Contractivity of the Method of Successive Approximations for Optimal Control

Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications in controls and learning), their study is receiving increasing attention. This work starts with the simple observation that, given a strongly system, its adjoint system also contracting, same rate, respect to dual norm, under time reversal. As main implication of this contractivity, we show that classic Method Successive Approximations (MSA), an indirect method optimal control, contraction mapping for short optimization intervals or large rates. Consequently, establish new convergence conditions MSA algorithm, which further imply uniqueness control sufficiency Pontryagin's minimum principle additional assumptions.