Robust adaptive control
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software
Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software
Parametric identification of robotic systems with stable time-varying Hopfield networks
Neural Computing and Applications
Hopfield Neural Networks for Parametric Identification of Dynamical Systems
Neural Processing Letters
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
Hopfield neural networks for on-line parameter estimation
Neural Networks
Identification of Dynamical Systems
Identification of Dynamical Systems
Modelling the HIV-AIDS Cuban Epidemics with Hopfield Neural Networks
IWANN '03 Proceedings of the 7th International Work-Conference on Artificial and Natural Neural Networks: Part II: Artificial Neural Nets Problem Solving Methods
Estimation of the rate of detection of infected individuals in an epidemiological model
IWANN'07 Proceedings of the 9th international work conference on Artificial neural networks
System identification-A survey
Automatica (Journal of IFAC)
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An algorithm for estimating time-varying parameters of dynamical systems is proposed, within the large family of prediction error methods. The algorithm is based on the ability of Hopfield neural networks to solve optimisation problems, since its formulation can be summarized as minimisation of the prediction error by means of a continuous Hopfield network. In previous work, it was proved, under mild assumptions, that the estimates converge towards the actual values of parameters and the estimation error remains asymptotically bounded in the presence of measurement noise. The novelty of this work is the advance in the robustness analysis, by considering deterministic disturbances, which do not fulfil the usual statistical hypothesis such as normality and uncorrelatedness. A model of HIV epidemics in Cuba is used as suitable benchmark, which is confirmed by the computation of the sensitivity matrix. The results show a promising performance, in comparison to the conventional Least Squares Estimator. Indeed, the estimation error is almost always lower in the proposed method that in least squares, and it is never significantly higher. Further, from a qualitative point of view, the estimate provided by the Hopfield estimator is smoother, with no overshoot that could eventually destabilize a closed control loop. A significant finding is the fact that the form of the perturbation affects critically the dynamical behaviour and magnitude of the estimation, since the estimation error asymptotically vanishes when the disturbances are additive, but not when they are multiplicative. To summarize, we can conclude that the proposed estimator is an efficient and robust method to estimate time-varying parameters of dynamical systems.