Adaptive fuzzy prescribed performance control for MIMO nonlinear systems with unknown control direction and unknown dead-zone inputs

In this study, an adaptive fuzzy prescribed performance control approach is developed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems with unknown control direction and unknown dead-zone inputs. The properties of symmetric matrix are exploited to design adaptive fuzzy prescribed performance controller, and a Nussbaum-type function is incorporated in the controller to estimate the unknown control direction. This method has two prominent advantages: it does not require the priori knowledge of control direction and only three parameters need to be updated on-line for this MIMO systems. It is proved that all the signals in the resulting closed-loop system are bounded and that the tracking errors converge to a small residual set with the prescribed performance bounds. The effectiveness of the proposed approach is validated by simulation results.     

Modeling and control compensation of nonlinear friction using adaptive fuzzy systems

System performance in terms of control accuracy and stability is usually negatively affected by friction occurrences in mechanical systems. Thus, it is important to model the friction properly so that it can be used in controller design. This paper employs adaptive fuzzy systems to approximate unknown nonlinear friction functions, and applies the estimation of friction in proportional-derivative (PD) control law to enhance the control performance. On the basis of Lyapunov stability theory, a bound of tracking errors of the closed-loop control system is derived. Techniques proposed in this paper have been applied to a typical motion control system for simulation studies. The results obtained demonstrate that our proposed method in this paper has good potential in controlling many mechanical systems with unknown nonlinear friction.     

Finite-time decentralized adaptive neural constrained control for interconnected nonlinear time-delay systems with dynamics couplings among subsystems

The problem of finite-time decentralized neural adaptive constrained control is studied for large-scale nonlinear time-delay systems in the non-affine form. The main features of the considered system are that 1) unknown unmatched time-delay interactions are considered, 2) the couplings among the nested subsystems are involved in uncertain nonlinear systems, 3) based on finite-time stability approach, asymmetric saturation actuators and output constraints are studied in large-scale systems. First, the smooth asymmetric saturation nonlinearity and barrier Lyapunov functions are used to achieve the input and output constraints. Second, the appropriately designed Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities. Note that, due to unknown time-delay interactions and the couplings among subsystems, the controller design is more meaningful and challenging. At last, based on finite-time stability theory and Lyapunov stability theory, a decentralized adaptive controller is proposed, which decreases the number of learning parameters. It is shown that the designed controller can ensure that all closed-loop signals are bounded and the tracking error converges to a small neighborhood of the origin. The simulation studies are presented to show the effectiveness of the proposed method.     

Memoryless disturbance-observer-based adaptive tracking of uncertain pure-feedback nonlinear time-delay systems with unmatched disturbances

This paper presents a delay-independent nonlinear disturbance observer (NDO) design methodology for adaptive tracking of uncertain pure-feedback nonlinear systems in the presence of unknown time delays and unmatched external disturbances. Compared with all existing NDO-based control results for uncertain lower-triangular nonlinear systems where unknown time delays have been not considered, the main contribution of this paper is to develop a delay-independent design strategy to construct an NDO-based adaptive tracking scheme in the presence of unknown time-delayed nonlinearities and non-affine nonlinearities unmatched in the control input. The proposed delay-independent scheme is constructed by employing the appropriate Lyapunov-Krasovskii functionals and the same function approximators for the NDO and the controller. It is shown that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin.     

Discrete-time direct adaptive control for robotic systems based on model-free and if–then rules operation

An adaptive controller for a class of nonlinear discrete-time systems is proposed for robotic systems under the assumption that the parameters and structure of system dynamics are all unknown. This controller is designed with the concept of model-free adaptive control requiring only the input–output of the unknown plant. The robotic system has been generalized to be a nonaffine discrete-time system under reasonable assumptions. The adaptive scheme called fuzzy rules emulated network (FREN) is implemented as a direct controller. The IF–THEN rules for FREN have been defined by the knowledge according to the relation between input and output of the robotic system without any compensator for the unknown mathematical model or nonlinearities. The underlying physical specifications of robotic system such as the operating range, maximum joint velocity, and so on have been considered to initialize the membership functions and adjustable parameters of FREN. The adaptation scheme is developed according to convergence analysis established for both adjustable parameters and the tracking error. The performance of the proposed controller is validated by the experimental system with a 7-degrees-of-freedom robotic arm operated in velocity-mode control.     

