Efficient and Reliable Numerical Solution of Dynamic Optimization

Details

Dynamic optimization is integral to many aspects of science and engineering, commonly found in trajectory optimization, optimal control (e.g. model predictive control, MPC), state estimation, system identification and design synthesis problems. A key characteristic of dynamic optimization problems (DOPs) is that the decision variables can be functions or trajectories, leading to infinite-dimensional optimization problems that are often more challenging to solve.

This project will focus on the continued development of a new type of direct transcription method named the integrated residual methods. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in the state-of-art method of direct collocation, the new approach focuses on minimizing and/or constraining the squared norm of the dynamic constraint residuals integrated along the solution trajectories, hence obtaining solutions with better properties in terms of accuracy, reliability, and constraint satisfaction. This new framework would also allow higher flexibility in managing the trade-offs between solution accuracy, optimality, and computational efficiency, to better adapt to the need of online implementations such as in MPC.

Upon the successful completion of this project, the PhD candidate will become an expert in addressing challenging DOPs arising from a wide range of engineering fields, including aerospace, automotive, robotics and mechatronics.