Date on Master's Thesis/Doctoral Dissertation
Electrical and Computer Engineering
Electrical Engineering, PhD
Committee Co-Chair (if applicable)
Radial Basis Function; Optimal Control; Trajectory Optimization; Costate Estimation; Drug Dosing; Anemia Management
This work presents two direct methods based on the radial basis function (RBF) interpolation and arbitrary discretization for solving continuous-time optimal control problems: RBF Collocation Method and RBF-Galerkin Method. Both methods take advantage of choosing any global RBF as the interpolant function and any arbitrary points (meshless or on a mesh) as the discretization points. The first approach is called the RBF collocation method, in which states and controls are parameterized using a global RBF, and constraints are satisfied at arbitrary discrete nodes (collocation points) to convert the continuous-time optimal control problem to a nonlinear programming (NLP) problem. The resulted NLP is quite sparse and can be efficiently solved by well-developed sparse solvers. The second proposed method is a hybrid approach combining RBF interpolation with Galerkin error projection for solving optimal control problems. The proposed solution, called the RBF-Galerkin method, applies a Galerkin projection to the residuals of the optimal control problem that make them orthogonal to every member of the RBF basis functions. Also, RBF-Galerkin costate mapping theorem will be developed describing an exact equivalency between the Karush–Kuhn–Tucker (KKT) conditions of the NLP problem resulted from the RBF-Galerkin method and discretized form of the first-order necessary conditions of the optimal control problem, if a set of conditions holds. Several examples are provided to verify the feasibility and viability of the RBF method and the RBF-Galerkin approach as means of finding accurate solutions to general optimal control problems. Then, the RBF-Galerkin method is applied to a very important drug dosing application: anemia management in chronic kidney disease. A multiple receding horizon control (MRHC) approach based on the RBF-Galerkin method is developed for individualized dosing of an anemia drug for hemodialysis patients. Simulation results are compared with a population-oriented clinical protocol as well as an individual-based control method for anemia management to investigate the efficacy of the proposed method.
Mirinejad, Hossein, "A radial basis function method for solving optimal control problems." (2016). Electronic Theses and Dissertations. Paper 2389.