Reachability set subspace computation for nonlinear systems using sampling methods

Computational savings in reachability set subspace computation are realized by carefully applying transversality conditions to trajectory samplings of the full reachability set. Differential constraints on the initial state and initial constraint Lagrange multiplier are developed that enforce the necessary conditions of optimality as total trajectory duration increases. Results are validated against known linear analytical results and an example is given where a 1-dimensional subspace of a 6-dimensional nonlinear problem is computed.