A key challenge in relative orbital motion is the design of nonlinear controllers that provide formal stability guarantees for the nonlinear dynamics while systematically incorporating operational constraints such as actuator saturation and sensor field-of-view requirements. In this paper, we present a computational framework for designing certified nonlinear controllers for orbital control under circular chief orbit. Our approach provides a unified solution leveraging three key steps: polynomial lifting to express the non-polynomial orbital dynamics in a polynomial form, the use of a dual Lyapunov theory for stability certification, and sum-of-squares optimization for tractable controller synthesis. Numerical simulations confirm effective constraint handling, including input saturation and geometric keep-in regions, and enhanced robustness to significant state measurement noise in comparison to LQR.
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