Novel fuzzy adaptive finite-time nonsmooth control for uncertain nonlinear systems

In this article, a novel fuzzy adaptive finite-time nonsmooth controller is developed to handle the finite-time tracking problem for a class of uncertain nonlinear systems. Different from traditional fuzzy adaptive approximation methods, proposed method contains only one adaptive parameter, no matter how many states there are in the system. By constructing a new Lyapunov function with prescribed performance bound, the transient and steady performances of control system can be ensured. Further, based on a criterion of finite-time semiglobal practical stability and backstepping technology, a novel fuzzy adaptive finite-time nonsmooth control method is designed. It can be demonstrated that proposed control can effectively ensure tracking error tends to small neighborhood in a finite time. Finally, two examples have been simulated by the proposed control method, and it shows effective tracking performance.     

Adaptive finite-time tracking control for output-constrained nonlinear systems with non-strict-feedback structure

This article investigates the issue of adaptive finite-time tracking control for a category of output-constrained nonlinear systems in a non-strict-feedback form. First, by utilizing the structural characteristics of radial basis function neural networks (RBF NNs), a backstepping design method is extended from strict-feedback systems to a kind of more general systems, and NNs are employed to approximate unknown nonlinear functions. In addition, the system output is constrained to the specified region by applying the barrier Lyapunov function (BLF) technique. Furthermore, the finite-time stability of the system is proved by employing the Bhat and Bernstein theorem. As a result, an adaptive finite-time tracking control scheme for the output-constrained nonlinear systems with non-strict-feedback structure is proposed by applying RBF NNs, BLF, finite-time stability theory, and adaptive backstepping technique. It is demonstrated the finite-time stability of the system, the prescribed convergence of the system output and tracking error, the boundedness of adaptive parameters and state variables. Finally, a simulation example is implemented to illustrate the effectiveness of the presented neural control scheme.     

Adaptive finite-time consensus tracking control for nonlinear multiagent systems in nonstrict feedback form with full-state constraints

In this article, the fuzzy adaptive finite-time consensus tracking control problem for nonstrict feedback nonlinear multiagent systems with full-state constraints is studied. The finite-time control based on command filtered backstepping is proposed to guarantee the finite-time convergence and eliminate the explosion of complexity problem caused by backstepping process, and the errors in the filtering process are compensated by using error compensation mechanism. Furthermore, based on the fuzzy logic systems, the uncertain nonlinear dynamics are approximated and the problem of state variables in nonstrict feedback form is solved by using the property of basis functions. The barrier Lyapunov functions are introduced to guarantee that all system states and compensated tracking error signals are constrained in the designed regions. A simulation example is given to verify the superiority of the proposed algorithm.     

Adaptive fuzzy finite-time quantized control for stochastic nonlinear systems with full state constraints

This article studies the adaptive fuzzy finite-time quantized control problem of stochastic nonlinear nonstrict-feedback systems with full state constraints. During the control design process, fuzzy logic systems are used to identify the unknown nonlinear functions, integral barrier Lyapunov functions are employed to solve the state constrained problem. In the frame of backstepping design, an adaptive fuzzy finite-time quantized control scheme is developed. Based on the stochastic finite-time Lyapunov stability theory, it can be guaranteed that the closed-loop system is semiglobal finite-time stable in probability, and the tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to testify the effectiveness of the developed control scheme.     

Adaptive fuzzy finite-time fault-tolerant control of nonlinear systems with state constraints and input quantization

This article concentrates on an adaptive finite-time fault-tolerant fuzzy tracking control problem for nonstrict feedback nonlinear systems with input quantization and full-state constraints. By utilizing the fuzzy logic systems and less adjustable parameters method, the unknown nonlinear functions are addressed in each step process. In addition, a dynamic surface control technique combined with fuzzy control is introduced to tackle the variable separation problem. The problem for the effect of quantization and unlimited number of actuator faults is tackled by a damping term with smooth function in the intermediate control law. Finite-time stability is achieved by combining barrier Lyapunov functions and backstepping method. The finite-time controller is designed such that all the responses of the systems are semiglobal practical finite-time stable and ensured to remain in the predefined compact sets while tracking error converges to a small neighborhood of the origin in finite time. Finally, simulation examples are utilized to testify the validity of the investigated strategy.     

Adaptive fuzzy finite-time consensus tracking for multiple Euler-Lagrange systems with unknown control directions

In this paper, the problem of adaptive fuzzy finite-time consensus tracking control for multiple Euler-Lagrange systems (ELSs) with uncertain dynamics and unknown control directions (UCDs) is investigated. The computational complexity problem in conventional backstepping is avoided by using finite-time command filter (FTCF), and the error in the filtering process is eliminated through error compensation signals. The fuzzy logic system combined with the adaptive control technique is applied to approximate and estimate the unknown nonlinear dynamics of ELS. The Nussbaum function-based continuous and nonsmooth input control torque is established to eliminate the influence of UCDs, and the proposed control scheme can guarantee the consensus tracking errors converge to the desired neighborhood of the origin within a finite time. Numerical simulation is used to test the effectiveness of the given algorithm.     

