In this work, a user-friendly MATLAB tool is introduced to solve nonlinear optimal control problems by applying collocation techniques using Coupled Radial Basis Functions (CRBFs). CRBFs are a new class of Radial Basis Functions combined with a conical spline r^5, which provides the advantage of insensitivity to the shape parameter while maintaining accuracy and robustness. To solve optimal control problems, software tools are often employed to implement numerical methods and apply advanced techniques to solving differential equations. Although several commercial software tools exist for solving optimal control problems, such as ICLOCS2, GPOPS, and DIDO, there are no options available that utilize adaptive collocation with CRBFs. A unified MATLAB tool named Radial Optimal Control Software (ROCS) is introduced and not only implements the CRBF method, but also enables any user, from professionals to students, to solve nonlinear optimal control problems through a user-friendly interface. The tool accepts user input for boundary conditions, necessary conditions, and the governing equations of motion. The two-point boundary value problem (TPBVP) is approximated through collocation using CRBFs, and the resulting nonlinear algebraic equations (NAEs) are solved with a MATLAB solver. The tool's usefulness and application are demonstrated by solving classical nonlinear optimal control problems and comparing the results with the solutions found in the literature. Compared to classical numerical method techniques, the present tool is shown to solve optimal control problems more efficiently for the same level of accuracy. By introducing this unified MATLAB tool to solving nonlinear optimal control problems, the intent is to enable professionals and students to solve nonlinear optimal control problems, e.g., in astrodynamics and space-flight mechanics, without the need for extensive manipulation of code in existing software tools and without extensive knowledge of applying numerical solvers.
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Master of Science in Aerospace Engineering (M.S.A.E.)
College of Engineering and Computer Science
Mechanical and Aerospace Engineering
Aerospace Engineering; Guidance Control Dynamics Online
Length of Campus-only Access
Masters Thesis (Open Access)
Kelly, Bethany, "A Unified Tool For Adaptive Collocation Techniques Applied to Solving Optimal Control Problems" (2022). Electronic Theses and Dissertations, 2020-. 1588.