Master's Thesis Proposal

Peter Lehmann

(Advisor: Prof. Theodorou)

"Maximum Entropy Sequential Quadratic Programming"

Tuesday, December 10

11:30 a.m. - 12:00 p.m.

Coda C1315 Grant Park 
756 W Peachtree St NW
 

Abstract

Trajectory optimization (TO) plays a critical role across a broad spectrum of scientific and engineering fields, including robotics, energy and power systems, economics, and transportation systems. Through the lens of optimal control, TO often involves solving constrained optimization problems with non-convex objective function, nonlinear state and actuation constraints, and nonlinear dynamics. A widely used technique to solve such problems is Sequential Quadratic Programming (SQP). This method iteratively solves a series of quadratic subproblems, each of which relies on first- and second-order approximations of the constraints and cost around a nominal trajectory. However, since each subproblem only captures local information, SQP can suffer from converging to local minima. To overcome this limitation, this thesis proposes Maximum Entropy Sequential Quadratic Programming (ME-SQP). The proposed algorithm considers a stochastic policy and introduces an entropic regularization into the objective function. Based on the regularized optimization problem, this study aims to identify an approximation of the optimal stochastic policy, which enables incorporating the maximum entropy principle into SQP. The resulting ME-SQP algorithm creates a scheme of interchanged optimization and sampling steps to encourage exploration during optimization. To evaluate the method’s efficacy, ME-SQP will be compared experimentally with regular SQP and existing entropic regularized dynamic optimizer across several TO tasks.

Committee

•    Prof. Evangelos Theodorou – School of Aerospace Engineering (advisor)
•    Prof. Kyriakos Vamvoudakis – School of Aerospace Engineering
•    Prof. Lu Gan – School of Aerospace Engineering