论文信息 - Convergence of the gradient algorithm for linear regression models in the continuous and discrete time cases

Convergence of the gradient algorithm for linear regression models in the continuous and discrete time cases

We establish convergence to zero of the solutions of \dot \tilde θ(t) = −φ(t)φ(t) \tilde θ(t) or \tilde θ(t) = \tilde θ(t − 1) − φ(t)φ(t) \tilde θ(t − 1) under a possibly " vanishing persistent " excitation condition.

Laurent Praly | L. Praly

[1] Riccardo Marino,et al. Nonlinear control design: geometric, adaptive and robust , 1995 .

[2] Dirk Aeyels,et al. On the convergence of a time-variant linear differential equation arising in identification , 1994, Kybernetika.

[3] Han-Fu Chen,et al. Identification and Stochastic Adaptive Control , 1991 .

[4] K. Narendra,et al. On the uniform asymptotic stability of certain linear nonautonomous differential equations , 1976 .

[5] Wei Ren,et al. Stochastic adaptive prediction and model reference control , 1994, IEEE Trans. Autom. Control..