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An application of recursive covariance lattice algorithms to the adaptive estimation and control of a manipulator with one flexible link is presented. These algorithms are a set of pure order recursive lattice equations, which can in principle identify the effective order and the corresponding parameters of an ARMA prediction model of the manipulator. The reduced-order prediction model represents the significant dynamics of the plant, and is used to generate control sequences by minimising a weighted performance index. In the simulations, the manipulator is modelled by the finite element method and Langrange's equations. The performance and robustness of the lattice filter and the adaptive controller is demonstrated by numerical results.