Browsing by Subject "Optimal control"

Now showing 1 - 5 of 5
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    Characteristic information required for human motor control:Computational aspects and neural mechanisms.
    (2010-08) Christopoulos, Vassilios N.
    Motor behavior involves creating and executing appropriate action plans based on goals and relevant information. This information characterizes the state of environment, the task and the state of actions performed. The perceptual system gathers this information from different sources: touch, vision, audition, scent and taste. Despite the richness of environment and the sophistication of our sensory system, it is not possible to extract a complete and accurate representation of the required states for motor behavior because of noise and ambiguity. Consequently, people effectively have “limited information” and therefore may not be certain about the outcomes of specific actions. For motor behavior to be robust to uncertainty, the brain needs to represent both relevant states and their uncertainties, and it needs to build compensation for uncertainty into its motor strategy. Generating motor behavior requires the brain to convert goals and information into action sequences, and the flexibility of human motor behavior suggests that brain implements a complex control model. The primary goal of this work is to improve the characterization of this control model by studying motor compensation for uncertainty and determining the neural mechanisms underlying information processing and the control model. Part of this thesis focuses on studying human compensation strategies in natural tasks like grasping. We experimentally tested the hypothesis that people compensate for object position uncertainty by adopting strategies that minimize the impact of uncertainty in grasp success. As we hypothesized, we found that people compensate for object position uncertainty by approaching the object along the direction of maximal position uncertainty. Additionally, we modeled the grasping task within the optimal control framework and found that human strategies share many characteristics with optimal strategies for grasping objects with position uncertainty. We are also interested to understand how the brain encodes and processes information relevant to movements. To accomplish this, we studied the spatial and temporal interactions of cortical regions underlying continuous and sequential movements using magnetoencephalography (MEG). Particularly, we took data from a previous study, in which subjects continuously copied a pentagon shape for 45 s using an XY joystick. Using Box-Jenkins time series analysis techniques, we found that neural interactions and variability of movement direction are integrated in a feedforward-feedback scheme. MEG sensors related to feedforward scheme were distributed around the left motor cortex and the cerebellum, whereas sensors related to feedback scheme had a strong focus around the parietal and the temporal cortices.
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    Constrained Buckling of Variable Length Elastica
    (2017-10) Liakou, Anna
    The physical understanding of the response of slender elastic bodies restrained inside constraints under various loading and boundary conditions is of a great importance in engineering and medical applications. The research work presented in this thesis is especially concerned with the buckling response of an elastic rod (the elastica) subjected to unilateral constraints under axial compression. It seeks to address two main issues: (i) the conditions that lead to the onset of instability, and (ii) the factors that define the bifurcation diagram. Two distinct classes of problems are analyzed; (i) the classical buckling problem of a constant length elastica and (ii) the insertion buckling problem of a variable length elastica. Their main difference is the generation of a configurational force at the insertion point of the sliding sleeve in the insertion problem, which is not present in the classical problem. The thesis describes two distinct methodologies that can solve these constrained buckling problems; (1) a geometry-based method, and (2) an optimal control method. The geometry-based method is used to analyze the post-buckling response of a weightless planar elastica subjected to unilateral constraints. The method rests on assuming a deformed shape of the elastica and on uniquely segmenting the elastica consistent with a single canonical segment (clamped-pinned). An asymptotic solution of the canonical problem is then derived and the complete solution of the constrained elastica is constructed by assembling the solution for each segment. Nevertheless, the application of the optimal control method is more generic. It can be used to solve any constrained buckling problem under general boundary and loading conditions. Based on Hamiltonian mechanics, the optimality conditions, which constitute the Pontryagin’s minimum principle, involve the minimization of the Hamiltonian with respect to the control variables, the canonical equations and the transversality conditions. The main advantage of the optimal control method is the assumption of strong rather than weak variation of the involved variables, which leads to the additional Weierstrass necessary condition (“optimal” equilibrium state). Based on it, several factors such as the effect of the self-weight of the elastica and the clearance of the walls are investigated.
