Design of a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems

This paper presents a simplified adaptive fuzzy backstepping control for uncertain discrete-time nonlinear systems. It is assumed that the systems are described by a discrete-time equation with nonlinear uncertainties to be viewed as the modelling errors and the unknown external disturbances, and the states are observed with measurement noises. To design the simplified adaptive fuzzy backstepping control, the modelling errors are approximated by using the fuzzy inference approach based on the extended single-input rule modules, and the estimates for the unmeasurable states and the adjustable parameters are derived by using the weighted and its simplified weighted least squares estimators. It is proved that the states are ultimately bounded, and the estimation errors remain in the vicinity of zero. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.     

Design of an adaptive fuzzy sliding mode control for uncertain discrete-time nonlinear systems based on noisy measurements

This paper presents the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain discrete-time nonlinear dynamic systems. The dynamic systems are described by a discrete-time state equation with nonlinear uncertainties, and the uncertainties include the modelling errors and the external disturbances to be unknown but nonlinear with the bounded properties. The states are measured by the restriction of measurement sensors and the contamination with independent measurement noises. The nonlinear uncertainties are approximated by using the fuzzy IF-THEN rules based on the universal approximation theorem, and the approximation error is compensated by adding an adaptive complementary term to the proposed AFSMC. The fuzzy inference approach based on the extended single input rule modules is proposed to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are obtained by using the weighted least squares estimator and its simplified one. It is proved that under some conditions the estimation errors will remain in the vicinity of zero as time increases, and the states are ultimately bounded subject to the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of a simple numerical system.     

Convergence analysis for reduced-order adaptive controller design of uncertain SISO linear systems with noisy output measurements

We consider in this article a class of uncertain SISO linear systems that are subject to system and measurement noises. Reduced-order adaptive controller designs have been proposed before for such systems by the authors and stability analysis of the closed-loop systems has been established. Here we analyse, further, the robustness properties for these reduced-order adaptive control systems by providing detailed convergence analysis results for the key closed-loop signals and parameter estimates. We rigorously prove that, whenever the exogenous disturbance input is of finite energy and bounded, and the reference trajectory and its derivatives up to rth order are bounded, r being the relative degree of the transfer function of the true system, a set of signals, including the tracking error, the estimation error between the system output and its estimate, the projection signal, are of finite energy and converge to zero; and the system states and their estimates exhibit asymptotic behaviours with certain formats. With an additional persistency of excitation condition, it is also proved that the estimate and the worst-case estimate of the state vector asymptotically track the actual state vector; and the estimate and the worst-case estimate of the unknown parameter vector converge to the true value. A numerical example is given to illustrate the theoretical findings.     

Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes

A moving-horizon state estimation problem is addressed for a class of nonlinear discrete-time systems with bounded noises acting on the system and measurement equations. As the statistics of such disturbances and of the initial state are assumed to be unknown, we use a generalized least-squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding-window strategy. For the resulting estimator, the existence of bounding sequences on the estimation error is proved. In the absence of noises, exponential convergence to zero is obtained. Moreover, suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value. The approximate solution can be determined either on-line by directly minimizing the cost function or off-line by using a nonlinear parameterized function. Simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended Kalman filter.     

A flat-zone modification for robust adaptive control of nonlinearoutput feedback systems with unknown high-frequency gains

This note deals with adaptive control of perturbed nonlinear output feedback systems with unknown high-frequency gains. The disturbances in the systems are assumed to be bounded, but the bounds are unknown. A flat-zone modification is proposed to incorporate both the bound estimation and Nussbaum gain design in the nonlinear adaptive control. To ensure the differentiability of stabilizing functions needed for backstepping design, high order terms are introduced in the Lyapunov function candidate with a flat zone around the neighborhood of the origin. The output tracking error converges to an arbitrarily small interval around zero     

