Parameter Estimation and Adaptive Control of Euler-Lagrange Systems Using the Power Balance Equation Parameterization

Both the paper and the candidate solution derive the same linear regression equation y = Ω^T θ from the Euler–Lagrange power balance Ė = q̇^T G τ and the linear parameterization of T + U, then apply the same first-order LTI filter H(p) = 1/(p+λ) to obtain filtered signals whose difference obeys v̇ = −λv. The paper states the result directly (Proposition 2.1) and implicitly assumes the standard zero initial conditions when “applying the LTI filter,” while the model’s solution makes this initialization explicit and notes the exponentially decaying mismatch for arbitrary initial conditions. The logical content and proof technique are essentially the same, with the model adding a useful clarification about initialization.