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Scholarly Works (2 results)

Thesis
Peer Reviewed

Applications of Orthogonal-Polynomial Approximations and Inverse-Optimal Control in Astrodynamics.

UC San Diego Electronic Theses and Dissertations (2024)

This dissertation addresses the pressing challenges in space situational awareness (SSA) and space debris management by developing advanced computational methods to enhance the precision and efficiency of orbit propagation and trajectory optimization. The research emphasizes the application of orthogonal polynomials—specifically Chebyshev and Legendre polynomials—known for their superior approximation properties, and the innovative use of inverse-optimal control in astrodynamics.

Chapter 3 of the dissertation introduces several advancements in gravity modeling. First, it introduces a normalized, singularity-free Cartesian formulation of the spherical harmonics model. This formulation overcomes the traditional model's limitations such as pole singularities and computational inefficiency. Additionally, it incorporates a finite element model (FEM) that is locally valid and reduces the computational demands by adapting the degree of spherical harmonics based on the radial distance, particularly beneficial for satellites in elliptical orbits. The adaptive FEM approach, coupled with parallel computing techniques, demonstrates potential speedups of up to 200 times, depending on the implementation specifics, thus addressing high computational costs associated with traditional global models.

Chapter 4 shifts focus to numerical integration, moving beyond conventional methods like explicit Runge-Kutta or multistep methods to explore orthogonal polynomial-based methods—Chebyshev-Picard and Gauss-Legendre collocation. Chebyshev-Picard methods are formulated in a matrix form to facilitate efficient parallel processing, significantly enhancing computational speeds in handling high-order gravity fields. The research bridges these methods with implicit Runge-Kutta methods, establishing their stability and accuracy. Innovations such as feedback-accelerated iterations and adaptive time-stepping further refine the numerical integration process, optimizing efficiency and adaptability in practical applications.

Chapter 5 explores trajectory optimization using a Lyapunov-based controller that simplifies the generation of initial guesses for both direct and indirect optimization methods. By employing an inverse-optimal-control framework, the dissertation identifies and minimizes specific cost functions, leading to the derivation of corresponding costates. These costates are utilized to solve time-optimal, orbit-transfer problems effectively, demonstrating the CCM controller's capability to maintain robust performance, even in the presence of gravity perturbations.

Article
Peer Reviewed

Percutaneous Mechanical Aspiration for Infective Endocarditis: Proceedings From an Inaugural Multidisciplinary Summit and Comprehensive Review.

UCLA Previously Published Works (2024)

The clinical presentation and epidemiology of infective endocarditis (IE) have evolved over time. While the cornerstones of IE treatment remain antimicrobial therapy and surgery, percutaneous mechanical aspiration (PMA) has emerged as an option for carefully selected patients as a complementary modality, based on retrospective data, case series, and expert experience. In this comprehensive review, we summarize the proceedings from an inaugural summit dedicated to the discussion of PMA in the global management of IE, consisting of experts across multiple disciplines from diverse geographic regions and care environments. After conceptualizing the 3 major roles of PMA as a bridge to decision, destination therapy, and adjunctive therapy, we then review the clinical scenarios in which PMA might be considered by IE subtype. We discuss patient selection, the rationale for intervention, and the most recent evidence for each. Next, we consider PMA for IE in the larger context of our health care system across 3 domains: clinical collaboration, financial considerations, and academic innovation, emphasizing the importance of interdisciplinary teams and cross-organizational partnerships, reimbursement models, and the need for high-quality research. Finally, we outline what we determined to be the most pressing outstanding questions in this space. In doing so, we propose a national consortium to help organize efforts to move this field forward and share our progress in these endeavors to date. PMA for IE has great promise, but significant work remains if we are to fully realize its potential to safely and effectively improve outcomes for modern endocarditis patients.

Cover page: Percutaneous Mechanical Aspiration for Infective Endocarditis: Proceedings From an Inaugural Multidisciplinary Summit and Comprehensive Review.