Browsing by Subject "nonlinear"

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    Advancing Deep Learning For Scientific Inverse Problems
    (2023-09) Zhuang, Zhong
    Artificial intelligence (AI) has ushered in a new paradigm for addressing scientific complexities, harnessing the computational prowess of robust machines and sophisticated algorithms tailored to domain-specific constraints. Across diverse domains encompass- ing scientific and engineering landscapes such as astronomy, biomedical science, and material science, the emergence of inverse problems is inherent. These quandaries are distinguished by the overarching objective of elucidating the reconstruction of meticulously structured entities from observational data, buoyed by a foundational bedrock of prior knowledge. In a generalized sense, the inverse problem is cast as Y = F(x), subject to the constraint G(x) = 0, wherein F denotes the function orchestrating the transformation of object x to observation Y, while G embodies the constraints imposed by pre-existing knowledge. Owing to the intrinsic characteristics of F—often marked by pronounced nonlinearity—inverse problems seldom conform to well-posed paradigms. Herein lies the significance of AI tools that leverage the extraction of latent insights from voluminous empirical data, epitomizing the realm of data-driven AI tools. This innovation extends the purview of inference beyond the bounds of human-established priors and experiential wisdom. However, the scientific realm stands in contrast to the more prolific AI domains, as the availability and fidelity of data are not perpetually assured in the context of inverse problems. Consequently, a promising avenue emerges in the form of singular-instance AI tools, underpinned by the potency of formidable constructs such as deep neural networks (DNNs). Operating autonomously from expansive data repositories, these tools offer an alternative avenue to address inverse problems within the scientific continuum. Within this work, we delineate our recent endeavors directed at catalyzing break- throughs in the resolution of intricate scientific inverse problems. Central to our approach are pragmatic strategies that harmoniously blend the attributes of data-driven and singular-instance AI tools into coherent pipelines. These endeavors culminate in a iiinovel problem-solving landscape that bridges the domains of AI and science, encapsulating the essence of innovation and advancement.
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    Simulation and Control of Nonholonomic Differential Drive Mobile Platforms
    (2017-12) Norr, Scott
    Abstract This thesis explores the application of non-linear control techniques to an inexpensive robot with limited computing ability. A basis for the kinematic description of the Differential Drive Mobile Robot (DDMR) is presented. The dynamics of wheeled robots are developed. The state space of DDMR platforms is found to be non-linear. A control law, based on a paper by Kanayama, is developed and determined to be bounded by a Lyapunov function and asymptotically stable. Using MATLAB, the entire closed-loop system is modeled with difference equations. Methods for tuning the control gains are explored. A modest prototype robot is constructed using a modest 8-bit processor. Reasonable correlation between the physical robot and the simulated robot is observed. Constraints do not hinder the robot’s ability to successfully implement a non-linear control scheme. The MATLAB simulation and physical robot correlate well. The control law is shown to be practical for inexpensive robotic platforms.