage pursuit strategy while trading off the accuracy of sensory information for the speed of response to the stimuli is explored. In the final part of this thesis, we consider a cognitive description of starling flocks by treating each flock as a single decision-making entity. We use observations made from several flocking events and formulate a data smoothing problem using the game-theoretic formulation in this thesis to understand the temporal evolution of fractions of the relative kinetic energy allocated to the different behavioral modes. We propose a function, the optimal cost arising out of the solution to an underlying optimal control problem, as a measure of cognitive effort involved in producing these behaviors. Lastly, we conclude with a discussion on ongoing work, some challenges and future research directions.
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    Surface Tension Free Boundary Problems: Formulation, Optimal Control and Numerics
    (2013) Carlos, Patrick Sodré; Nochetto, Ricardo H; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    The goal of this work is to treat the formulation, optimal control and numerical analysis of free boundary problems with surface tension effects. From a formulation point of view, we introduce a (dimension independent) abstract framework which captures the essential behavior of free boundary problems with surface tension effects. We then apply this framework to two scenarios. The first is where the underlying bulk system is governed by the Laplacian with non-homogeneous essential boundary condition, and the second is modeled by the Stokes equations with slip and no-slip boundary conditions. We do not impose a fixed contact angle between the free surface and any fixed part of the boundary. Although the formulation and numerics involving the Laplacian was available in the literature, the Stokes free boundary problem in Rn is novel. To obtain this last result we also had to prove the existence and uniqueness in Sobolev spaces for the pure slip problem for domains of type C1,\epsilon. This is a significant improvement over the current best result involving C1,1 domains. The results from the abstract formulation also carry over to the optimal control aspect. We obtain differentiability conditions which guarantee existence and (local) uniqueness of a minimizer to well-behaved cost functions. In the Laplacian case we go beyond the theoretical results and give precise second-order sufficient conditions for the (local) uniqueness of a minimizer for cost functions of the tracking type. The contribution in this area is significant in the sense that sufficient conditions are usually only assumed to be true, while we actually show that it indeed holds for our specific problem. The last piece of this work is the numerical treatment of the free boundary optimal control problem based on the Laplace equation. We are able to prove optimal convergence results using the finite element method. Moreover, we construct experiments to study the behavior of various metrics associated with the optimization problem.
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    A GENERAL MODEL OF BARRIER ISLAND EROSION MANAGEMENTWITH APPLICATION TO OPTIMAL RESPONSE UNDER SEA LEVEL RISE
    (2004-04-29) Landry, Craig Elliott; McConnell, Kenneth E; Agricultural and Resource Economics
    This dissertation lays out a conceptual model for managing beach erosion on barrier islands. Households affected by erosion management are identified as beach visitors and coastal homeowners. The returns from beach quality accruing to beach visitors are assessed via travel cost theory, combining revealed preference and contingent behavior data, while the returns from beach quality accruing to coastal homeowners are assessed using hedonic price theory and data from multiple housing markets. An optimal control model is formulated, which takes into account (i) distinct beach user groups, (ii) joint services of beaches (both recreational and loss-mitigating), (iii) active and passive beach management options, (iv) costs of beach maintenance, and (v) the dynamic motion of beach quality. Optimality conditions define efficient beach nourishment operations, as well as the optimal terminal time for active management (i.e. beach nourishment) on barrier island beaches. Empirical results illustrate the optimal beach width for a particular site and the schedule of nourishment operations detailing the amount of sand to be placed on the beach in each time period. The analysis presents estimates of the terminal time of active management for a particular site, and how the terminal time varies with (i) the rate of sea level rise, (ii) the value of threatened coastal property, and (iii) the magnitude of fixed beach nourishment costs.