MEMS Seminar: “A Novel Computational Framework for the Numerical Solution of Complex Constrained Optimal Control Problems”

Thomas Lord Department of Mechanical Engineering & Materials Science, Fall 2023 Seminar Series with Anil V. Rao, PhD, Professor of Mechanical and Aerospace Engineering, University of Florida. Title: "A Novel Computational Framework for the Numerical Solution of Complex Constrained Optimal Control Problems." Abstract: A novel computational framework is described for solving complex constrained nonlinear optimal control problems. The framework has a wide variety of applications in aerospace and mechanical engineering. The basis of the framework is the new class of hp-adaptive Gaussian quadrature methods that transcribe the continuous optimal control problem to a finite-dimensional nonlinear optimization problem. The hp-adaptive methods have the feature that high accuracy can be obtained with a significantly smaller mesh when compared with traditional fixed-order methods while accurately capturing nonsmoothness or rapidly changing behavior. The hp-adaptive methods employed using advanced sparse nonlinear programming (NLP) solvers. The derivatives required by the NLP solvers are obtained using a new approach to algorithmic differentiation where efficient derivative source code is produced through a method that combines operator overloading with source transformation. The mathematical foundation of the framework is provided and examples are given that demonstrate the improvement over previously developed approaches. Finally, future directions of the approach are discussed.

ANIL V. Rao (BS, mechanical engineering, Cornell; AB, mathematics with distinction, Cornell; MSE, aerospace engineering, Univ. of Michigan; MA & PhD, Princeton. After earning his PhD, Dr. Rao joined The Aerospace Corp. in Los Angeles. Subsequently, he was a Senior Member of the Technical Staff at The Charles Stark Draper Lab. in Cambridge, MA. While at Draper, from 2001 to 2006, he was an adjunct faculty in the Dept. of Aerospace & Mechanical Engineering at Boston Univ. where he taught the core undergrad dynamics course. Since 2006 he has been on faculty in the Dept. of Mechanical & Aerospace Engineering at the Univ. of Florida, where he is a Professor and the Director of the Vehicle Dynamics and Optimization Lab. His research interests include computational methods for optimal control and trajectory optimization, nonlinear optimization, space flight mechanics, orbital mechanics, guidance, and navigation.