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    Design, control and energy optimization of a rapid-prototyping hybrid powertrain research platform
    (2014-01) Wang, Yu
    This thesis focuses on the architecture design, dynamic modeling and system control of a rapid-prototyping hybrid automotive powertrain research platform and on this basis, conducts a series of research work on the powertrain control and energy/emissions optimization of the hybrid vehicle system. This hybrid powertrain research platform leverages the fast dynamic response of a transient hydrostatic dynamometer to mimic the dynamics of various hybrid power sources and hybrid architectures and therefore, creates an accurate and highly flexible emulation tool for hybrid powertrain operations. This design will greatly speed up the research progress and reduce the economic cost of the study on various hybrid architectures and control methodologies. The design, control and optimization of this research platform include the detailed research achievements in three levels of the proposed system:1) Low-level system (hydrostatic dynamometer) design and control:with regards to the low-level system, the design, modeling, nonlinear control and experimental validation of a transient hydrostatic dynamometer are accomplished, which provides the hardware ingredient for the research platform and ensures the dynamics emulation capability of the system.2) Mid-level system (hybrid powertrain system) design and control:with regards to the mid-level system, the design and experimental investigation of the multivariable hybrid powertrain control within the hybrid powertrain research platform are achieved; on this basis, the systematic integration and coordination of the energy optimization, hybrid powertrain control, hardware-in-the-loop vehicle simulation and hybrid torque emulation are conducted within a closed-loop architecture.3) High-level system (hybrid energy and emission management) control and optimization:the high-level system design consists of the fuel efficiency optimization ("Stochastic Dynamic Programming - Extremum Seeking" hybrid energy management strategy) and transient emission optimization (Two-Mode hybrid energy management strategy), which are not only the advanced studies in the core area of the hybrid powertrain technology development, but also can be considered as the functionality demonstrations of the designed hybrid powertrain research platform.
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    Designing optimal strategies for surveillance and control of invasive forest pests.
    (2011-04) Horie, Tetsuya
    This thesis focuses on the theme of detecting and managing invasive forest pests. First, we model optimal detection of sub-populations of invasive species that establish ahead of an advancing front. We find that the uninfested landscape is divided into two zones, characterized by different dynamically optimal management plans: a suppression zone and an eradication zone. In the suppression zone, optimal detection effort increases with distance from the front. At the distance where the suppression zone yields to the eradication zone, optimal detection effort plateaus at its maximum level. Second, we develop a model of optimal surveillance and control of forest pathogens and apply it to the case of oak wilt in a region within Anoka County, Minnesota. We develop a cost curve associated with the expected fraction of healthy trees saved from becoming infected. We also explore characteristics of sites selected for surveillance. In particular, we examine the characteristics of sites that make them high-priority sites for surveillance when the budget level is relatively low. We find that the best surveillance strategy is to prioritize sites with relatively low expected unit surveillance cost per tree saved from infection. Our results offer practical guidance to managers in charge of deciding how and where to spend limited public dollars when the goal is to reduce the number of trees newly infected by oak wilt. Third, we model a private landowners' forest protection problem, in which each landowner decides among three possible strategies: prevention, monitoring and treatment, and no treatment. We find that the proportion of landowners taking preventive and no action increases as the accuracy of monitoring decreases; monitoring ceases to be chosen when monitoring accuracy declines below a threshold value. We also investigate the possible effects of a policy that raises the accuracy of monitoring on social welfare in both the landowners' equilibrium and the full information social optimum. We find that the policy closes the gap in social welfare between the landowners' equilibrium and the full information social optimum. However, it decreases social welfare in the full information social optimum.
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    Forward and Inverse Methods in Optimal Control and Dynamic Game Theory
    (2019-08) Awasthi, Chaitanya
    Optimal control theory is ubiquitous in mathematical sciences and engineering. However, in a classroom setting we barely move beyond linear quadratic regulator problems, if at all. In this work, we demystify the necessary conditions of optimality associated with nonlinear optimal control by deriving them from first principles. We also present two numerical schemes for solving these problems. Moving forward, we present an extension of inverse optimal control, which is the problem of computing a cost function with respect to which observed state and control trajectories are optimal. This extension helps us to handle systems which are subjected to state and/or control constraints. We then generalize the methodology of optimal control theory to solve constrained non-zero sum dynamic games. Dynamic games are optimization problems involving several players who are trying to optimize their respective cost functions subject to constraints. We present a novel method to compute Nash equilibrium associated with a game by combining aspects from direct and indirect methods of solving optimal control problems. Finally, we study constrained inverse dynamic games, which is a problem analogous to constrained inverse optimal control method. Here, we show that an inverse dynamic game problem can be decoupled and solved as an inverse optimal control problem for each of the players individually. Throughout the work, examples are provided to demonstrate efficacy of the methods developed.