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Numerical Methods for Dynamic Optimization

Dynamic optimization is integral to many aspects of science and engineering, commonly found in trajectory optimization, optimal control, 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.

My current focus is on the development of a type of direct transcription method named the integrated residual methods. This is an excellent starting point to develop new DOP solution methods and next-generation software toolboxes. The advancements would allow DOPs to be formulated intuitively based on the problems' mission specifications and successfully solved thereafter, making the method easily accessible for scientists and engineers.

Optimization-based Control

Optimization-based control explores the use of optimization algorithms for feedback control of dynamical systems. For example, model predictive control (MPC) is a widely used optimization-based control method, allowing systematic and optimal handling of constraints, nonlinearities and uncertainties.

The area I am particularly interested in is the design of optimization-based control with the optimization problem formulated directly based on the original problem specifications. Although such problems are typically more difficult to solve numerically, the difficulties are often offset by the availability of guarantees in solution properties, so that any local optimum solution (to a certain extent, even any feasible solution) can be considered suitable for real-world implementation.

Control and Simulation of Aerospace Systems

I have a strong interest in the control and simulation of aerospace systems, particularly when unconventional and counterintuitive solutions are needed. My current focuses are on

• Development of tool-chains that can be integrated into the aircraft's daily operations (e.g. as next-generation flight management systems), where optimal flight trajectories can be automatically obtained based on the information regarding aircraft aerodynamics, propulsion, departure and arrival airport, atmospheric conditions and any relevant air traffic control restrictions,
• Optimal energy management for electric, hydrogen and hybrid aircraft concepts,
• Multi-disciplinary optimal design of aerospace vehicles and flight control systems, for example, regarding the optimal sizing and placement of flight control surfaces, and the integration of distributed propulsion systems in flight control designs,
• Guidance and automatic control for the safe recovery of airliners in extreme conditions known as upset, such as stall and spin,
• Next-generation flight simulator concepts, e.g. ones that are suitable for upset recovery training