Single-approximation-based adaptive control of a class of nonlinear time-delay systems

This paper presents a simple adaptive control approach for uncertain strict-feedback nonlinear systems with unknown time-varying delays. All nonlinear functions and time delays in the systems are assumed to be unknown. Compared with the existing works, the contribution of this study is the design of a simple adaptive control law using single function approximator, without the implementation of virtual controllers derived from the backstepping design procedure. Unlike the existing backstepping methods, virtual controllers are only used as intermediate signals for designing the actual control. Therefore, the proposed control scheme is simpler than the existing methods for strict-feedback time-delay systems because the problems of using multiple approximators and calculating virtual controllers are eliminated. In addition, it is shown that all signals in the closed-loop system are uniformly ultimately bounded.     

Adaptive fuzzy dynamic surface control for a class of perturbed nonlinear time-varying delay systems with unknown dead-zone

In this paper,adaptive dynamic surface control(DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone.Fuzzy logic systems are used to approximate the unknown nonlinear functions.Then,by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach,the adaptive fuzzy tracking controller is designed.Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing backstepping-based methods.The main advantages of our approach include:1) for the n-th-order nonlinear systems,only one parameter needs to be adjusted online in the controller design procedure,which reduces the computation burden greatly.Moreover,the input of the dead-zone with only one adjusted parameter is much simpler than the ones in the existing results;2) the proposed control scheme does not need to know the time delays and their upper bounds.It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound,Finally,simulation results demonstrate the effectiveness of the proposed approach.     

Adaptive Neural Network-Based Control for a Class of Nonlinear Pure-Feedback Systems With Time-Varying Full State Constraints

In this paper, an adaptive neural network (NN) control approach is proposed for nonlinear pure-feedback systems with time-varying full state constraints. The pure-feedback systems of this paper are assumed to possess nonlinear function uncertainties. By using the mean value theorem, pure-feedback systems can be transformed into strict feedback forms. For the newly generated systems, NNs are employed to approximate unknown items. Based on the adaptive control scheme and backstepping algorithm, an intelligent controller is designed. At the same time, time-varying Barrier Lyapunov functions (BLFs) with error variables are adopted to avoid violating full state constraints in every step of the backstepping design. All closedloop signals are uniformly ultimately bounded and the output tracking error converges to the neighborhood of zero, which can be verified by using the Lyapunov stability theorem. Two simulation examples reveal the performance of the adaptive NN control approach.      

Adaptive robust stabilisation of uncertain nonlinear dynamical systems: an improved backstepping approach

The main purpose of this paper is to propose a design approach by which some simple adaptive robust controllers can be synthesised for a class of uncertain nonlinear dynamical systems which can be transformed into uncertain strict-feedback nonlinear systems. In this paper, an improved backstepping design approach is presented to synthesising a class of continuous adaptive robust state-feedback controllers with a rather simple structure. The improved backstepping design approach can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm. In particular, it is not required to know the nonlinear upper bound functions of uncertainties. In the light of the presented approach, the state-feedback controllers can be constructed to be linear in the state, with the time-varying control gains which can be self-tuned by the adaptive laws. Similar to the conventional backstepping algorithm, the improved backstepping approach can be extended to a rather large class of uncertain nonlinear systems, and by combining the improved backstepping approach with other control methods, it may be expected to obtain a number of interesting results.     

Prescribed performance adaptive neural tracking control for strict-feedback Markovian jump nonlinear systems with time-varying delay

A prescribed performance adaptive neural tracking control problem is investigated for strict-feedback Markovian jump nonlinear systems with time-varying delay. First, a new prescribed performance constraint variable is proposed to generate the virtual control that forces the tracking error to fall within prescribed boundaries. Combining with the approximation capability of neural networks and backstepping design, the adaptive tracking controller is designed. The designed controller is independent on time delay by constructing appropriate Lyapunov functions to offset the unknown time-varying delays. It is proved that the closed-loop system is uniformly ultimately bounded in probability, and that both steady-state and transient-state performances are guaranteed. Finally, simulation results are given to illustrate the effectiveness of the proposed approach.     