非线性互联系统的分散混合自适应智能控制

针对一类高阶互联MIMO非线性系统，利用TS模糊系统和神经网络的通用逼近能力，在神经网络控制器中引入模糊基函数，提出一种分散混合自适应智能控制器设计的新方案．基于等价控制思想，设计分散自适应控制器，无需计算TS模型．通过对不确定项进行自适应估计，取消了其存在已知上界的假设．通过理论分析，证明了闭环智能控制系统所有信号有界，跟踪误差收敛到零．     

Adaptive rejection of multi-periodic disturbances for a class of linear systems

This paper deals with adaptive rejection of general multi-periodic disturbances for a class of linear systems via output feedback. The multi-periodic disturbance is a superposition of several general periodic disturbances. Assume that all periods of the multi-periodic disturbance are known. A method of estimating the multi-periodic disturbance and its derivatives is presented, which can ensure these estimate errors converge to zero. Based on these estimation methods, we present a new adaptive control method for disturbance rejection, which guarantees that in the closed-loop system, all the signals are bounded and the output converges to zero. A simulation example is presented to verify the effectiveness of the control scheme.     

Composite Adaptive Control of Uncertain Euler‐Lagrange Systems with Parameter Convergence without PE Condition

This work proposes a novel composite adaptive controller for uncertain Euler‐Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. The proposed adaptive controller ensures exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met. Simulation results corroborate the efficacy of the proposed technique and also establishes it's robustness property in the presence of unmodeled bounded disturbance.     

Robustness analysis of discrete-time indirect model reference adaptive control with normalized adaptive laws

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control (MRAC) with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter axe also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.     

Estimation of wiener nonlinear systems with measurement noises utilizing correlation analysis and Kalman filter

This paper is concerned with parameter estimation of Wiener systems with measurement noises employing correlation analysis method and adaptive Kalman filter. The presented Wiener system consists of two series blocks, that is, a dynamic block represented by auto-regressive moving average (ARMA) model, and static nonlinear block established by neural fuzzy model. Aim at estimating separately the two blocks, the separable signals are introduced. First, applying the separable signals to decouple the identification of linear dynamic block from that of static nonlinear block, then ARMA model parameters are estimated employing correlation function-based least squares principle. Moreover, aiming at handle with error caused by colored measurement noise, adaptive Kalman filter technique and cluster method are introduced to estimate parameter of the nonlinear block and noises model, enhancing parameter estimation precision. The accuracy and applicability of estimated scheme presented are verified through numerical simulation and nonlinear process, the results demonstrate that it is feasible for estimating the Wiener systems in the presence of colored measurement noises.     

含有有色噪声的非线性分数阶系统自适应扩展卡尔曼滤波器

研究了含有未知参数的情况下，分别含有分数阶有色过程噪声和有色测量噪声的连续时间非线性分数阶系统状态估计问题.采用Grünwald-Letnikov （G-L）差分方法和1阶泰勒展开公式，对描述连续时间非线性分数阶系统的状态方程进行离散化和线性化.构造由状态量、未知参数和分数阶有色噪声的增广向量，设计自适应分数阶扩展卡尔曼滤波算法实现对有色噪声情况下的连续时间非线性分数阶系统的状态和参数的估计.最后，通过分析两个仿真实例，验证了提出算法的有效性.     

Adaptive sliding mode control for a class of uncertain discrete-time systems using multi-rate output measurement

This article is concerned with the design of an adaptive sliding mode control (SMC) for a class of uncertain discrete-time systems using the multi-rate output measurement. The states of the discrete-time systems are assumed to be taken in the multi-rate output measurement by the contamination with measurement noise. The uncertainties are assumed not to satisfy the matching condition, and are expressed in a parameterised form. A least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed in a batch form by using the noisy multi-rate output measurement. The proposed adaptive SMC is designed by using the sliding surface expressed as the linear state function and the estimates obtained from the LSE. It is proved that the estimation errors converge to zero as time tends to infinite, and the states of the system are bounded under the action of the proposed adaptive SMC. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.     

