Applications of Induced Tensor Norms to Guidance Navigation and Control

The paper develops Taylor–series-based error bounds for flow maps and guidance problems using state transition tensors and induced tensor norms, e.g., the second- and higher-order expansions of the flow map and their big-O remainders (see the flow/STT definitions and Taylor expansions, including the second-order truncation and mth-order form in the paper’s Eqs. (3)–(11) and surrounding text ). For the transfer problem, the paper’s miss-distance bound expresses the position error in terms of the desired final position via the linear inverse Φrv−1 (Eqs. (72)–(75), (77)–(78)) ; it likewise bounds the initial-velocity error (Eq. (81)) . The model solution proves a rigorous Taylor remainder bound with an explicit Lipschitz-based O(∥h∥m+2) term and then derives the position–velocity split bound directly in terms of δv0; reparametrizing by δr*f via δv(1) = Φrv−1 δr*f recovers the paper’s form. Thus the paper’s results and the model’s solution are consistent; the model gives a more explicit analytic remainder bound, while the paper states results in big-O form and expresses guidance errors in δr*f rather than δv0.