Adaptive fuzzy robust tracking controller design via small gain approach and its application

An adaptive fuzzy robust tracking control (AFRTC) algorithm is proposed for a class of nonlinear systems with the uncertain system function and uncertain gain function, which are all the unstructured (or nonrepeatable) state-dependent unknown nonlinear functions arising from modeling errors and external disturbances. The Takagi-Sugeno type fuzzy logic systems are used to approximate unknown uncertain functions and the AFRTC algorithm is designed by use of the input-to-state stability approach and small gain theorem. The algorithm is highlighted by three advantages: 1) the uniform ultimate boundedness of the closed-loop adaptive systems in the presence of nonrepeatable uncertainties can be guaranteed; 2) the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed; and 3) the adaptive mechanism with minimal learning parameterizations can be obtained. The performance and limitations of the proposed method are discussed. The uses of the AFRTC for the tracking control design of a pole-balancing robot system and a ship autopilot system to maintain the ship on a predetermined heading are demonstrated through two numerical examples. Simulation results show the effectiveness of the control scheme.     

Adaptive fuzzy backstepping output feedback control of nonlinear uncertain systems with unknown virtual control coefficients using MT-filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO nonlinear uncertain systems with unmeasured states and unknown virtual control coefficients. The fuzzy logic systems are used to model the uncertain nonlinear systems. The MT-filters and the state observer are designed to estimate the unmeasured states. Using backstepping design principle and combining the Nussbaum gain functions, an adaptive fuzzy output feedback control scheme is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of origin. A simulation is included to illustrate the effectiveness of the proposed approach.     

A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems

In this paper, a robust adaptive tracking control problem is discussed for a general class of strict-feedback uncertain nonlinear systems. The systems may possess a wide class of uncertainties referred to as unstructured uncertainties, which are not linearly parameterized and do not have any prior knowledge of the bounding functions. The Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach. One is the robust adaptive fuzzy tracking controller (RAFTC) for the system without input gain uncertainty. The other is the robust adaptive fuzzy sliding tracking controller (RAFSTC) for the system with input gain uncertainty. Both algorithms have two advantages, those are, semi-global uniform ultimate boundedness of adaptive control system in the presence of unstructured uncertainties and the adaptive mechanism with minimal learning parameterizations. Four application examples, including a pendulum system with motor, a one-link robot, a ship roll stabilization with actuator and a single-link manipulator with flexible joint, are used to demonstrate the effectiveness and performance of proposed schemes.     

Adaptive fuzzy H/sub /spl infin// stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach

A novel adaptive fuzzy controller with H/sub /spl infin// performance is proposed for a wide class of strict-feedback canonical nonlinear systems. The systems may possess a class of uncertainties referred to as unstructured uncertain functions, which are not linearly parameterized and have no prior knowledge of the bound. The Takagi-Sugeno-type fuzzy logic systems are used to approximate the uncertainties and a systematic design procedure is developed for synthesis of adaptive fuzzy control with H/sub /spl infin// performance, which combines the backstepping technique and generalized small gain approach. The method preserves the three advantages, those are, the semiglobal uniform ultimate bound of adaptive control in the presence of unstructured uncertainties can be guaranteed, the adaptive mechanism with only one learning parameter is obtained and the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques can be removed. Performance and limitations of proposed method are discussed and illustrated with simulation results.     

Adaptive Fuzzy Control for Nonlinear Time‐Delay Systems with Dynamical Uncertainties

In this paper, an adaptive fuzzy backstepping robust control approach is proposed for a class of SISO nonlinear strict‐feedback systems. The nonlinear systems addressed in this paper are assumed to possess three uncertainties: (i) the unstructured uncertainties; (ii) the time delays; and (iii) the dynamics uncertainties. In adaptive backstepping recursive design, fuzzy logic systems are used to approximate the unstructured uncertainties. A nonlinear damping technique and Lyapunov–Krasovskii functions are introduced to cancel the effects of the dynamics uncertainties and deal with the time delays, respectively. Combining the backstepping technique and a small gain approach, a stable adaptive fuzzy robust control approach is developed. It is proved that all the signals of the closed‐loop system are semi‐golablly uniformaly ultimately bounded (SUUB). The effectiveness of the proposed approach is illustrated by a simulation example.     

