MIMO非仿射非线性系统的自适应模糊控制

针对一类多输入多输出非仿射非线性系统,设计了一种自适应模糊H∞控制方案,该方案把自适应模糊控制和高增益观测器结合起来.利用多变量的隐函数定理,证明了非仿射系统控制器的存在性.通过设计高增益观测器,解决了系统的状态不可测量问题,实现系统的输出反馈控制,模糊自适应控制增强了系统在线逼近干扰及处理系统不确定的能力.仿真结果表明了控制方案的有效性及优越性.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Global tracking of nonlinear systems with simultaneous unknown time‐varying state and input delays

This paper presents the design of a robust control law for a class of nonlinear dynamical systems subjected to parametric uncertainty and simultaneous unknown, variable state and input delays. A novel controller is developed, which consists of a filtered tracking error and the integral of previous values of control input where the limits of integration are dependent on the known bound of the input delay. Lyapunov‐Krasovskii functionals–based stability analysis guarantees a global uniformly ultimately bounded tracking result where sufficient conditions on controller gains and maximum allowable delay are derived. The performance and robustness of the controller are evaluated by simulation on a two‐link robot manipulator for different combinations of time‐varying state and input delays.     

Adaptive output‐feedback tracking for nonlinear systems with rather general control coefficients

This paper studies the problem of global practical tracking by output feedback for a class of uncertain nonlinear systems with unmeasured state‐dependent growth and unknown time‐varying control coefficients. Compared with the closely related works, the remarkableness of this paper is that the upper and lower bounds of unknown control coefficients are not required to be known a priori. Motivated by our recent works, by combining the methods of universal control and deadzone with the backstepping technique and skillfully constructing a novel Lyapunov function, we propose a new adaptive tracking control scheme with appropriate design parameters. The new scheme guarantees that the state of the resulting closed‐loop system is globally bounded while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Two examples, including a practical example, are given to illustrate the effectiveness of the theoretical results.     

Adaptive output feedback regulation for a class of uncertain nonlinear systems

In this paper, the problem of global state regulation by output feedback is investigated for a class of uncertain nonlinear systems satisfying some relaxed upper‐triangular‐type condition. Using a linear dynamic gain observer with two dynamic gains and introducing two appropriate change of coordinates, we give a constructive design procedure for the linear‐like output feedback stabilizing controller. It is proved that the proposed controller globally regulates all the states of the uncertain system and maintains global boundedness of the closed‐loop system. An example is provided to demonstrate the effectiveness of the proposed design scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive event‐triggered global fast finite‐time control for a class of uncertain nonlinear systems

This article designs an adaptive event‐triggered controller to solve the problem of global finite‐time stabilization for a class of uncertain nonlinear systems. By using the symbol function technique, the event‐triggered error is completely compensated, the adaptive technique and the back‐stepping method are simultaneously applied to the controller design, and the new way of designing controller is completed on the basis of fast finite‐time stability theory. Subsequently, taking Lyapunov stability theorem into account, the system stability is proved, and the system is demonstrated by contradiction to be non‐zeno. Finally, giving a simulation example to display the feasibility of this method.     

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.     

Adaptive finite‐time fault‐tolerant tracking control for a class of MIMO nonlinear systems with output constraints

In this work, we present a novel adaptive finite‐time fault‐tolerant control algorithm for a class of multi‐input multi‐output nonlinear systems with constraint requirement on the system output tracking error. Both parametric and nonparametric system uncertainties can be effectively dealt with by the proposed control scheme. The gain functions of the nonlinear systems under discussion, especially the control input gain function, can be not fully known and state‐dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, finite‐time convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output tracking error will not be violated during operation. An illustrative example on a robot manipulator model is presented in the end to further demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.     

Adaptive quantized tracking control for uncertain switched nonstrict‐feedback nonlinear systems with discrete and distributed time‐varying delays

This paper is concerned with an adaptive tracking problem for a more general class of switched nonstrict‐feedback nonlinear time‐delay systems in the presence of quantized input. The system structure in a nonstrict‐feedback form, the discrete and distributed time‐varying delays, the sector‐bounded quantized input, and arbitrary switching behavior are involved in the considered systems. In particular, to overcome the difficulties from the distributed time‐varying delays and the sector‐bounded quantized input, the mean‐value theorem for integrals and some special techniques are exploited respectively. Moreover, by combining the Lyapunov‐Razumikhin method, dynamic surface control technique, fuzzy logic systems approximation, and variable separation technique, a quadratic common Lyapunov function is easily built for all subsystems and a common adaptive quantized control scheme containing only 1 adaptive parameter is proposed. It is shown that the tracking error converges to an adjustable neighborhood of the origin whereas all signals of the closed‐loop systems are semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to verify the feasibility and effectiveness of the proposed design methodology.     

