Browsing by Subject "Control Theory"

Now showing 1 - 4 of 4
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    Conceptual Modeling of Adaptive Therapy Dosing for Chemotherapeutic Administration in Cancer Allows for the Direct Comparison of Continuous and Adaptive Dosing Regimes
    (2022-05) McGehee, Cordelia
    Adaptive therapy of cytotoxic (cell killing) chemotherapy has been proposed as a method to prolong progression-free survival in certain cancers when underlying cell-cell competition between sensitive and resistant cancer cells is present. Traditionally, cytotoxic chemotherapy dosing is administered at the maximal tolerated dose with the goal of rapidly shrinking tumor growth. In the case of a tumor where underlying intratumoral cell-cell competition between a drug sensitive and drug resistant population leads to competition for resources, it is hypothesized that maximally killing the sensitive cell population allows for competitive release of the resistant cell population and outgrowth of a chemotherapy resistant tumor. In adaptive therapy, chemotherapy is administered when a tumor reaches a certain upper threshold and then is discontinued when the tumor shrinks to a specified lower threshold. The purpose of this strategy is to use the sensitive cell population to inhibit the growth of the resistant cell population and increase the length of time to competitive release and outgrowth of the resistant cell population. In this thesis, a modified Lotka-Volterra competition model is explored across competition parameters in order to analytically address 1) the optimality of continuous fixed dose versus adaptive dosing schedules and 2) the role of drug dose and mechanism of action in the choice of dosing regime. Using this model, several novel results are shown. First, for certain parameters, complete tumor eradication can be achieved in the presence of a resistant subpopulation under adaptive cytotoxic or continuous antiproliferative (decreasing growth rate) dosing schedules. Second, in this parameter space, fixed dose antiproliferative dosing schedules are more robust than cytotoxic adaptive regimes to uncertainty in initial conditions. Third, in parameter spaces where eradication of the resistant cell population is not feasible, both fixed dose antiproliferative schedules and cytotoxic adaptive therapy schedules may result in delayed resistant cell outgrowth over maximum tolerated dose and are comparable in their benefits. Overall, these results indicate that both antiproliferative continuous fixed dose therapy and cytotoxic adap-tive therapy can be used for tumor management in the case of underlying intratumoral competition between chemotherapy sensitive and chemotherapy resistant cells.
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    Persistency of Excitation, Nonlinear Function Approximation, and Stochastic Contraction Analysis for Learning in Model Reference Adaptive Control
    (2023-08) Lekang, Tyler
    Machine learning has achieved unprecedented levels of success recently, in the areas of language processing and modeling, image and video classification and generation, and recommendation and dynamic pricing systems. The control of dynamic systems has also benefited from these advancements in learning, particularly in the areas of reinforcement learning for tasks such as robotic navigation and control of nuclear fusion processes. We wish to study learning in another area where it can naturally be applied: adaptive control systems. These systems must estimate and identify uncertainties in the plant inorder to apply their adaptive control laws. We study the areas of stochastic contraction and convex projection, persistency of excitation, and function approximation, with an eye towards this application. The first part of the thesis is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and determining appropriate step sizes for simulations. To this end, we extend a methodology from (unconstrained) stochastic differential equations (SDEs) which provides contractions in a specially chosen Wasserstein distance. This theory focuses on unconstrained SDEs with fairly restrictive assumptions on the drift terms. Typical adaptive control schemes place constraints on the learned parameters and their update rules violate the drift conditions. To this end, we extend the contraction theory to the case of constrained systems represented by reflected stochastic differential equations and generalize the allowable drifts. We show how the general theory can be used to derive quantitative contraction bounds on a nonlinear stochastic adaptive regulation problem. ivThe second part of the thesis defines geometric criteria which are then used to establish sufficient conditions for persistency of excitation with vector functions constructed from single hidden-layer neural networks with step or ReLU activation functions. We show that these conditions hold when employing reference system tracking, as is commonly done in adaptive control. We demonstrate the results numerically on a system with linearly parameterized activations of this type and show that the parameter estimates converge to the true values with the sufficient conditions met. The third part of the thesis studies function approximation. Classical results in neural network approximation theory show how arbitrary continuous functions can be approximated by networks with a single hidden layer, under mild assumptions on the activation function. However, the classical theory does not give a constructive means to generate the network parameters that achieve a desired accuracy. Recent results have demonstrated that for specialized activation functions, such as ReLUs, high accuracy can be achieved via linear combinations of randomly initialized activations. These recent works utilize specialized integral representations of target functions that depend on the specific activation functions used. This paper defines mollified integral representations, which provide a means to form integral representations of target functions using activations for which no direct integral representation is currently known. The new construction enables approximation guarantees for randomly initialized networks using any activation for which there exists an established base approximation which may not be constructive. We extend the results to the supremum norm and show how this enables application to an extended, approximate version of (linear) model reference adaptive control.
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    Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems
    (2016-07)
    Conference Proceedings and Presentations for the 22nd International Symposium on Mathematical Theory of Networks and Systems
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    A Unified Framework for Understanding Distributed Optimization Algorithms: System Design and its Applications
    (2023-11) Zhang, Xinwei
    More than ever before, technology advances across the spectrum have meant that we have individualized and decentralized access to data, resources, and human capital. The capability to utilize massively and distributedly generated data (e.g., personal shopping records) and distributed computation (e.g., fast smartphone processors) has simplified our lives, facilitated optimal resource allocation, and unlocked innovation across industries. Distributed algorithms play a central role in the optimal operation of distributed systems in many applications, such as machine learning, signal processing, and control. Significant research efforts have been devoted to developing and analyzing new algorithms for various applications. However, existing methods are still facing difficulties in using computational resources and distributed data safely and efficiently. The three major challenges in state-of-the-art distributed systems are 1) finding appropriate models to describe the resources and problems in the system, 2) developing a general approach to solving problems efficiently, and 3) ensuring participants' privacy. My thesis research focuses on building an algorithmic framework to resolve these fundamental and practical challenges. This thesis provides a fresh perspective to understand, analyze, and design distributed optimization algorithms. Through the lens of multi-rate feedback control, this thesis theoretically proves that a wide class of distributed algorithms, including popular decentralized and federated schemes, can be viewed as discretizing a certain continuous-time feedback control system, possibly with multiple sampling rates, while preserving the same convergence behavior. Further, the proposed system unifies the stochasticities in a wide range of distributed optimization algorithms as several types of noises injected into the control system, and provides a uniform convergence analysis to a class of distributed stochastic optimization algorithms. The control-based framework is applied to designing new algorithms in decentralized optimization and federated learning to meet different system requirements including achieving convergence, optimal performance, or meeting privacy concerns. In summary, this thesis establishes a control-based framework to understand, analyze, and design distributed optimization algorithms, with applications in decentralized optimization and federated learning algorithm design.