Direct adaptive fuzzy backstepping control of uncertain nonlinear systems in the presence of input saturation

In this paper, a novel direct adaptive fuzzy control approach is presented for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are directly used to tackle unknown nonlinear functions, and the adaptive fuzzy tracking controller is constructed by using the backstepping recursive design techniques. To overcome the problem of input saturation, a new auxiliary design system and Nussbaum gain functions are incorporated into the control scheme, respectively. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood of the origin. A simulation example is included to illustrate the effectiveness of the proposed approach. Two key advantages of the scheme are that (i) the direct adaptive fuzzy control method is proposed for uncertain nonlinear system with input saturation by using Nussbaum function technique and (ii) The number of the online adaptive learning parameters is reduced.     

Adaptive fuzzy control of MIMO nonlinear systems with fuzzy dead zones

In this paper, the problem of adaptive fuzzy tracking control is investigated for a class of multi-input multi-output nonlinear systems with fuzzy dead zones. The virtual control gain functions and uncertain functions considered in the studied system are all unknown. Fuzzy logic systems are employed to approximate the unknown functions. With the combination of adaptive backstepping design technique and dynamic surface control method, the problem caused by differentiating nonlinear functions repeatedly is avoided. Furthermore, only one adaptive parameter needs to be updated online for each subsystem, which reduces the computation burden considerably. The presented controller not only guarantees the desired control performance, but also guarantees the boundedness of all closed-loop signals. Simulation results are shown to demonstrate the effectiveness of the proposed algorithm.     

不确定非线性多智能体系统的分布式模糊自适应镇定控制

针对一类具有未知非线性和未知参数摄动的非线性多智能体系统, 提出一种分布式模糊自适应镇定控制方法. 基于邻接智能体信息和部分智能体的自身信息, 分别设计静态耦合和动态耦合的分布式模糊自适应控制律. 基于Lyapunov 稳定性理论, 证明了所提出的控制器能使得系统状态最终稳定于原点的邻域内. 仿真实例验证了所提出方法的有效性.

     

Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach

This paper presents a novel robust adaptive fuzzy tracking controller (RAFTC) for a wide class of perturbed strict-feedback nonlinear systems with both unknown system and virtual control gain nonlinearities. For unknown system nonlinearities, two types for them are included: one naturally satisfies the “triangularity condition” and may possess a class of unstructured uncertain functions which are not linearly parameterized, while the other is partially known and consists of parametric uncertainties and known “bounding functions”. The Takagi–Sugeno type fuzzy logic systems are used to approximate unknown system nonlinearities and a systematic design procedure is developed for synthesis of RAFTC by combining the backstepping technique and generalized small-gain approach. The algorithm proposed is highlighted by three advantages: (i) the semi-global uniform ultimate bound of RAFTC in the presence of perturbed uncertainties and unknown virtual control gain nonlinearities can be guaranteed, (ii) the adaptive mechanism with minimal learning parameterizations is obtained and (iii) the possible controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques can be removed. Performance and limitations of proposed method are discussed and illustrated with simulation results.     

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

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of SISO nonlinear strict-feedback systems with unknown sign of high-frequency gain and the unmeasured states. The nonlinear systems addressed in this paper are assumed to possess the unmodeled dynamics, dynamical disturbances and unknown nonlinear functions, where the unknown nonlinear functions are not linearly parameterized, and no prior knowledge of their bounds is available. In the recursive designing, fuzzy logic systems are used to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unmodeled dynamics and the unknown sign of the high-frequency gain, respectively. Based on Lyapunov function method, a stable adaptive fuzzy output feedback control scheme is developed. It is mathematically proved that the proposed adaptive fuzzy control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded, the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.     

Adaptive fuzzy decentralized control for a class of large-scale nonlinear systems.

In this paper, direct and indirect adaptive output-feedback fuzzy decentralized controllers for a class of uncertain large-scale nonlinear systems are developed. The proposed controllers do not need the availability of the state variables. By designing the state observer, the adaptive fuzzy systems, which are used to model the unknown functions, can be constructed using the state estimations, and a new hybrid adaptive fuzzy control methodology is proposed by combining the adaptive fuzzy systems with H infinity control and the sliding mode control techniques. Based on Lyapunov stability theorem, the stability of the closed-loop systems can be verified. Moreover, the proposed overall control schemes guarantee that all the signals involved are bounded and achieve the H infinity-tracking performance. To demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.     