非线性时滞系统自适应模糊动态面控制

针对含完全未知时滞的不确定非线性系统的控制问题,提出了一种自适应模糊动态面控制方案.首先采用模糊逻辑系统逼近系统的未知时滞函数,进而用参考信号代换逼近器输入中的未知时滞信号,取消了对未知时滞常作的假设,摆脱了控制器构造对时滞假设条件的依赖性.模糊逼近和时滞代换产生的误差则采用自适应边界技术处理.基于Lyapunov-Krasovskii泛函,证明了闭环系统所有信号半全局一致最终有界,通过调节设计参数可以实现任意的跟踪精度.仿真实例进一步说明了该方案的可行性.     

FUZZY MODEL-FOLLOWING ADAPTIVE CONTROL DESIGN FOR ROBOT MANIPULATORS

ＦＵＺＺＹＭＯＤＥＬ－ＦＯＬＬＯＷＩＮＧＡＤＡＰＴＩＶＥＣＯＮＴＲＯＬＤＥＳＩＧＷＦＯＲＲＯＢＯＴＭＡＮＩＰＵＬＡＴＯＲＳＦＵＺＺＹＭＯＤＥＬ－ＦＯＬＬＯＷＩＮＧＡＤＡＰＴＩＶＥＣＯＮＴＲＯＬＤＥＳＩＧＷＦＯＲＲＯＢＯＴＭＡＮＩＰＵＬＡＴＯＲＳＺｈａ...     

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms.     

Command filter based adaptive fuzzy bipartite output consensus tracking of nonlinear coopetition multi-agent systems with input saturation

This paper is concerned with the adaptive bipartite output consensus tracking problem of high-order nonlinear coopetition multi-agent systems with input saturation under a signed directed graph. A distributed fuzzy-based command filtered backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by the fuzzy logic system (FLS). The errors compensation mechanism is constructed to eliminate the errors caused by filters. Under the proposed control scheme, we only need to design one adaptive law for each agent, and it is proved that the bipartite output tracking errors converge into the desired neighborhood and all the closed-loop signals are bounded although the input saturation exists. Two numerical examples are included to verify the effectiveness of given scheme.     

On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach

In this paper, the position and force tracking control problem of cooperative robot manipulator system handling a common rigid object with unknown dynamical models and unknown external disturbances is investigated. The universal approximation properties of fuzzy logic systems are employed to estimate the unknown system dynamics. On the other hand, by defining new state variables based on the integral and differential of position and orientation errors of the grasped object, the error system of coordinated robot manipulators is constructed. Subsequently by defining the appropriate change of coordinates and using the backstepping design strategy, an adaptive fuzzy backstepping position tracking control scheme is proposed for multi-robot manipulator systems. By utilizing the properties of internal forces, extra terms are also added to the control signals to consider the force tracking problem. Moreover, it is shown that the proposed adaptive fuzzy backstepping position/force control approach ensures all the signals of the closed loop system uniformly ultimately bounded and tracking errors of both positions and forces can converge to small desired values by proper selection of the design parameters. Finally, the theoretic achievements are tested on the two three-link planar robot manipulators cooperatively handling a common object to illustrate the effectiveness of the proposed approach.     

Adaptive control of nonlinear uncertain active suspension systems with prescribed performance

This paper proposes adaptive control designs for vehicle active suspension systems with unknown nonlinear dynamics (e.g., nonlinear spring and piece-wise linear damper dynamics). An adaptive control is first proposed to stabilize the vertical vehicle displacement and thus to improve the ride comfort and to guarantee other suspension requirements (e.g., road holding and suspension space limitation) concerning the vehicle safety and mechanical constraints. An augmented neural network is developed to online compensate for the unknown nonlinearities, and a novel adaptive law is developed to estimate both NN weights and uncertain model parameters (e.g., sprung mass), where the parameter estimation error is used as a leakage term superimposed on the classical adaptations. To further improve the control performance and simplify the parameter tuning, a prescribed performance function (PPF) characterizing the error convergence rate, maximum overshoot and steady-state error is used to propose another adaptive control. The stability for the closed-loop system is proved and particular performance requirements are analyzed. Simulations are included to illustrate the effectiveness of the proposed control schemes.     

