Felipe Arenas-Uribe

Felipe Arenas-Uribe, Hasan A. Poonawala, Jesse B. Hoagg

Optimal control problems with discrete-valued inputs are challenging due to the mixed-integer nature of the resulting optimization problems, which are generally intractable for real-time, safety-critical applications. Lossless convexification offers an alternative by reformulating mixed-integer programs as convex programs that can be solved efficiently. This paper develops a lossless convexification for optimal control problems of linear systems. We extend existing results by showing that system normality is preserved when reformulating Lagrange-form problems into Mayer-form via an epigraph transformation, and under simple geometric conditions on the input set the solution to the relaxed convex problem is the solution to the original non-convex problem. These results enable real-time computation of optimal discrete-valued controls without resorting to mixed-integer optimization. Numerical results from Monte Carlo simulations confirm that the proposed algorithm consistently yields discrete-valued control inputs with computation times compatible with safety-critical real-time applications.

Felipe Arenas-Uribe, T. Michael Seigler, Jesse B. Hoagg

Soft landing on small celestial bodies (SCBs) poses unique challenges, as gravitational models poorly characterize the higher-order gravitational effects of SCBs. Existing control approaches lack guarantees for safety under gravitational uncertainty. This paper proposes a three-stage control architecture that combines disturbance estimation, trajectory tracking, and safety enforcement. An extended high-gain observer estimates gravitational disturbances online, a feedback-linearizing controller tracks a reference trajectory, and a minimum-intervention quadratic program enforces state and input constraints while remaining close to the nominal control. The proposed approach enables aggressive yet safe maneuvers despite gravitational uncertainty. Numerical simulations demonstrate the effectiveness of the controller in achieving soft-landing on irregularly shaped SCBs, highlighting its potential for autonomous SCB missions.