Adaptive dynamic surface control for MIMO nonlinear time-varying systems with prescribed tracking performance

In this paper, an adaptive dynamic surface control scheme is proposed for a class of multi-input multi-output (MIMO) nonlinear time-varying systems. By fusing a bound estimation approach, a smooth function and a time-varying matrix factorisation, the obstacle caused by unknown time-varying parameters is circumvented. The proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step. Moreover, all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot. Such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Adaptive discrete neural observer design for nonlinear systems with unknown time‐delay

This paper focuses on the adaptive observer design for nonlinear discrete‐time MIMO systems with unknown time‐delay and nonlinear dynamics. The delayed states involved in the system are arguments of a nonlinear function and only the estimated delay is utilized. By constructing an appropriate Lyapunov–Krasovskii function, the delay estimation error is considered in the observer parameter design. The proposed method is then extended to the system with a nonlinear output measurement equation and the delayed dynamics. With the help of a high‐order neural network (HONN), the requirement for a precise system model, the linear‐in‐the‐parameters (LIP) assumption of the delayed states, the Lipschitz or norm‐boundedness assumption of unknown nonlinearities are removed. A novel converse Lyapunov technical lemma is also developed and used to prove the uniform ultimate boundedness of the proposed observer. The effectiveness of the proposed results is verified by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive output feedback control for a class of planar nonlinear systems

This paper is concerned with the problem of global adaptive stabilization by output feedback for a class of planar nonlinear systems with uncertain control coefficient and unknown growth rate. The control coefficient is not supposed to have known upper bound, and this relaxes the corresponding requirement in the existing literature (see e.g. 1 , 2 . First, by the universal control method, an observer is constructed based on the dynamic high‐gain K‐filters. Then, the control design procedure is developed to obtain the stabilizing controller and dynamic compensator for the uncertainties in the control coefficient. It is shown that the global stability of the closed‐loop system can be guaranteed by the appropriate choice of the design parameters. A simulation example is also provided to illustrate the correctness of the theoretical results. © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.     

Sliding mode adaptive control for a class of nonlinear time‐varying systems

In this work, the problem of designing a control scheme capable of controlling dynamical systems with unknown time‐varying parameters and disturbances is proposed. In contrast with other works, based on two techniques, ie, adaptive backstepping and sliding modes, an improved method that guarantees the output asymptotic tracking of a smooth reference signal, the stability of the closed‐loop system, and the identification errors' boundedness is developed. By means of sliding mode observers, the adaptation errors' required information is extracted and injected to adaptive laws. The behavior of the proposed control scheme is analyzed by the Lyapunov method. The performance of the proposed system is verified with an academic example.     

Adaptive logic‐based switching fault‐tolerant controller design for nonlinear uncertain systems

This paper deals with the problem of fault‐tolerant control (FTC) for a class of nonlinear uncertain systems against actuator faults using adaptive logic‐based switching control method. The uncertainties under consideration are assumed to be dominated by a bounding system which is linear in growth in the unmeasurable states but can be a continuous function of the system output, with unknown growth rates. Several types of common actuator faults, e.g., bias, loss‐of‐effectiveness, stuck and hard‐over faults are integrated by a unified fault model. By utilizing a novel adaptive logic‐based switching control scheme, the actuator faults can be detected and automatically accommodated by switching from the stuck actuator to the healthy or even partly losing‐effectiveness one with bias, in the presence of large parametric uncertainty. In particular, two switching logics for updating the gain in the output feedback controllers are designed to ensure the global stability of the nominal (fault‐free) system and the boundedness of all closed‐loop signals of the faulty system, respectively. Two simulation examples of an aircraft wing model and a single‐link flexible‐joint robot are given to show the effectiveness of the proposed FTC controller. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive decentralized finite‐time output tracking control for MIMO interconnected nonlinear systems with output constraints and actuator faults