Neural networks-based adaptive finite-time prescribed performance fault-tolerant control of switched nonlinear systems

In this article, the adaptive finite-time fault-tolerant control problem is considered for a class of switched nonlinear systems in nonstrict-feedback form with actuator fault. The problem of finite-time fault-tolerant control is solved by introducing a finite-time performance function. Meanwhile, the completely unknown nonlinear functions exist in the switched system are identified by the neural networks. Based on the common Lyapunov function method with adaptive backstepping technique, the finite-time fault-tolerant controller is designed. The proposed control strategy can guarantee that the tracking error converges to a prescribed zone at a finite-time and all system variables remain semiglobally practical finite-time stable. Numerical examples are offered to verify the feasibility of the theoretical result.     

Adaptive neural finite-time output-feedback tracking control for nonlinear stochastic nonstrict-feedback systems with input saturation

In this paper, an observer-based adaptive neural output-feedback control scheme is developed for a class of nonlinear stochastic nonstrict-feedback systems with input saturation in finite-time interval. The mean value theorem and the property of the smooth function are applied to cope with the difficulties caused by the existence of input saturation. According to the universal approximation capability of the radial basis function neural network, it will be utilized to compensate the unknown nonlinear functions. Based on the state observer, the finite-time Lyapunov stability theorem, we propose an adaptive neural output-feedback control scheme for nonlinear stochastic systems in nonstrict-feedback form. The developed controller guarantees that the system output signal can track the given reference signal trajectory, and all closed-loop signals are semi-globally finite-time stability in probability. The observer errors and the tracking error can converge to a small neighborhood of the origin. Finally, simulation results demonstrate the effectiveness of the developed control scheme.     

Finite-time adaptive control for nonlinear systems with uncertain parameters based on the command filters

The trajectory tracking control problem for a class of nonlinear systems with uncertain parameters is considered in this article. A new adaptive finite-time tracking control is designed based on the adaptive backstepping method via the command filters. The command filter mechanism can avoid the calculation of partial derivatives and solve the “explosion of complexity” in the backstepping design. The compensation signals are introduced to eliminate errors produced by the command filters. The proposed adaptive backstepping control can guarantee the tracking error remains in a small neighborhood of the origin in finite time, while the practical finite-time stability of the control systems with uncertain parameters is proven by the stability criterion. The effectiveness of the proposed scheme is verified by some simulation results.     

Adaptive finite-time output feedback control for Markov jumping nonlinear systems

In this article, the problem of output feedback tracking control for uncertain Markov jumping nonlinear systems is studied. A finite-time control scheme based on command filtered backstepping and adaptive neural network (NN) technique is given. The finite-time command filter solves the problem of differential explosions for virtual control signals, the NN is utilized to approximate the uncertain nonlinear dynamics and the adaptive NN observer is applied to restructure the state of system. The finite-time error compensation mechanism is established to compensate the errors brought by filtering process. The proposed finite-time tracking control algorithm can ensure that the solution of the closed-loop system is practically finite-time stable in mean square. Two simulation examples are employed to demonstrate the effectiveness of the proposed control algorithm.     

Adaptive control for switched uncertain nonlinear systems with time‐varying output constraint and input saturation

This paper is concerned with adaptive tracking control for switched uncertain nonlinear systems, which contain the time‐varying output constraint (TVOC) and input asymmetric saturation characteristic. In response to the unknown functions, the fuzzy logic systems are adopted. The controller is constructed by the backstepping technique. Based on the Tangent Barrier Lyapunov Function (BLF‐Tan), an adaptive switched control scheme is designed. It is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded with TVOC under arbitrary switchings. Furthermore, the effectiveness of presented control method is validated via the simulation example.     

Adaptive control design for MIMO switched nonlinear systems with full state constraints

This paper presents an adaptive fuzzy control approach of multiple‐input–multiple‐output (MIMO) switched uncertain systems, which involve time‐varying full state constraints (TFSCs) and unknown disturbances. In the design procedure, the fuzzy logic systems are adopted to approximate the unknown functions in the systems. The adaptive fuzzy controller is set up by backstepping technique. According to the tangent barrier Lyapunov function (BLF‐Tan), a novel adaptive MIMO switched nonlinear control algorithm is designed. Under the rule of arbitrary switchings and the proposed control laws, it is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero with TFSCs. Furthermore, the simulation example validates the effectiveness of presented control strategy.     