Modeling and output tracking of transverse flux permanent magnet machines using high gain observer and RBF neural network

This paper deals with modeling and adaptive output tracking of a transverse flux permanent magnet machine as a nonlinear system with unknown nonlinearities by utilizing high gain observer and radial basis function networks. The proposed model is developed based on computing the permeance between rotor and stator using quasiflux tubes. Based on this model, the techniques of feedback linearization and H_∞ control are used to design an adaptive control law for compensating the unknown nonlinear parts, such as the effect of cogging torque, as a disturbance is decreased onto the rotor angle and angular velocity tracking performances. Finally, the capability of the proposed method in tracking both the angle and the angular velocity is shown in the simulation results.     

State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities

This paper presents three fuzzy adaptive controllers for a class of uncertain multivariable nonlinear systems with both sector nonlinearities and dead zones: two first controllers are state feedbacks and the last controller is an output feedback. The design of the first controller concerns systems with symmetric and positive definite control–gain matrix, while the second control design is extended to the case of nonsymmetric control–gain matrix thanks to an appropriate decomposition, namely the product of a symmetric positive definite matrix, a diagonal matrix with diagonal entries +1 or ?1, and a unity upper triangular matrix. The third controller is an output feedback extension of the second controller. In this controller, a high-gain observer is incorporated to estimate the unmeasurable states. An appropriate adaptive fuzzy logic system is used to reasonably approximate the uncertain functions. A Lyapunov approach is adopted to derive the parameter adaptation laws and prove the stability of those control systems as well as the exponential convergence of their underlying tracking errors within an adjustable region. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.     

Nonlinear adaptive control based on fuzzy sliding mode technique and fuzzy-based compensator

It is difficult to efficiently control nonlinear systems in the presence of uncertainty and disturbance (UAD). One of the main reasons derives from the negative impact of the unknown features of UAD as well as the response delay of the control system on the accuracy rate in the real time of the control signal. In order to deal with this, we propose a new controller named CO-FSMC for a class of nonlinear control systems subjected to UAD, which is constituted of a fuzzy sliding mode controller (FSMC) and a fuzzy-based compensator (CO). Firstly, the FSMC and CO are designed independently, and then an adaptive fuzzy structure is discovered to combine them. Solutions for avoiding the singular cases of the fuzzy-based function approximation and reducing the calculating cost are proposed. Based on the solutions, fuzzy sliding mode technique, lumped disturbance observer and Lyapunov stability analysis, a closed-loop adaptive control law is formulated. Simulations along with a real application based on a semi-active train-car suspension are performed to fully evaluate the method. The obtained results reflected that vibration of the chassis mass is insensitive to UAD. Compared with the other fuzzy sliding mode control strategies, the CO-FSMC can provide the best control ability to reduce unwanted vibrations.     

Indirect adaptive fuzzy fault-tolerant tracking control for MIMO nonlinear systems with actuator and sensor failures

In this paper, an active fuzzy fault tolerant tracking control (AFFTTC) scheme is developed for a class of multi-input multi-output (MIMO) unknown nonlinear systems in the presence of unknown actuator faults, sensor failures and external disturbance. The developed control scheme deals with four kinds of faults for both sensors and actuators. The bias, drift, and loss of accuracy additive faults are considered along with the loss of effectiveness multiplicative fault. A fuzzy adaptive controller based on back-stepping design is developed to deal with actuator failures and unknown system dynamics. However, an additional robust control term is added to deal with sensor faults, approximation errors, and external disturbances. Lyapunov theory is used to prove the stability of the closed loop system. Numerical simulations on a quadrotor are presented to show the effectiveness of the proposed approach.     