In this work, we present a novel adaptive decentralized finite‐time fault‐tolerant control algorithm for a class of multi‐input–multi‐output interconnected nonlinear systems with output constraint requirements for each vertex. The actuator for each system can be subject to unknown multiplicative and additive faults. Parametric system uncertainties that model the system dynamics for each vertex can be effectively dealt with by the proposed control scheme. The control input gain functions of the nonlinear systems can be not fully known and state dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, with the use of graph theory, finite‐time convergence of the system output tracking error into a small set around zero is guaranteed for each vertex, while the time‐varying constraint requirement on the system output tracking error for each vertex will not be violated during operation. An illustrative example on 2 interacting 2‐degree‐of‐freedom robot manipulators is presented in the end to further demonstrate the effectiveness of the proposed control scheme.     

Adaptive output feedback stabilization for a class of nonlinear systems with inherent nonlinearities and uncertainties

This paper investigates the problem of adaptive stabilization by output feedback for a class of uncertain nonlinear systems. The distinguishing feature of such a class of systems is the presence of uncertain control coefficient and unmeasured states dependent growth with growth rate of polynomial‐of‐output multiplying an unknown constant. First, new high‐gain K‐filters with two dynamic gains are introduced, and an appropriate state observer is constructed based on the K‐filters. Then, motivated by the universal control idea, the backstepping scheme is successfully developed for the adaptive output feedback control design. By appropriate choice of the design parameters, the global stability of the closed‐loop system can be guaranteed. Finally, numerical simulations are provided to illustrate the correctness of the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Global tracking sliding mode control for a class of nonlinear systems via variable gain observer

A novel output‐feedback sliding mode control strategy is proposed for a class of single‐input single‐output (SISO) uncertain time‐varying nonlinear systems for which a norm state estimator can be implemented. Such a class encompasses minimum‐phase systems with nonlinearities affinely norm bounded by unmeasured states with growth rate depending nonlinearly on the measured system output and on the internal states related with the zero‐dynamics. The sliding surface is generated by using the state of a high gain observer (HGO) whereas a peaking free control amplitude is obtained via a norm observer. In contrast to the existing semi‐global sliding mode control solutions available in the literature for the class of plants considered here, the proposed scheme is free of peaking and achieves global tracking with respect to a small residual set. The key idea is to design a time‐varying HGO gain implementable from measurable signals. Copyright © 2010 John Wiley & Sons, Ltd.     

Practical time‐varying formation tracking for high‐order nonlinear multiagent systems with multiple leaders based on the distributed disturbance observer

Practical time‐varying formation tracking analysis and design problems for high‐order nonlinear multiagent systems with directed interaction topologies are investigated by using the distributed disturbance observer, where the time‐varying formation tracking error can be controlled within an arbitrarily small bound. Different from the previous work, there exists a predefined time‐varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the leaders can be multiple, and the dynamics of each follower has heterogeneous nonlinearity and disturbance. First, a distributed disturbance observer‐based practical time‐varying formation tracking protocol is constructed using neighboring relative information, where only a part of the followers, which are named as well‐informed ones, are required to obtain the information of the multiple leaders. The proposed protocol can process the heterogeneous nonlinearity, the disturbance of each follower, and the unknown control inputs of the leaders simultaneously. Then, an algorithm with 2 steps is presented to design the practical time‐varying formation tracking protocol by solving an algebraic Riccati equation and an algebraic equation, where the time‐varying formation tracking feasibility condition is introduced. Moreover, the stability of the closed‐loop multiagent system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, a numerical simulation example is provided to illustrate the effectiveness of the obtained theoretical results.     

Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

This paper is concerned with the tracking control problem for a class of multiple‐input–multiple‐output systems with unmatched disturbances and the unknown additive and multiplicative nonlinearities. The objective is to provide a low‐complexity control solution in the sense that (i) approximating structures are not involved, despite unknown nonlinearities and (ii) iterative calculations of command derivatives are avoided in the backstepping design. A robust adaptive control strategy is proposed to fulfill the task. In the control design, a new‐type adaptive law is first developed to update Nussbaum gains to handle control direction uncertainties, while ensuring Nussbaum gains bounded. Then, the potential robustness of error constraint techniques is exploited to counteract the effects of unknown nonlinearities and disturbances and achieve predefined transient and steady‐state tracking performance. Finally, simulation results are given to illustrate the above theoretical findings.