Zhao-Xu Yang

A novel meta-cognitive fuzzy-neural model with backstepping strategy for adaptive control of uncertain nonlinear systems

A significant increase of system complexity and state changes requires an effective data-driven system identification and machine learning algorithm to deal with the control of nonlinear systems. Using streams of data collected from the system, the data-driven controller aims to stabilize the unknown nonlinear systems with modeling uncertainties and external disturbances. The paper proposes a novel data-driven adaptive control approach with the backstepping strategy for online control of unknown nonlinear systems with no human intervention. A new meta-cognitive fuzzy-neural model is first introduced to construct the unknown system dynamics and utilize the self-adaptive tracking error as the learning parameters to determine the deletion of the state data, adapt the structure and parameters of the controller using the information extracted from nonstationary data streams. Subsequently, the control law is constructed based on the meta-cognitive fuzzy-neural model rather than the actual systems and the backstepping control strategy. Then, the stability analysis of the closed-loop system is presented from the Lyapunov function and shows that the tracking errors converge to zero. In the proposed control scheme, the bound of the control input is considered and ensured via the stable projection-type adaptation laws of the parameters. Moreover, in order to further save online computation time, only the parameters of the rule nearest to the current state are updated while those of other rules maintain unchanged. This is different from the existing studies where the parameters of all rules are updated. Finally, various simulation results from an inverted pendulum system and a thrust active magnetic bearing system demonstrate the superior performance of the proposed meta-cognitive fuzzy-neural control approach.

Adaptive backstepping control for magnetic bearing system via feedforward networks with random hidden nodes

This paper presents an adaptive backstepping neural controller (ABNC) to achieve precise rotor position tracking for a nonlinear active magnetic bearing (AMB) system with modeling uncertainties and external disturbances. In the proposed ABNC, the single-hidden layer feedforward networks (SLFNs) are used to approximate the unknown nonlinearities of dynamic systems and then based on the approximated models, the neural controller is constructed. Different from the existing methods, the hidden node parameters of the SLFNs are determined using the recently proposed neural algorithm named extreme learning machine (ELM), where these parameters are assigned randomly without adjusting. This simplifies the controller design process. Using the Lyapunov theory, stable tuning rules are derived for the update of the output weights of the SLFNs and a proof of stability in the uniformly bounded sense is given for the resulting controller. Moreover, to relax the online computation burden existing in the ABNC, a simplified ABNC (Simpl_ABNC) with less parameters to be adjusted online is proposed to improve the control performance. Finally the simulation results demonstrate that the proposed ABNC and Simpl_ABNC achieve better tracking performance comparing with other controllers including PID controller, conventional backstepping controller and adaptive backstepping sliding mode controller. Also the results show that the Simpl_ABNC has much less computation complexity and also better tracking performance than the ABNC.

Matrix differentiation for capacity region of Gaussian multiple access channels under weighted total power constraint

Maximization the capacity region of Gaussian multiple access channels with vector inputs and vector outputs has been extensively studied in existing schemes. Although these schemes are proven effective in various real-life applications, they are inapplicable to deal with channels with matrix variables subjected to certain constraints. In this work, we present a new framework to estimate the capacity region of Gaussian multiple access channels with matrix inputs and outputs under weighted total power constraints. We propose an optimization model to address this issue and prove its concavity. By introducing an I-chain rule for matrix differentiation, the gradient of the objective function involving matrix variables can be obtained. An algorithm, named normalized projected gradient method (NPGM) is developed to find the global optimal solution for the proposed model. The convergence of NPGM is established by utilizing projection and normalization operators. Simulation results provide an interesting insight that NPGM can manage the existent situations within an unified framework, and provide a novel universal technical solution to optimize the capacity region under weighted total power constraints.