Nussbaum gain adaptive fuzzy control for switched nonlinear systems with predefined output and full time-varying states constraints

In this paper, the problem of adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with unknown control direction is studied. Aiming at the problem, an adaptive control scheme with Nussbaum gain technology is constructed by using the average dwell time (ADT) method and the backstepping method to overcome the unknown control direction, and time-varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure the full-state constraints satisfaction. The proposed control scheme guarantees that all closed-loop signals remain bounded under a class of switching signals with ADT, while the output tracking error converges to a small neighborhood of the zero. An important innovation of this design method is that the unknown control direction, asymmetric time-varying full state constraints, and predefined time-varying output requirements are simultaneously considered in uncertain switched nonlinear systems for the first time. We set a moment in advance, and make the systems comply with the constraint conditions before running the moment by the shift function nested in the first time-varying ABLF. Finally, a simulation example verifies the effectiveness of the proposed scheme.     

Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.     

Tuning functions‐based robust adaptive tracking control of a class of nonlinear systems with time delays

In this paper, an adaptive backstepping tracking control scheme is proposed for a class of nonlinear state time‐varying delay systems, which are subject to parametric uncertainties and external disturbances. The bounds of the time delays and their derivatives are assumed to be unknown. Tuning functions method is exploited to construct the control law and adaptive laws. Unknown time‐varying delays are compensated by using appropriate Lyapunov–Krasovskii functional. It is shown that the proposed controller can guarantee the boundedness of all the closed‐loop signals. The tracking performance can be adjusted by choosing suitable design parameters. At the end, a simulation example is provided to illustrate the effectiveness of the design procedure. Copyright © 2011 John Wiley & Sons, Ltd.     

Fuzzy adaptive output feedback control for a class of switched non-triangular structure nonlinear systems with time-varying delays

This paper investigates an adaptive fuzzy output feedback control design problem for switched nonlinear system in non-triangular structure form. The discussed system contains unknown nonlinear dynamics, unmeasured states and unknown time-varying delays under a batch of switching signals. Fuzzy logic systems are utilised to learn unknown nonlinear dynamics and construct a fuzzy switched nonlinear observer. By combining the property of fuzzy basis function with Lyapunov–Krasovskii functional and the command filter, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the closed-loop control system is proved via Lyapunov stability theory and average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme.     

控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.     

控制方向未知的时变非线性系统鲁棒控制

针对一类具有未知时变控制方向、不确定时变参数以及未知时变有界干扰的严反馈非线性系统,给出一种带有死区修正算法的鲁棒控制方法.在控制系数符号未知的情况下,通过在反步法中引入Nussbaum增益和死区修正技术,得到一种修正的鲁棒反步设计方法.该方法不需要未知时变控制系数的上下界先验知识以及不确定参数和外界干扰的上界信息.算法保证了闭环系统所有信号的有界性,同时使得跟踪误差收敛于零的任意小邻域内.     

Adaptive neural control for pure-feedback nonlinear time-delay systems with unknown dead-zone: a Lyapunov-Razumikhin method

This paper addresses the problem of adaptive neural control for a class of uncertain pure-feedback nonlinear systems with multiple unknown state time-varying delays and unknown dead-zone. Based on a novel combination of the Razumikhin functional method, the backstepping technique and the neural network parameterization, an adaptive neural control scheme is developed for such systems. All closed-loop signals are shown to be semiglobally uniformly ultimately bounded, and the tracking error remains in a small neighborhood of the origin. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control schemes.     

Distributed fuzzy adaptive event-triggered finite-time consensus tracking control for uncertain nonlinear multi-agent systems with asymmetric output constraint

This article investigates the consensus problem for uncertain nonlinear multi-agent systems (MASs) with asymmetric output constraint. Different from BLF-based constraint consensus tracking control, a novel approach based on nonlinear state-dependent function is proposed to solve the asymmetric output constraint, which need not convert output constraint into tracking error bound. First-order sliding mode differentiator is incorporated into each step of backstepping control design to reduce computation burden. Further, in combination of proposed event-triggered mechanism based on time-varying threshold, a distributed fuzzy adaptive event-triggered finite-time consensus method is developed. It can ensure that the consensus tracking error tends to a small neighbor in a finite time and the asymmetric output constraint of each subsystem is not violated. Two simulations are given to demonstrate the effectiveness of control method.     