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.     

Identification Recurrent Type 2 Fuzzy Wavelet Neural Network and L2‐Gain Adaptive Variable Sliding Mode Robust Control of Electro‐Hydraulic Servo System (EHSS)

An electro‐hydraulic servo system (EHSS) is a kind of system with the characteristics of time‐variant, serious nonlinearity, parameter and structural uncertainty, and uncertain load disturbance in most cases. These characteristics make it very difficult to realize highly accurate control by conventional methods. In order to solve the above problems, this paper introduces a recurrent type 2 fuzzy wavelet neural network to approximate the unknown nonlinear functions of the dynamic systems through tuning by the desired adaptive law. Based on the identification by recurrent type 2 fuzzy wavelet neural network, a L2 gain design method, combining gain adaptive variable sliding mode control with H infinity control, is proposed for load disturbance, thereby accommodating uncertainties that are the main factors affecting system stability and accuracy in EHSS. In this algorithm, a recurrent type 2 fuzzy wavelet neural network is employed to evaluate the unknown dynamic characteristics of the system and gain adaptive variable sliding mode control to compensate for evaluating errors, and H infinity control to suppress the effect on system by load disturbance. The experiment results show that the proposed system L2 gain design method can make the system exhibit strong robustness to parameter variation and load disturbance.     

Adaptive sliding mode control for MIMO nonlinear systems based on fuzzy logic scheme

In this study an indirect adaptive sliding mode control (SMC) based on a fuzzy logic scheme is proposed to strengthen the tracking control performance of a general class of multi-input multi-output (MIMO) nonlinear uncertain systems. Combining reaching law approach and fuzzy universal approximation theorem, the proposed design procedure combines the advantages of fuzzy logic control, adaptive control and sliding mode control. The stability of the control systems is proved in the sense of the Lyapunov second stability theorem. Two simulation studies are presented to demonstrate the effectiveness of our new hybrid control algorithm.     

Adaptive fuzzy control for multi-input multi-output nonlinear systems with unknown dead-zone inputs

This paper presents an adaptive fuzzy control scheme for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with the nonsymmetric control gain matrix and the unknown dead-zone inputs. In this scheme, fuzzy systems are used to approximate the unknown nonlinear functions and the estimated symmetric gain matrix is decomposed into a product of one diagonal matrix and two orthogonal matrices. Based on the decomposition results, a controller is developed, therefore, the possible controller singularity problem and the parameter initialization condition constraints problem are avoided. In addition, a dynamic robust controller is employed to compensate for the lumped errors. It is proved that all the signals in the proposed closed-loop system are bounded and that the tracking errors converge asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.     

Adaptive fuzzy dynamic surface control for uncertain nonlinear systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.     

一类严格反馈系统变比例增益精确微分补偿控制

针对包含不确定函数和未知外部扰动的一类严格反馈型非线性系统,提出基于精确扰动观测器的变比例增益自适应模糊控制器.系统中的未知不确定函数由模糊逻辑系统在线逼近,同时将模糊逻辑系统的逼近误差和未知外部扰动定义为总扰动,利用精确扰动观测器进行精确微分补偿控制. 将非线性函数应用于设计可调节的输出反馈增益,有效消除系统的稳态误差,使得系统跟踪误差可以控制在零的任意小邻域内.最后,通过Lyapunov定理证明闭环系统中所有信号均是有界的.数值仿真表明了所提出方案的有效性.     

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

A novel fuzzy terminal sliding mode control （FTSMC） scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.     

Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system

A novel fuzzy terminal sliding mode control (FTSMC) scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.     

张恩勤,施颂椒,徐立鸿

针对一类不确定非线性系统提出一种新的模糊自适应控制方法。用模糊逻辑系统逼近未知函数,并根据前一步参考误差来修正模糊逻辑系统的输入,以此对逼近误差进行补偿。该方法不但能保证闭环系统稳定,而且可使跟踪误差收敛于原点或原点的一个小领域内。仿真结果验证了此方法的有效性。