Nonlinear adaptive robust backstepping force control of hydraulic load simulator: Theory and experiments

High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back-stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.     

Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS

This paper presents a novel observer-based decentralized hybrid adaptive fuzzy control scheme for a class of large-scale continuous-time multiple-input multiple-output (MIMO) uncertain nonlinear systems whose state variables are unmeasurable. The scheme integrates fuzzy logic systems, state observers, and strictly positive real conditions to deal with three issues in the control of a large-scale MIMO uncertain nonlinear system: algorithm design, controller singularity, and transient response. Then, the design of the hybrid adaptive fuzzy controller is extended to address a general large-scale uncertain nonlinear system. It is shown that the resultant closed-loop large-scale system keeps asymptotically stable and the tracking error converges to zero. The better characteristics of our scheme are demonstrated by simulations.     

Fault tolerant control for modified quadrotor via adaptive type-2 fuzzy backstepping subject to actuator faults

In this paper, a robust attitude and position control of a novel modified quadrotor unmanned aerial vehicles (UAV) which has higher drive capability as well as greater robustness against actuator faults than conventional quad-rotor UAV has been developed. A robust backstepping controller with adaptive interval type-2 fuzzy logic is proposed to control the attitude and position of the modified quadrotor under actuator faults. Besides globally stabilizing the system amid other disturbances, the insensitivity to the model errors and parametric uncertainties are the asset of the backstepping approach. The adaptive interval type-2 fuzzy logic as fault observer can effectively estimate the lumped faults without the knowledge of their bounds for the modified quadrotor UAV. Additionally, the type-2 fuzzy systems are utilized to approximate the local nonlinearities of each subsystem under actuator faults, next and in order to achieve the expected tracking performance, we used Lyapunov theory stability and convergence analysis to online adjust adaptive laws. As a result, the uniformly ultimate stability of the modified quadrotor system is proved. Finally, the performances of the proposed control method are evaluated by simulation and the results demonstrate the effectiveness of the proposed control strategy for the modified quadrotor in vertical flights in presence of actuator faults.     

Decentralized adaptive neural prescribed performance control for high-order stochastic switched nonlinear interconnected systems with unknown system dynamics

In this paper, the problem of decentralized adaptive neural backstepping control is investigated for high-order stochastic nonlinear systems with unknown interconnected nonlinearity and prescribed performance under arbitrary switchings. For the control of high-order nonlinear interconnected systems, it is assumed that unknown system dynamics and arbitrary switching signals are unknown. First, by utilizing the prescribed performance control (PPC), the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, at each recursive step, only one adaptive parameter is constructed to overcome the over-parameterization, and RBF neural networks are employed to tackle the difficulties caused by completely unknown system dynamics. At last, based on the common Lyapunov stability method, the decentralized adaptive neural control method is proposed, which decreases the number of learning parameters. It is shown that the designed common controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the prescribed tracking control performance is guaranteed under arbitrary switchings. The simulation results are presented to further illustrate the effectiveness of the proposed control scheme.     

Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input

Based on the universal approximation property of the fuzzy-neural networks, an adaptive fuzzy-neural observer design algorithm is studied for a class of nonlinear SISO systems with both a completely unknown function and an unknown dead-zone input. The fuzzy-neural networks are used to approximate the unknown nonlinear function. Because it is assumed that the system states are unmeasured, an observer needs to be designed to estimate those unmeasured states. In the previous works with the observer design based on the universal approximator, when the dead-zone input appears it is ignored and the stability of the closed-loop system will be affected. In this paper, the proposed algorithm overcomes the affections of dead-zone input for the stability of the systems. Moreover, the dead-zone parameters are assumed to be unknown and will be adjusted adaptively as well as the sign function being introduced to compensate the dead-zone. With the aid of the Lyapunov analysis method, the stability of the closed-loop system is proven. A simulation example is provided to illustrate the feasibility of the control algorithm presented in this paper.