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Local basis functions offer computational efficiency when used in nonlinear adaptive control schemes. However, commonly used robust weight (parameter) update methods do not result in acceptable performance when applied to underdamped systems. This is because persistent oscillation in the inputs encourages severe weight drift, in turn requiring large robust terms that significantly limit the performance. In particular, the methods of leakage, c-modification, dead/one, and weight projection sacrifice performance to halt this weight drift. In contrast, it is observed (in simulations) that application of the proposed method halts the weight drift without sacrificing the performance.