An optimal control approach was previously developed to estimate state trajectories from noisy measurements of inaccurately-modelled systems. This optimization problem takes the form of a two-point boundary value problem; solution of this two-point boundary value problem yields estimates for both the optimal states and the error in the initial model. If the form of this model error is known, a model may be obtained by using a least squares fit to estimate unknown model coefficients. The resulting model error model may then be used to update the original system model. This approach has been used in the past to produce accurate models for single degree of freedom nonlinear systems. This paper briefly describes the approach, and applies it to produce an accurate model of a multiple degree of freedom system with cubic nonlinearity.
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