Self-evolving kernel recursive least squares algorithm for control and prediction

This paper presents a self-evolving kernel recursive least squares (KRLS) algorithm which implements the modelling of unknown nonlinear systems in reproducing kernel Hilbert spaces (RKHS). The prime motivation of this development is a reformulation of the well known KRLS algorithm which inevitably increases the computational complexity to the cases where data arrive sequentially. The self-evolving KRLS algorithm utilizes the measurement of kernel evaluation and adaptive approximation error to determine the learning system with a structure of a suitable size that involves recruiting and dimension reduction of the kernel vector during the adaptive learning phase without predefining them. This self-evolving procedure allows the algorithm to operate online, often in real time, reducing the computational time and improving the learning performance. This algorithm is finally utilized in the applications of online adaptive control and time series prediction where the system is described as a unknown function by Nonlinear AutoRegressive with Exogenous inputs model. Simulation results from an inverted pendulum system and Time Series Data Library demonstrate the satisfactory performance of the proposed self-evolving KRLS algorithm.

Robust kernel-based model reference adaptive control for unstable aircraft

In this article, a robust kernel-based model reference adaptive control is proposed for an unstable nonlinear aircraft. The heart of the proposed kernel-based model reference adaptive control scheme comprises an offline neural identifier and an online neural controller. In the offline neural identifier, the kernel-based unified extreme learning machine algorithm is used to identify the aircraft model with the available input–output data in a finite time interval. The finite time interval is selected to avoid the response of the unstable aircraft growing unbounded. In the kernel-based unified extreme learning machine, the hidden layer feature mapping is determined by the kernel matrix. However, the unified extreme learning machine is a batch learning algorithm and is not suitable for the online control learning. To solve the problem, a recursive version of the unified extreme learning machine is developed in this study. Based on a given reference model and the identified model, the recursive version of the unified extreme learning machine algorithm is applied to construct the online control law to compensate for the changes in the aircraft dynamics or characteristics. The performance of the proposed kernel-based model reference adaptive control scheme is validated through the simulation studies of a locally nonlinear longitudinal high-performance aircraft. Simulation studies are also compared with a model reference adaptive control based on the back-propagation algorithm and a model reference adaptive control based on the basic extreme learning machine algorithm in terms of the identification and tracking abilities. The results show that the proposed kernel-based model reference adaptive control can achieve better identification and tracking performance.

Nonparametric robust adaptive controller for tracking AMB systems

This paper presents a nonparametric robust adaptive controller for precisely tracking a nonlinear active magnetic bearing (AMB) system on the axial direction. The nonlinearities of AMB systems are approximated using a nonparametric method, based on which the controller is designed based on the well known backstepping procedure. It is shown that when we only estimate the bound, instead of all individuals, of the unknown weights in the nonparametric approximation, less parameters are required to be adjusted in designing the online control law. By doing this, the computational burden and the performance of the controller can be significantly lightened. The convergence of the proposed control law is proven under the Lyapunov synthesis, and the effectiveness is verified and demonstrated by simulation results.

An entropy-based method for estimating demographic trends

In this paper, an entropy-based method is proposed to forecast the demographical changes of countries. We formulate the estimation of future demographical profiles as a constrained optimization problem, anchored on the empirically validated assumption that the entropy of age distribution is increasing in time. The procedure of the proposed method involves three stages, namely: 1) Prediction of the age distribution of a countrys population based on an “age-structured population model”; 2) Estimation the age distribution of each individual household size with an entropy-based formulation based on an “individual household size model”; and 3) Estimation the number of each household size based on a “total household size model”. The last stage is achieved by projecting the age distribution of the countrys population (obtained in stage 1) onto the age distributions of individual household sizes (obtained in stage 2). The effectiveness of the proposed method is demonstrated by feeding real world data, and it is general and versatile enough to be extended to other time dependent demographic variables.

Adaptive backstepping neural controller for nonlinear thrust active magnetic bearing system

This paper presents an adaptive backstepping neural (ABN) controller to achieve precise position tracking on the axial direction for a nonlinear thrust active magnetic bearing (TAMB) system. The proposed controller is constructed based on the single-hidden layer feedforward network (SLFN) for approximating the unknown nonlinearities of dynamic systems. Different from the existing methods the parameters of the SLFNs are modifie using the recently proposed neural algorithm named extreme learning machine (ELM), where the parameters of the hidden nodes are assigned randomly without adjusting. This simplifie the controller design process. The output weights are updated based on the Lyapunov synthesis approach to guarantee the stability of the overall control system. Finally the simulation results demonstrate that better tracking performance is achieved by the ABN controller than that of the conventional backstepping controller.