A roadmap for optimal control: the right way to commute

Area of Science:

• Astrodynamics
• Optimal Control Theory
• Space Mission Design

Background:

• Optimal control theory is fundamental to astrodynamics challenges like trajectory optimization and attitude control.
• Traditional optimal control frameworks (Bellman, Pontryagin) are often perceived as computationally difficult.
• Alternative methods are sought to address the increasing performance demands of modern space systems.

Purpose of the Study:

• To outline theoretical issues in astrodynamics arising from practical, advanced mission design problems.
• To highlight the covector mapping principle as a computationally tractable approach to optimal control.
• To connect modern computational techniques with classical mathematical principles for astrodynamics.

Main Methods:

• Exploration of the covector mapping principle as a neoclassical approach to optimal control.
• Leveraging advancements in approximation theory, set-valued analysis, and computing technology.
• Analysis of theoretical challenges in the context of practical astrodynamics applications.

Main Results:

• The covector mapping principle transforms complex optimal control problems into more manageable ones.
• This approach integrates classical mathematical insights with modern computational tools.
• It addresses the need for higher performance in advanced space system designs.

Conclusions:

• The covector mapping principle offers an accessible and powerful framework for solving difficult astrodynamics problems.
• This method is crucial for enabling the design and execution of advanced space missions.
• Continued research in this area is vital for future space exploration and system capabilities.