http://hdl.handle.net/1721.1/7766 2013-05-25T21:11:12Z http://hdl.handle.net/1721.1/77858 A new technique for identification and control of systems with unknown parameters. Schmidt, George Thomas Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. Thesis. 1971. Sc.D.; Microfiche copy available in Barker.; Vita.; Bibliography: leaves 172-176. 1971-01-01T00:00:00Z http://hdl.handle.net/1721.1/77133 Unsteady adjoint analysis for output sensitivity and mesh adaptation Krakos, Joshua Ambre Adjoint analysis in computational fluid dynamics (CFD) has been applied to design optimization and mesh adaptation, but due to the relative expense of unsteady analysis these applications have predominantly been for steady problems. As the use of adjoint methods continues to becomes more prevalent, more problems are encountered for which steady analysis may not be appropriate. This thesis examines three aspects of unsteady adjoint analysis. First, this work investigates problems exhibiting small-scale output unsteadiness when solved with time-inaccurate iterative solvers. It is demonstrated that unconverged steady flow calculations, even with small output unsteadiness, can lead to significant variability in the estimated output sensitivity due to the arbitrary choice of unconverged state upon which the linearization is performed. Further, time-inaccurate "unsteady" iterative solutions depend on the iterative method used and may exhibit different output and output sensitivity compared to the steady flow or time-accurate unsteady flow. With the motivation for unsteady simulation established, output and output parameter sensitivities of periodic unsteady problems are sought using finite-time averaging. Periodic outputs computed over a finite time span are found to converge slowly and output sensitivities may be nonconvergent when the period of oscillation is a function of the parameter of interest. A theoretical basis for this lack of convergence is identified and output windowing is proposed to alleviate its effect. Output windowing is shown to enable the accurate computation of periodic output sensitivities and to decrease simulation time to compute periodic outputs and sensitivities. Finally, a spatial mesh adaptation approach is developed for unsteady wake problems and other problems with smooth and persistent regions of unsteadiness. For this class of problems, a higher-order discretization coupled with a single spatial mesh approach is appropriate to capture both steady and unsteady regions. The method proposed herein extends the anisotropic, output-based Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm of Yano and Darmofal to optimize the spatial mesh driven by an unsteady flow field. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.; Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.; Includes bibliographical references (p. 123-135). 2012-01-01T00:00:00Z http://hdl.handle.net/1721.1/77100 Robust distributed planning strategies for autonomous multi-agent teams Ponda, Sameera S The increased use of autonomous robotic agents, such as unmanned aerial vehicles (UAVs) and ground rovers, for complex missions has motivated the development of autonomous task allocation and planning methods that ensure spatial and temporal coordination for teams of cooperating agents. The basic problem can be formulated as a combinatorial optimization (mixed-integer program) involving nonlinear and time-varying system dynamics. For most problems of interest, optimal solution methods are computationally intractable (NP-Hard), and centralized planning approaches, which usually require high bandwidth connections with a ground station (e.g. to transmit received sensor data, and to dispense agent plans), are resource intensive and react slowly to local changes in dynamic environments. Distributed approximate algorithms, where agents plan individually and coordinate with each other locally through consensus protocols, can alleviate many of these issues and have been successfully used to develop real-time conflict-free solutions for heterogeneous networked teams. An important issue associated with autonomous planning is that many of the algorithms rely on underlying system models and parameters which are often subject to uncertainty. This uncertainty can result from many sources including: inaccurate modeling due to simplifications, assumptions, and/or parameter errors; fundamentally nondeterministic processes (e.g. sensor readings, stochastic dynamics); and dynamic local information changes. As discrepancies between the planner models and the actual system dynamics increase, mission performance typically degrades. The impact of these discrepancies on the overall quality of the plan is usually hard to quantify in advance due to nonlinear effects, coupling between tasks and agents, and interdependencies between system constraints. However, if uncertainty models of planning parameters are available, they can be leveraged to create robust plans that explicitly hedge against the inherent uncertainty given allowable risk thresholds. This thesis presents real-time robust distributed planning strategies that can be used to plan for multi-agent networked teams operating in stochastic and dynamic environments. One class of distributed combinatorial planning algorithms involves using auction algorithms augmented with consensus protocols to allocate tasks amongst a team of agents while resolving conflicting assignments locally between the agents. A particular algorithm in this class is the Consensus-Based Bundle Algorithm (CBBA), a distributed auction protocol that guarantees conflict-free solutions despite inconsistencies in situational awareness across the team. CBBA runs in polynomial time, demonstrating good scalability with increasing numbers of agents and tasks. This thesis builds upon the CBBA framework to address many realistic considerations associated with planning for networked teams, including time-critical mission constraints, limited communication between agents, and stochastic operating environments. A particular focus of this work is a robust extension to CBBA that handles distributed planning in stochastic environments given probabilistic parameter models and different stochastic metrics. The Robust CBBA algorithm proposed in this thesis provides a distributed real-time framework which can leverage different stochastic metrics to hedge against parameter uncertainty. In mission scenarios where low probability of failure is required, a chance-constrained stochastic metric can be used to provide probabilistic guarantees on achievable mission performance given allowable risk thresholds. This thesis proposes a distributed chance-constrained approximation that can be used within the Robust CBBA framework, and derives constraints on individual risk allocations to guarantee equivalence between the centralized chance-constrained optimization and the distributed approximation. Different risk allocation strategies for homogeneous and heterogeneous teams are proposed that approximate the agent and mission score distributions a priori, and results are provided showing improved performance in time-critical mission scenarios given allowable risk thresholds. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.; Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.; Includes bibliographical references (p. 225-244). 2012-01-01T00:00:00Z http://hdl.handle.net/1721.1/77098 Efficiency loss in resource allocation games Xu, Yunjian The overarching goals of this thesis are to quantify the efficiency loss due to market participant strategic behavior, and to design proper pricing mechanisms that reduce the efficiency loss. The concept of efficiency loss is intimately related to the concept of "price of anarchy," which was advanced by Koutsoupias and Papadimitriou, and compares the maximum social welfare with that achieved at a worst Nash equilibrium. This thesis focuses on the following two topics: (i) For a market with an arbitrary number of participants, how much is the Nash equilibrium close, in the sense of price of anarchy, to a social optimum? (ii) For a resource allocation/pricing mechanism, is the social welfare achieved at an economic equilibrium asymptotically optimal, as the number of market participants goes to infinity? Regarding the first topic, we quantify the efficiency loss in classical Cournot oligopoly games, where multiple oligopolists compete by choosing quantities. We also compare the total profit earned at a Cournot equilibrium to the maximum possible total profit that would be obtained if the suppliers were to collude. For the second topic, related to the efficiency in large economics, we analyze the efficiency of Kelly's proportional allocation mechanism in large-scale wireless communication systems. We study a corresponding Bayesian game in which each user has incomplete information on the state or type of the other users, and show that the social welfare achieved at a Bayes-Nash equilibrium is asymptotically optimal, as the number of users increases to infinity. Finally, for electricity delivery systems, we propose a new dynamic pricing mechanism that explicitly encourages consumers to adapt their consumption so as to offset the variability of demand on conventional units. Through a dynamic game-theoretic formulation, we show that the proposed pricing mechanism achieves social optimality asymptotically, as the number of consumers increases to infinity. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.; Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.; Includes bibliographical references (p. 167-176). 2012-01-01T00:00:00Z