Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.     

Direct adaptive fuzzy control for nonlinear systems with time-varying delays

This paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict-feedback systems with time-varying delays. Based on the Razumikhin function approach, a novel adaptive fuzzy controller is designed. The proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. Different from the existing adaptive fuzzy control methodology, the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems. As a result, the proposed adaptive controller has a simpler form and requires fewer adaptation parameters.     

一类具有未建模动态的非线性系统模糊自适应鲁棒控制

针对一类单输入单输出未建模动态不确定非线性系统,提出一种模糊自适应backstepping控制方法.设计中利用模糊逻辑系统逼近系统的未知函数,应用非线性阻尼项抵消系统的非线性不确定项,通过引入一个动态信号克服未建模动态.该模糊自适应控制方法保证了整个闭环系统的有界性,输出信号可调节到零的小邻域内.仿真结果进一步验证了该方法的有效性.     

Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, a novel adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear time-delay systems with the lower triangular form. Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the backstepping approach. The proposed controller guarantees uniform ultimate boundedness of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme.     

Direct adaptive fuzzy control of nonlinear strict-feedback systems

This paper focuses on adaptive fuzzy tracking control for a class of uncertain single-input /single-output nonlinear strict-feedback systems. Fuzzy logic systems are directly used to approximate unknown and desired control signals and a novel direct adaptive fuzzy tracking controller is constructed via backstepping. The proposed adaptive fuzzy controller guarantees that the output of the closed-loop system converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. A main advantage of the proposed controller is that it contains only one adaptive parameter that needs to be updated online. Finally, an example is used to show the effectiveness of the proposed approach.     

Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.     

Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems

In this paper, a new fuzzy adaptive control approach is developed for a class of SISO strict-feedback nonlinear systems, in which the nonlinear functions are unknown and the states are not available for feedback. By fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive high-gain observer is designed to estimate the unmeasured states. Under the framework of the backstepping design, fuzzy adaptive output feedback control is constructed recursively. It is shown that the proposed fuzzy adaptive control approach guarantees the semi-global boundedness property for all the signals of the resulting closed-loop system. Simulation results are included to illustrate the effectiveness of the proposed techniques.     

Robust adaptive fuzzy VSS control for a class of uncertain nonlinear systems using small gain design

In this paper, a novel robust adaptive fuzzy variable structure control (RAFVSC) scheme is proposed for a class of uncertain nonlinear systems. The uncertain nonlinear system and gain functions originating from modeling errors and external disturbances are all unstructured (or non-repeatable), state-dependent and completely unknown. The Takagi–Sugeno type fuzzy logic systems are used to approximate uncertain functions in the systems and the RAFVSC is designed by use of the input-to-state stability (ISS) approach and small gain theorem. In the algorithm, there are three advantages which are that the asymptotic stability of adaptive control in the presence of unstructured uncertainties can be guaranteed, the possible controller singularity problem in some of existing adaptive control schemes using feedback linearization techniques can be removed and the adaptive mechanism with minimal learning parameterizations can be achieved. The performance and effectiveness of the proposed methods are discussed and illustrated with two simulation examples.     

A design for a class of nonlinear systems with delay time using fuzzy logic

 The goal of this paper is to design a controller for a class of nonlinear systems with delay time using fuzzy logic. The control scheme considered in this paper integrates a fuzzy component and a sliding control component. In the former, the fuzzy system can be considered as a universal approximator to approximate the unknown functions in plant. In the latter, a variable structure control with a sector guarantees the global stability of the closed-loop system when a variable, involving tracking error, travels outside of the sector. The adaptive laws to adjust the parameters in the system are developed based on the Lyapunov synthesis approach. It is shown that the proposed adaptive controller guarantees tracking error, between the outputs of the considered system and desired␣values, to be asymptotical in decay.     

