基于预设性能的非仿射非线性系统自适应有限时间控制

针对一类具有死区的非仿射非线性系统,将预设性能控制与有限时间控制相结合,提出一种具有预设性能的自适应有限时间跟踪控制方法.基于Backstepping技术、模糊逻辑系统及有限时间Lyapunov稳定理论,给出使系统半全局实际有限时间稳定(semi-globally practically finite-time stable,SGPFS)的充分条件和设计步骤.该控制策略不仅使系统的输出误差在有限时间内收敛到一个预先设定区域,同时保证其收敛速度、最大超调量和稳态误差均满足预先设定的性能要求.最后通过仿真示例验证了所提出设计方法的有效性.     

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

This work considers an input and output constraint control problem for pure‐feedback systems with nonaffine functions possibly being in‐differentiable. A locally semibounded and continuous condition for nonaffine functions is presented to guarantee the controllability, and the nonaffine system is transformed to an equivalent pseudoaffine one based on the mild condition. Combined with backstepping technique, a novel prescribed performance controller with new performance functions is constructed to circumvent high frequency chattering in control input. An auxiliary system with bounded compensation term is utilized in this paper, successfully avoiding the overrun of control input. The methodology achieves the desired transient and steady‐state performance and presents excellent robustness against the system uncertainty. Finally, two numerical simulations are performed to demonstrate the effectiveness of the proposed approach.     

Robust decentralized adaptive fuzzy control for a class of large‐scale MIMO nonlinear systems

In this paper, a novel decentralized robust adaptive fuzzy control scheme is proposed for a class of large‐scale multiple‐input multiple‐output uncertain nonlinear systems. By virtue of fuzzy logic systems and the regularized inverse matrix, the decentralized robust indirect adaptive fuzzy controller is developed such that the controller singularity problem is addressed under a united design framework; no a priori knowledge of the bounds on lumped uncertainties are being required. The closed‐loop large‐scale system is proved to be asymptotically stable. Simulation results confirmed the validity of the approach presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive fuzzy output feedback decentralized control of pure‐feedback nonlinear large‐scale systems

In this paper, an adaptive fuzzy decentralized output feedback control approach is presented for a class of uncertain nonlinear pure‐feedback large‐scale systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the immeasurable states. On the basis of the adaptive backstepping recursive design technique, an adaptive fuzzy decentralized output feedback is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded (SUUB), and that the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive decentralized fault‐tolerant tracking control for large‐scale nonlinear systems with input quantization

In this paper, an adaptive decentralized tracking control scheme is designed for large‐scale nonlinear systems with input quantization, actuator faults, and external disturbance. The nonlinearities, time‐varying actuator faults, and disturbance are assumed to exist unknown upper and lower bounds. Then, an adaptive decentralized fault‐tolerant tracking control method is designed without using backstepping technique and neural networks. In the proposed control scheme, adaptive mechanisms are used to compensate the effects of unknown nonlinearities, input quantization, actuator faults, and disturbance. The designed adaptive control strategy can guarantee that all the signals of each subsystem are bounded and the tracking errors of all subsystems converge asymptotically to zero. Finally, simulation results are provided to illustrate the effectiveness of the designed approach.     

基于Backstepping 的非仿射非线性系统鲁棒控制

针对一类不确定非仿射非线性系统的跟踪控制问题, 提出一种鲁棒Backstepping 控制策略. 首先, 为利用仿 射非线性方法设计控制器, 给出一种适用于全局的非仿射非线性近似方法; 然后, 设计快速收敛非线性微分器以估计复合干扰和获取虚拟信号的微分, 进而给出不确定非仿射非线性系统的复合控制器, 其中鲁棒项和阻尼项分别用于减少逼近误差和近似方法中动态误差对系统跟踪的影响; 最后, 通过仿真实验验证了所提出方法的有效性.     

Supervisory switching‐based prescribed performance control of unknown nonlinear systems against actuator failures

This article studies the fault‐tolerant control problem for unknown nonlinear strict‐feedback systems subject to actuator failures yet with dynamic redundancies. The prescribed performance control methodology is newly combined with a modification‐based supervisory switching strategy to solve the problem. To implement failure detection, the performance function is properly modified to synthesize a monitoring function to supervise the behavior of an error variable. Once a failure is detected, the current actuator is shut down and the backup actuator is switched in to execute the reconfigured control command. Compared with the existing results, (1) the postfailure and postswitching tracking performance is improved, other than uniform ultimate boundedness and (2) the dependence on extra robust control schemes (eg, adaptive or approximating structures) to deal with model uncertainties or the need to compute analytic derivatives of virtual control signals in the backstepping design is eliminated.     

Decentralized event‐triggered control of large‐scale nonlinear systems

This paper studies the decentralized event‐triggered control of large‐scale nonlinear systems. We consider a class of decentralized control systems that are transformable into an interconnection of input‐to‐state stable subsystems with the sampling errors as the inputs. The sampling events for each subsystem are triggered by a threshold signal, and the threshold signals for the subsystems are independent with each other for the decentralized implementation. By appropriately designing the event‐triggering mechanisms, it is shown that infinitely fast sampling can be avoided for each subsystem and asymptotic regulation is achievable for the large‐scale system. The proposed design is based on the ISS small‐gain arguments, and is validated by a benchmark example of controlling two coupled inverted pendulums.     

