Slider: On the Design and Modeling of a 2D Floating Satellite Platform

The paper formulates the thruster allocation as a convex quadratic program Minimize J = x^T x subject to A x = b and box bounds x_lb ≤ x ≤ x_ub, with A ∈ R^{3×8} fixed by geometry, and motivates pseudo-inverse ideas and PWM realization, but it does not supply derivations of the closed-form equality-only solution, KKT conditions, feasibility characterization, or algorithmic convergence guarantees (the text simply states the optimization and proceeds to simulations) . The candidate model fills these gaps: it gives the unique minimum-norm equality-only solution x = A^T(AA^T)^{-1}b (under full row rank), states and uses the KKT system for the bounded case with an active-set reduction, characterizes feasibility via b ∈ A([x_lb, x_ub]), and outlines a standard active-set algorithm with termination to a KKT point for strictly convex QPs—each step consistent with standard convex optimization theory. Hence the paper’s presentation of the allocation logic is correct but incomplete, while the model’s solution is correct and complete at the level requested.