Robust control for disturbed buck converters based on two GPI observers

The output voltage tracking problem of a disturbed buck converter is investigated in this paper via a GPI observer-based approach. Control performances of the converters are always influenced by undesirable effects of disturbances. These disturbances usually are of time-varying forms. Conventional backstepping schemes cannot achieve satisfactory performances in handling time-varying disturbances. By adding integral actions into the controller, only the slow-varying disturbances are asymptotically compensated in this way. In this paper, two GPI observers are constructed to estimate the lumped time-varying disturbances. By introducing the disturbance estimations into the design process, a composite GPI observer-based robust control scheme is developed. The proposed algorithm performs a promising disturbance rejection ability. Rigorous stability is guaranteed. Experimental results in the presence of time-varying disturbances are illustrated to show the feasibility of the proposed composite method.     

Observer-based adaptive fuzzy tracking control for a class of MIMO nonlinear systems with unknown dead zones and time-varying delays

The adaptive tracking control strategy is investigated for a class of multi-input and multi-output pure-feedback nonlinear delayed systems with unknown dead-zone inputs. This problem is challenging due to the existence of unknown dead zones, time-varying delays and unavoidable state variables. By constructing fuzzy approximators and state observers, the difficulties from unknown nonlinearities and unavailable state variables are surmounted, respectively. Lyapunov–Krasovskii functions are introduced to deal with the time-varying delays. The adaptive controllers are designed by a backstepping method and adaptive technique so that the closed-loop systems remain stable and the target signals can be tracked within a small error as well. At last, two examples are provided to show the effectiveness of the proposed scheme.     

基于S类函数的严格反馈非线性周期系统的自适应控制

针对一类严格反馈非线性周期系统, 在周期非线性可时变参数化的条件下设计自适应控制器. 通过将周期时变参数展开成傅里叶级数, 并采用微分自适应律估计未知系数, 进行控制器反推设计. 引入S类函数, 并在控制器设计中应用S类函数处理截断误差项对系统跟踪性能的影响, 同时, S类函数能确保虚拟控制的可微. 给出几种不同的S类函数设计, 分析比较将其应用于控制器设计时产生的不同效果. 理论分析与仿真结果表明, 提出的控制方法能够实现系统输出跟踪期望轨迹, 且闭环系统所有信号有界.     

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     

时变时滞非线性系统自适应神经网络控制

对于一类具有未知时变时滞和虚拟控制系数的不确定严格反馈非线性系统,基于后推设计提出一种自适应神经网络控制方案.选取适当的Lyapunov-Krasovskii泛函补偿未知时变时滞不确定项.通过构造连续的待逼近函数来解决利用神经网络对未知非线性函数进行逼近时出现的奇异问题.通过引入一个新的中间变量,保证了虚拟控制求导的正确性.仿真算例表明,所设计的控制器能保证闭环系统所有信号是半全局一致终结有界的,且跟踪误差收敛到零的一个邻域内.     

Adaptive output-feedback regulation for nonlinear delayed systems using neural network

A novel adaptive neural network （NN） output-feedback regulation algorithm for a class of nonlinear time-varying timedelay systems is proposed. Both the designed observer and controller are independent of time delay. Different from the existing results, where the upper bounding functions of time-delay terms are assumed to be known, we only use an NN to compensate for all unknown upper bounding functions without that assumption. The proposed design method is proved to be able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed system, and the system output is proved to converge to a small neighborhood of the origin. The simulation results verify the effectiveness of the control scheme.     

非线性时滞系统基于降阶观测器的反步镇定控制

针对一类状态未知的非线性严格反馈时滞系统, 本文提出了一种基于静态增益函数的输出反馈控制方案. 首先构造了降阶观测器以估计非线性系统的未知状态. 然后在Backstepping设计的每一步定义了具有控制增益函数 的新型Lyapunov-Krasovskii泛函以补偿未知时变时滞, 定义新的选择不唯一的连续控制增益函数以补偿非匹配项 以及Lyapunov-Krasovskii泛函补偿时滞时产生的非负项. 提出了一种无记忆输出反馈控制方案. 理论分析表明: 该 控制方案消除了未知时滞的影响, 保证了闭环系统所有信号的有界性, 并使系统实现渐近稳定. 最后仿真结果验证 了此控制方案的有效性.