Adaptive Stabilization of a Class of Reaction–Diffusion Systems

This paper is concerned with adaptive stabilization of a class of reaction–diffusion systems governed by a nonlinear partial differential equation of the first order in time but the fourth order in space. In the presence of bounded deterministic disturbances, the adaptive stabilizer is constructed by the concept of high-gain nonlinear output feedback and the estimation mechanism of the unknown parameters. In the control system the global asymptotic stability and the convergence of the system state to zero will be guaranteed.     

Partial-period adaptive repetitive control by symmetry

This paper presents a partial-period adaptive repetitive control method for a class of periodically time-varying nonlinear systems. To reduce the size of memory usage, the symmetric feature of periodic parameters is explored to form partial-period adaptation mechanisms. Both Half- and quarter-period adaptation strategies are proposed, and characterized analytically. The stability of the closed-loop system with each repetitive control is established, along with tracking error convergence to zero. In addition, the saturated-adaptation is suggested for providing bounded estimation.     

Dynamic surface active fault tolerant control design for the attitude control systems of UAV with actuator fault

In this paper, an active fault tolerant control (FTC) approach based on transient performance index is proposed for the attitude control systems of unmanned aerial vehicle (UAV) with actuator fault. The nonlinear attitude control system model for UAV with actuator faults is given, which represents the dynamic characteristics of UAV. A fault diagnosis component is used for fault detection and estimation. According to the fault estimation information obtained during the fault diagnosis, the fault tolerant control scheme is developed by adopting the adaptive dynamic surface control technique, which guarantees the asymptotic output tracking and ultimate uniform boundedness of the closed-loop attitude control systems of UAV in actuator faulty case. Further, a prescribed transient performance of the FTC attitude control systems is considered which characterizes the convergence rate and maximum overshoot of the attitude tracking error. Finally, simulation results are shown that the attitude control system states remain bounded and the output tracking errors converge to a neighborhood of zero.     

Cooperative control with distributed gain adaptation and connectivity estimation for directed networks

This paper addresses the problem of how to achieve superior performance by adaptively and distributively adjusting control gains of a cooperative control system. It is shown that according to distributed observations of changing network topologies and on the basis of online estimation of network connectivity, cooperative controls with adaptive gains can be synthesized to making the time derivative of the cooperative control Lyapunov function more negative and hence to improve stability and convergence of the overall system. For undirected networks, the proposed adaptive design reduces to improving the Fiedler eigenvalue (algebraic connectivity) as well as other eigenvalues. On the other hand, connectivity of a directed network is characterized by the property of the first left eigenvector(s) associated with its dominant eigenvalue, and in this paper, a distributed high‐gain observer design is proposed for each of the networked systems to utilize the same communication network among the systems. It is shown that even in the presence of transmission delays, the distributed estimators converge fast to the first left eigenvector(s) of the network. In addition, the expected consensus value(s) of the overall cooperative system under control is also estimated in a distributive manner. Rigorous analysis is carried out on estimation convergence and observer gain selection. It is shown that the proposed estimation and adaptive control designs are fully distributed, have guaranteed performance for all possible varying topologies as long as their dwelling times are bounded away from zero, and are robust with respect to excessively fast topology changes. Simulation results are included to demonstrate effectiveness of the proposed estimation and control schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

New results on explicit adaptive control design for nonlinear systems with polynomial conditions

This paper discusses the adaptive control problem for a class of nonlinear systems with polynomial growing conditions. By introducing a Lyapunov function which carries the quadratic terms and higher‐order terms of the transformed variables and constructing an appropriate dynamic gain, a new control strategy is presented to design an adaptive controller using only one parameter estimation. Compared with the existing results, the presented method avoids the over‐parameterization and significantly simplifies the control design. A modified version of the method which adopts no parameter estimation is also provided. It shows that all the signals of the closed‐loop system are bounded and the solution of the original system converges to zero. A simulation example is given to show the validness of the method.