Computing of first-order sensitivity information is crucial for many gradient-base optimization strategies where the algorithms employed plays a key role on determining the computational efficiency of an optimization process. This paper presents an algorithm which is able to determine the state derivatives in a fully recursive manner so to significantly reduce the cost of determining analytic first-order sensitivity information for large scale tree-type dynamic systems. Qualitative and quantitative validation on the operational requirement of the present method are made through analytical means and empirical studies.

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