多输入多输出非线性多时滞系统的直接自适应模糊跟踪控制

针对多输入多输出非线性多时滞系统,提出了一种直接自适应模糊跟踪控制方案．该方案有机综合了自适应控制和H∞ 控制,构建了一种自适应时滞模糊逻辑系统用来逼近有多重时滞的未知函数;设计了H∞ 补偿器来抵消模糊逼近误差和外部扰动．根据跟踪误差给出了参数调节规律,构造了包含时滞的李亚普诺夫函数,从而证明了误差闭环系统满足期望的H∞ 跟踪性能．仿真结果表明了该方案的可行性．     

Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems

An adaptive fuzzy control approach is proposed for a class of multiple-input-multiple-output (MIMO) nonlinear systems with completely unknown nonaffine functions. The MIMO systems are composed of n subsystems and each of subsystems is in the nested lower triangular form. It is difficult and complicated to control this class of systems due to the existence of unknown nonaffine functions and the couplings among the nested subsystems. This difficulty is overcome by introducing some special type Lyapunov functions and taking advantage of the mean-value theorem, the backstepping design method and the approximation property of the fuzzy systems. The proposed control approach can guarantee that all the signals in the closed-loop system are bounded. A simulation experiment is utilized to verify the feasibility of the proposed approach.     

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.     

Stable adaptive fuzzy control for MIMO nonlinear systems

In this paper, an indirect adaptive fuzzy control scheme is presented for a class of multi-input and multi-output (MIMO) nonlinear systems whose dynamics are poorly understood. Within this scheme, fuzzy systems are employed to approximate the plant’s unknown dynamics. In order to overcome the controller singularity problem, the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices, a robustifying control term is used to compensate for the lumped errors, and all parameter adaptive laws and robustifying control term are derived based on Lyapunov stability analysis. The proposed scheme guarantees that all the signals in the resulting closed-loop system are uniformly ultimately bounded (UUB). Moreover, the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large. A simulation example is used to demonstrate the effectiveness of the proposed control scheme.     

Adaptive backstepping output feedback control for SISO nonlinear system using fuzzy neural networks

In this paper, a new fuzzy-neural adaptive control approach is developed for a class of single-input and single-output （SISO） nonlinear systems with unmeasured states. Using fuzzy neural networks to approximate the unknown nonlinear functions, a fuzzy- neural adaptive observer is introduced for state estimation as well as system identification. Under the framework of the backstepping design, fuzzy-neural adaptive output feedback control is constructed recursively. It is proven that the proposed fuzzy adaptive control approach guarantees the global boundedness property for all the signals, driving the tracking error to a small neighbordhood of the origin. Simulation example is included to illustrate the effectiveness of the proposed approach.     

Model reference adaptive robust fuzzy control for ship steering autopilot with uncertain nonlinear systems

A novel model reference adaptive robust fuzzy control algorithm is presented for ship steering autopilot, which is an uncertain nonlinear system. In the proposed algorithm, fuzzy logic systems have been used to approximate lumped unknown function in the ship steering systems and the adaptive mechanism with minimal learning parameter, i.e. only one parameter, has been achieved by use of Lyapunov approach. The proposed methodology is verified using the simulation mode of the Dalian Maritime University's ocean-going training ship named Yulong. It is shown that the proposed algorithm guarantees that the ship steering autopilot system is asymptotically stable and its tracking error can approach to zero.     

Observer-based fuzzy adaptive fault control for a class of MIMO nonlinear systems

In this paper, the fault-tolerant control (FTC) problem is investigated for a class of multi-input multiple output nonlinear systems with time-varying delays, and an active FTC method is proposed. The controlled system contains unknown nonlinear functions, unknown control gain functions and actuator faults, which integrates time-varying bias and gain faults. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions and unknown control gain functions, fuzzy adaptive observers are used for fault detection and isolation. Further, based on the obtained information, an accommodation method is proposed for compensating the actuator faults. It is shown that all the variables of the closed-loop system are semi-globally uniformly bounded, the tracking error converges to an arbitrary small neighbourhood of the origin. A simulation is given to demonstrate the effectiveness of the proposed approach.     

Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead zone outputs

This paper focuses on an adaptive fuzzy tracking control problem for a class of pure-feedback stochastic nonlinear systems with unknown dead zone outputs. To overcome the design difficulty arising from the nonlinearity in the output mechanism, the new properties of Nussbaum function are employed and an auxiliary virtual controller is constructed. The proposed adaptive fuzzy control method guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error converges to a small neighbourhood of the origin in the sense of mean quartic value. Simulation results further demonstrate the effectiveness of the presented control algorithm.     

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.