Command filter-based adaptive neural network controller design for uncertain nonsmooth nonlinear systems with output constraint

This paper investigates the command filter-based adaptive neural network tracking control problem for uncertain nonsmooth nonlinear systems. First, an integral barrier Lyapunov function is introduced to deal with the symmetric output constraint and make the output comply with prescribed restrictions. Second, by the Filippov's differential inclusion theory and approximation theorem, the considered nonsmooth nonlinear system is converted to an equivalent smooth nonlinear system. Third, the Levant's differentiator is used to deal with the “explosion of complexity” problem. An error compensation mechanism is established to attenuate the effect of the filtering error on control performance. Then, an adaptive neural network controller is set up by resorting to the backstepping technique. It is strictly mathematically proved that the tracking error can converge to an arbitrarily small neighborhood of the origin and all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a numerical example and an application example of the robotic manipulator system are provided to demonstrate the availability of the proposed control strategy.     

永磁同步电动机随机系统有限时间模糊自适应反步控制

针对永磁同步电动机随机系统的位置跟踪控制问题,本文提出了有限时间模糊自适应反步控制方法。首先,本文考虑了永磁同步电动机在运行中产生的随机扰动问题,运用了模糊逻辑控制方法很好地处理了电机模型中随机非线性函数。其次,将有限时间控制运用到了永磁同步电动机随机非线性系统中,提高了系统的收敛速度、控制精度和抗干扰能力。最后,仿真结果验证了本文提出的控制方法的有效性。     

Adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems with input delays and state time‐varying delays

In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of MIMO nonlinear systems with input delays and state time‐varying delays. The unknown continuous nonlinear functions are expressed as the linearly parameterized form by using the fuzzy logic systems, and then, by combining the backstepping technique, the appropriate Lyapunov–Krasovskii functionals, and the ‘minimal learning parameters’ algorithms with the DSC 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. It is proven that the proposed design method can 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 are provided to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

This paper considers the problem of adaptive fuzzy output‐feedback tracking control for a class of switched stochastic nonlinear systems in pure‐feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output‐feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method.     

Adaptive fuzzy practical fixed-time control for uncertain nonlinear systems with actuator constraints

This article addresses an adaptive fuzzy practical fixed-time tracking control for nonlinear systems with unknown actuator constraints and uncertainty functions. First, fuzzy logic systems (FLSs) are used to identify uncertain functions. Then, by utilizing FLSs, backstepping technique, and finite-time stability theory, an adaptive fuzzy practical fixed-time control is proposed to obtain satisfactory tracking performance even when the actuator faults. The theoretical analysis verified that the closed-loop systems is practical fixed-time stable under the proposed control strategy, the tracking error converges to a small neighborhood of the origin in a fixed time, and the convergence time is independent of the state conditions. Finally, both numerical simulation and physical example demonstrates the effectiveness of the proposed control strategy.     

Nonlinear filtering-based output tracking error constraint control for permanent magnet synchronous motors with complete unknown coefficients

This article investigates the problem of the output tracking error constraint performance for permanent magnet synchronous motors with complete unknown coefficients. First, to achieve the output tracking error constraint performance, an improved barrier Lyapunov function combined with exponent-type performance is given. Then, to erase the effects of unknown coefficients, adaptive compensation strategy, fuzzy logic systems, and Nussbaum-type function are utilized, which relax the assumption requirement that the partial coefficients must be known in the related results. Further, to simplify the control design, a novel nonlinear filters-based dynamic surface control method is presented. Unlike the previous linear filters-based ones, it can achieve better control performance. It is proved that by utilizing the proposed method, all the signals in the closed-loop systems are bounded, and also the prescribed output tracking error constraint condition does not violate. Final, simulation example verify the effectiveness of our proposed method.     

Adaptive fuzzy finite-time decentralized control for large-scale stochastic nonlinear systems

An adaptive finite-time decentralized control algorithm for a class of large-scale stochastic nonlinear systems is presented. The fuzzy logic system is used to estimate uncertain nonlinearities. One advantage of the developed scheme is that each subsystem only needs to update one adaptive parameter, which alleviates the burden of online estimation. The dynamic surface control method is employed to reduce the “complexity explosion” caused by the repetitive derivation of the intermediate variable function in the backstepping control scheme. A new decentralized controller is designed so that all signals of the controlled system are bounded and the tracking error converges to a small residual set around the origin within a finite time. The simulation results of a numerical example illustrate the effectiveness of the method.     

一类刚性负载双轴伺服系统的非线性观测器控制设计策略

提出了一种基于非线性观测器的命令滤波自适应反步控制（OCFABC）方法,以解决具有 LuGre 摩擦模型的双轴伺服系统中的位置跟踪和速度同步问题。观测器用于系统摩擦补偿。命令滤波器作用于虚拟控制信号,解决反步法中的计算爆炸问题,建立误差补偿方程,提高跟踪精度。此外,还设计了速度同步信号,以达到更好的系统同步效果。利用Lyapunov理论分析了闭环系统的稳定性。最后,通过仿真和试验结果证明了所设计方法的有效性和优越性。