Adaptive fuzzy semi‐decentralized control for a class of large‐scale nonlinear systems with unknown interconnections

In this paper, a general method is developed to generate a stable adaptive fuzzy semi‐decentralized control for a class of large‐scale interconnected nonlinear systems with unknown nonlinear subsystems and unknown nonlinear interconnections. In the developed control algorithms, fuzzy logic systems, using fuzzy basis functions (FBF), are employed to approximate the unknown subsystems and interconnection functions without imposing any constraints or assumptions about the interconnections. The proposed controller consists of primary and auxiliary parts, where both direct and indirect adaptive approaches for the primary control part are aiming to maintain the closed‐loop stability, whereas the auxiliary control part is designed to attenuate the fuzzy approximation errors. By using Lyapunov stability method, the proposed semi‐decentralized adaptive fuzzy control system is proved to be globally stable, with converging tracking errors to a desired performance. Simulation examples are presented to illustrate the effectiveness of the proposed controller. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust approximation-free prescribed performance control for nonlinear systems and its application

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.     

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.     

Global decentralized sampled‐data output feedback stabilization for a class of large‐scale nonlinear systems with sensor and actuator failures

In this paper, we investigate global decentralized sampled‐data output feedback stabilization problem for a class of large‐scale nonlinear systems with time‐varying sensor and actuator failures. The considered systems include unknown time‐varying control coefficients and inherently nonlinear terms. Firstly, coordinate transformations are introduced with suitable scaling gains. Next, a reduced‐order observer is designed to estimate unmeasured states. Then, a decentralized sampled‐data fault‐tolerant control scheme is developed with an allowable sampling period. By constructing an appropriate Lyapunov function, it can be shown that all states of the resulting closed‐loop system are globally uniformly ultimately bounded. Finally, the validity of the proposed control approach is verified by using two examples.     

Adaptive dynamic surface control for uncertain nonaffine nonlinear systems

This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive NN output‐feedback decentralized stabilization for a class of large‐scale stochastic nonlinear strict‐feedback systems

In this paper, the decentralized adaptive neural network (NN) output‐feedback stabilization problem is investigated for a class of large‐scale stochastic nonlinear strict‐feedback systems, which interact through their outputs. The nonlinear interconnections are assumed to be bounded by some unknown nonlinear functions of the system outputs. In each subsystem, only a NN is employed to compensate for all unknown upper bounding functions, which depend on its own output. Therefore, the controller design for each subsystem only need its own information and is more simplified than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the whole closed‐loop system can be proved to be stable in probability by constructing an overall state‐quartic and parameter‐quadratic Lyapunov function. The simulation results demonstrate the effectiveness of the proposed control scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

This paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Arbitrary settling time control with prescribed performance for high-order nonlinear systems

This paper studies an arbitrary convergence time tracking controller design problem for high-order nonlinear systems. Our aim is to enhance the existing free-will arbitrary time control (FATC), which cannot track time-varying reference signals. To do so, a new nonautonomous equation is firstly introduced to enable an arbitrary settling time stability for one-order systems. Then, a prescribed performance control (PPC) technology is integrated for general high order systems. By a backstepping Lyapunov analysis with iteratively contructed nonautonomous equations, it is proved that the closed-loop system satisfies the prescribed performance and all signals of the closed-loop system are arbitrary settling time stable (ASTS). Compared with the existing results, the tracking control problem with arbitrary convergence time is addressed by a continuous control law, which shows a better transient performance also. Simulation results confirm the effectiveness of the proposed control method.     

Adaptive prescribed performance tracking control for strict‐feedback nonlinear systems with zero dynamics

This paper focuses on the adaptive tracking control problem for strict‐feedback nonlinear systems with zero dynamics via prescribed performance. Based on polynomial fitting, an adjustable performance function is firstly proposed, whose parameters can be adjusted in real time according to the tracking error. Furthermore, an adaptive prescribed performance tracking controller is constructed via the backstepping method, which guarantees that all the states in the closed‐loop system are bounded. Meanwhile, the output tracking error falls within an adjustable performance boundary and asymptotically converges to zero. Simulation comparison demonstrates the advantages of the developed controller as follows: (1) the parameters of the adjustable performance function are adjusted online according to the tracking errors for a faster convergent performance boundary; (2) the steady‐state performance of the system is further optimized simultaneously.     

Non-smooth state feedback prescribed performance control for interconnected nonlinear systems with unmodelled dynamics

This paper investigates the problem of non-smooth state feedback control for a group of high-order p-normal form interconnected nonlinear systems with prescribed performance. Each subsystem is in the form of triangular structure with the unmodelled dynamics. With the help of appropriate Lyapunov function, a state feedback controller is constructed via backstepping method. It is strictly proved that the closed-loop system is asymptotically stable and both transient and steady-state performances of the outputs are preserved. Finally, simulation results are presented to illustrate the effectiveness of proposed method.     

一类不确定非线性系统的预定性能自适应控制

本文研究了一类不确定严格反馈非线性系统的预定性能控制问题.为保证系统预定性能,引入了一个简单的障碍型Lyapunov函数.结合反推设计法,给出了一种新的自适应控制算法.理论与实验结果表明,所得控制器不仅保证了系统预定性能,且使得闭环系统所有信号有界.