Colloquium: Optimal Guidance under Constraints: Analytical and Numerical Approaches for Missile and Space Applications

Optimal guidance under constraints is essential in many aerospace applications, as real-world missions must adhere to strict physical, safety, and operational limitations, such as control bounds, collision-avoidance requirements, and terminal accuracy, while simultaneously achieving high performance, for example, by minimizing fuel consumption or aerodynamic drag.

This talk presents recent results on analytical and numerical approaches to solving constrained optimal control and differential game problems, with applications to missile guidance and evasion, as well as to space-related scenarios, including spacecraft orbital engagements, debris collision avoidance, and powered descent and landing. The proposed approaches exploit the underlying structure of these problems to solve them analytically, and when impossible, introduce efficient computational strategies that enable practical solutions to complex guidance problems.

Time permitting, we will also present a numerical methodology for efficiently implementing Orthogonal Collocation (Pseudospectral) methods for the transcription of optimal control problems. The methodology is based on accurate identification of model discontinuities and a polynomial-degree estimation, and provides well-fitted, smaller meshes substantially faster, reducing overall convergence time.