Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.     

近空间飞行器的多模型切换控制

针对受到扰动的变机翼后掠角近空间飞行器,研究一类基于多模型切换的多输入多输出非线性系统的模糊自适应鲁棒控制器的设计问题.通过构造公共Lyapunov函数设计系统的控制器,采用动态面控制方法避免了控制器设计中的计算膨胀问题,利用自适应模糊系统和鲁棒控制项在线消除系统中的未知干扰影响.仿真结果表明了该方法的有效性.     

Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems

This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.     

一类非线性非最小相位系统的直接自适应控制

针对一类不确定的离散时间非线性非最小相位动态系统,提出了一种基于神经网络和多模型的直接自适应控制方法．该控制方法由线性直接自适应控制器,神经网络非线性直接自适应控制器以及切换机构组成．线性控制器用来保证闭环系统输入输出信号有界,非线性控制器用来改善系统性能．切换策略通过对上述两种控制器的切换,保证闭环系统输入输出有界的同时,改善了系统性能．理论分析以及仿真结果表明了所提出的直接自适应控制方法的有效性．     

Global adaptive exponential stabilisation for nonlinear systems with multiple unknown control directions

In this paper, we address the global generalised exponential stabilisation problem for a class of lower-triangular systems with multiple unknown directions. Instead of the well-known Nussbaum-gain adaptive rule, a Lyapunov-based adaptive logic switching rule is proposed to seek the correct control directions for such systems. The main advantage of the proposed controller is that it can guarantee the global generalised exponential stability of closed-loop systems. Simulation examples are given to verify the effectiveness of the developed control approach.     

Direct adaptive fuzzy control for nonlinear systems with time-varying delays

This paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict-feedback systems with time-varying delays. Based on the Razumikhin function approach, a novel adaptive fuzzy controller is designed. The proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. Different from the existing adaptive fuzzy control methodology, the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems. As a result, the proposed adaptive controller has a simpler form and requires fewer adaptation parameters.     

Global adaptive control of nonlinearly parametrized systems

In this paper, we consider global adaptive control of nonlinearly parametrized systems in parametric-strict-feedback form. Unlike previous results, we do not require a priori bounds on the unknown parameters, which is as in the linear parametrization case. We also allow unknown parameters to be time-varying provided they are bounded. Our proposed adaptive controller is a switching type controller, in which the controller parameter is tuned in a switching manner via a switching logic. Global stability results of the closed-loop system have been proved.     

Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems

In this paper, we address the problem of neural networks (NNs) stabilization and disturbance rejection for a class of nonlinear switched impulsive systems. An adaptive NN feedback control scheme and an impulsive controller for output tracking error disturbance attenuation of nonlinear switched impulsive systems are given under all admissible switched strategy based on NN. The NN is used to compensate for the nonlinear uncertainties of switched impulsive systems, and the approximation error of NN is introduced to the adaptive law in order to improve the tracking attenuation quality of the switched impulsive systems. Impulsive controller is designed to attenuate effect of switching impulse. Under all admissible switching law, impulsive controller and adaptive NN feedback controller can guarantee asymptotic stability of tracking error and improve disturbance attenuation level of tracking error for the overall nonlinear switched impulsive system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control and stabilization methods.     

Globally Stable Adaptive Tracking Control for Uncertain Strict‐Feedback Systems Based on Neural Network Approximation

This paper addresses the problem of globally stable adaptive neural tracking control for a class of strict‐feedback nonlinear systems. Compared with the existing works, the salient properties of the proposed scheme are given as follows. First, a novel switching controller is developed, which consists of a traditional adaptive neural controller and an extra robust controller to pull back the transient outside of the approximation domain. Second, only two adaptive parameters need to be tuned online, and the computational burden is considerably alleviated in practice. Third, to design the desired switching controller via the backstepping technique, a novel switching function, which has continuous derivatives up to the nth order, is constructed. It is shown that the system output converges to a small neighborhood of the reference signal and the closed‐loop system is globally stable. Finally, an example is provided to verify the effectiveness of the proposed control method.     

Design of an adaptive terminal sliding‐function controller for nonlinear multivariable systems

This paper presents an adaptive terminal sliding‐function controller approach for controlling a class of nonlinear multivariable systems with uncertainty. An appropriate terminal sliding function (TSF) is designed and then applied to the control law. Based on the Lyapunov stability theory, the adaptive terminal sliding‐function controller for nonlinear multivariable systems guarantees that the TSF is asymptotically convergent. Different from classical terminal sliding mode control, which uses a discontinuous switching control law, the TSF control uses a continuous TSF and thus avoids the chattering problem. The simulation results demonstrate that the proposed method achieves satisfactory stability. Copyright © 2013 John Wiley & Sons, Ltd.     

Switching adaptive output-feedback control of nonlinearly parametrized systems

In this paper, we consider global adaptive output-feedback control of nonlinear systems in output-feedback form, with unknown parameters entering nonlinearly. Such unknown parameters are not required to lie in a known compact set. Our proposed adaptive output-feedback controller is a switching-type controller, in which the controller parameter is tuned in a switching manner via a switching logic. Global stability results of the closed-loop system have been proved.     

Synchronization of Multi-links Memristor-Based Switching Networks Under Uniform Random Attacks

A variety of influence factors are common to the support networks which are used as cyber-physical systems. In this paper, we consider the problem of finite-time and exponential synchronization for the memristor-based switching networks (MSNs) with multi-links and multiple time-varying delays under uniform random attacks via asymptotic controller and adaptive controller. We propose a more general system model and utilize an analytical method which is different from the classical analytical techniques like set-valued mappings technique and differential inclusions to preprocess the MSNs to a class of switching networks with some uncertain parameters. Then, based on appropriate Lyaponov functionals and linear matrix inequality, several useful criteria ensuring the finite-time synchronization or asymptotic synchronization of MSNs with multi-links and time-varying delays under uniform random attacks via designed control law are obtained. Finally, two numerical examples are designed to show the feasibility and the correctness of our proposed results.     

