Direct Transcription for Parameter Identification from Partial State Measurements

This paper develops a direct transcription framework for nonlinear parameter identification from partial and noisy state measurements. The method combines multiple shooting with Hermite–Simpson (HS) collocation to produce a sparse, well–conditioned nonlinear program in which the continuous dynamics are enforced through high–order equality constraints. An explicit analysis of the gradient structure enables efficient solution using standard sparse sequential quadratic programming (SQP) or interior–point solvers. The formulation is applied to two benchmark systems-an armature-controlled DC motor and a nonlinear active spring–mass–damper system-under several restricted measurement configurations. Numerical studies show that the proposed MS+HS scheme reliably reconstructs both trajectories and physical parameters, improves conditioning relative to single–shooting formulations, and remains robust under partial observability and nonlinear dynamics. The results demonstrate that high–order structured discretisation provides a scalable and accurate tool for inverse problems in control–oriented dynamical systems.