Most of classical adaptive laws used in adaptive control have been developed based on the gradient descent algorithm to minimize the control error. Hence, the sluggish convergence of tracking error may affect the online learning, making accurate parameter estimation difficult. The aim of this paper is to present a new adaptive law to achieve optimal parameter estimation, and then to showcase its application to adaptive control for a benchmark servo system to retain simultaneous convergence of both the estimation error and tracking error. For this purpose, an auxiliary filter is introduced to extract the estimation error, which is used to drive the adaptive law with a time varying gain to minimize a cost function of the estimation error to achieve fast, accurate parameter estimation. Finally, this new adaptation is incorporated into an adaptive nonsingular terminal sliding mode control (ANTSMC) for the considered servo system to obtain tracking control and parameter estimation simultaneously. The effectiveness of the developed method is validated by means of comparative simulations and experiments.

This paper presents an alternative adaptive parameter estimation framework for nonlinear systems with time-varying parameters. Unlike existing techniques that rely on the polynomial approximation of time-varying parameters, the proposed method can directly estimate the unknown time-varying parameters. Moreover, this paper proposes several new adaptive laws driven by the derived information of parameter estimation errors, which achieve faster convergence rate than conventional gradient descent algorithms. In particular, the exponential error convergence can be rigorously proved under the well-recognized persistent excitation condition. The robustness of the developed adaptive estimation schemes against bounded disturbances is also studied. Comparative simulation results reveal that the proposed approaches can achieve better estimation performance than several other estimation algorithms. Finally, the proposed parameter estimation methods are verified by conducting experiments based on a roto-magnet plant.

In this paper, we propose real-time adaptive parameter estimation methods for a polymer electrolyte membrane fuel cell (PEMFC) to facilitate the modeling and the subsequent control synthesis. Specifically, the electrochemical model of this fuel cell is in a nonlinearly parametric formulation. Hence, most of existing parameter estimation techniques for PEMFC mainly rely on the optimization approaches, requiring heavy computational costs or even offline implementation. In comparison to those methods, real-time adaptive parameter estimation methods for nonlinearly parametric system are developed in this paper. First, the nonlinearly parametric function is linearized by using the Taylor series expansion. Then, adaptive parameter estimation methods are proposed for estimating the constant or time-varying parameters of PEMFC. Different from the well-recognized adaptive parameter estimation methods, the proposed adaptive laws are driven by the extracted estimation errors, so that exponential convergence of the parameter estimation error can be guaranteed, without using any predictors or observers. Finally, practical experiments in a H-100 PEMFC system are conducted, which illustrate satisfactory performances of the presented parameter estimation methods under different operation scenarios.

Parameter estimation is vitalfor modeling and control of fuel cell systems. However, the nonlinear parameterization is an intrinsic characteristic in the fuel cell models such that classical parameter estimation schemes developed for linearly parameterized systems cannot be applied. In this article, an alternative framework of adaptive parameter estimation is designed to address the real-time parameter estimation for fuel cell systems. The parameter estimation can be divided into two cascaded components. First, the dynamics with the unknown parameters are estimated by a new unknown system dynamics estimator (USDE). Inspired by an invariant manifold, this USDE is designed by applying simple filter operations such that the information of the state derivative is not required. Second, an adaptive law driven by the function approximation error is proposed for recovering unknown model parameters. Exponential convergence of the estimated parameters to the true values can be proved under the monotonicity condition. Finally, experimental results on a practical proton exchange membrane fuel cell system are given to verify the effectiveness of the proposed schemes.

The Hammerstein model has proven its ability for modeling many industrial servo systems, but the corresponding parameter estimation remains as a challenging problem, especially for the purpose of achieving fast convergence. This article presents a fixed-time (FxT) adaptive parameter estimation scheme for Hammerstein systems with an asymmetric dead-zone to ensure the convergence of estimated parameters in fixed-time. A continuous piecewise linear function neural network is adopted to model the nonlinear dead-zone dynamics to remedy the use of intermediate variable. To avoid using the system state information, a K-filter is used to construct a relationship between the unknown system parameters and the input/output signals. Then, a new adaptive law based on the parameter error and the FxT scheme is developed to online estimate the lumped unknown parameters and ensure the fixed-time convergence, where an online updated auxiliary variable of regressor is suggested to eliminate the impact of the regressor on the convergence performance. Both numerical simulations and experimental results are given to demonstrate the effectiveness of proposed methods.