Nonlinear adaptive control for power integrator triangular systems by switching linear controllers

In this paper, a nonlinear adaptive stabilizer is designed for a class of power integrator triangular systems with the following four features: (i) the chained integrators have the powers of positive odd numbers, which makes the linearization of the studied system uncontrollable; (ii) the nonlinear function contains the virtual control variables; (iii) the bound of the nonlinear parameters entering the function nonlinearity is not required to be known a priori; and (iv) there exists an unknown control coefficient with the unknown bound in the control channel. Our proposed adaptive controller is a switching type controller, in which the designed adaptive stabilizer takes a two‐step procedure: a linear stabilizing controller containing the tuning gains is first designed by the adding a power integrator technique. Switching logic is then proposed to tune online the gains in a switching manner. The proposed adaptive controller globally asymptotically stabilizes the considered system in the sense that, for any initial conditions, the state converges to the origin while all the signals of the closed‐loop system are bounded. Simulation studies clarify and verify the approach. Copyright © 2014 John Wiley & Sons, Ltd.     

一种新型滑模控制器设计及仿真

对于一类非线性不确定系统,常规滑模控制器存在"抖振"现象和抗外部扰动作用不理想等问题.本文运用自适应模糊系统逼近滑模控制器参数,并引入一个自适应模糊参数连续逼近常规滑模控制器的开关函数,最后给出一种新型自适应模糊滑模控制器,该方法克服函数和边界层法的不足.仿真实验结果表明该方法增强非线性系统的抗干扰能力和鲁棒性,并大大地削弱系统的"抖振"现象.     

基于切换的多模型二阶段自适应控制器设计

针对一类具有参数跳变特性的离散时间系统,设计一类基于切换策略的新型多模型二阶段自适应控制器.该控制器首先将系统不确定参数的变化空间划分为多个子空间,在每个空间内建立多个自适应模型.为了克服多模型退化,保持模型的多样性以应对参数跳变,采用带约束的二阶段自适应方法对未知参数进行实时估计,并据此设计相应的子控制器;然后基于切换策略,选取该时刻的最优子控制器作为系统的控制器,从而减小系统暂态误差,提高系统动态性能;最后进行数值仿真研究,仿真结果表明该控制器结合了切换机制和二阶段自适应的优点,在相同模型数量的情况下,能够快速逼近参数跳变以后系统新的工作点,显著地缩短系统的过渡过程,提高暂态性能.     

Adaptive output feedback tracking control for a class of uncertain switched nonlinear systems under arbitrary switching

This paper investigates the problem of adaptive output feedback tracking for uncertain switched nonlinear systems, under arbitrary switching. First, an adaptive output feedback controller is designed, which ensures the boundedness of all the closed-loop signals. Then, a novel adaptive-based robust output feedback control is proposed to drive the tracking error to zero, in which the bound of disturbances is not required to be known in advance. Both control algorithms are based on the common Lyapunov function method, without any restrictions on dwell time. To evaluate the performance of the proposed output feedback control schemes, a numerical example is presented and discussed.     

任意切换下高能随机系统的神经网络预设控制

针对一类不确定高能随机非线性系统,开展自适应神经网络backstepping控制研究,并保证在任意切换信号下的预设跟踪性能.该高能系统假定系统动态和任意切换信号未知.首先,利用预设性能控制,保证跟踪控制性能;其次,RBF神经网络用来克服未知系统动态,仅用到单一自适应更新参数,从而克服过参数问题;最后,基于公共的Lyapunov稳定性理论提出自适应神经网络控制策略,并减少了学习参数.最终结果表明所设计的公共控制器能保证所有闭环信号半全局最终一致有界,并能在任意切换下保证预设的跟踪性能.仿真结果进一步表明所提出方法的有效性.     

Switching control of linear systems subject to asymmetric actuator saturation

In this paper, we study the saturation control problem for linear time-invariant (LTI) systems subject to asymmetric actuator saturation under a switching control framework. The LTI plant with asymmetric saturation is first transformed to an equivalent switched linear model with each subsystem subject to symmetric actuator saturation, based on which a dwell-time switching controller augmented with a controller state reset is then developed by using multiple Lyapunov functions. The controller synthesis conditions are formulated as linear matrix inequalities (LMIs), which can be solved efficiently. Simulation results are also included to illustrate the effectiveness and advantages of the proposed approach.     

Robust adaptive control for interval time-delay systems

1 Introduction The problem of time-delay is commonly encountered in various engineering systems, such as electric, pneumatic and hydraulic networks, long transmission lines, etc., and it is also a great source of systems instability and poor perfor- mance. During the last decades, we have seen an increasing interest for the control of this class of systems and many results have reported in the literature [1～5]. On the other hand, it has been recognized that nonlinear uncertainties are unavoid…     

Robust adaptive neuro-fuzzy control of uncertain nonholonomic systems

In this paper, we present an adaptive neuro-fuzzy controller design for a class of uncertain nonholonomic systems in the perturbed chained form with unknown virtual control coefficients and strong drift nonlinearities. The robust adaptive neuro-fuzzy control laws are developed using state scaling and backstepping. Semiglobal uniform ultimate bound-edness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neigh-borhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. By using fuzzy logic approximation, the proposed control is free of control singularity problem. An adaptive control-based switching strategy is proposed to overcome the uncontrollability problem associated with x 0 (t 0 ) = 0.