Adaptive Fuzzy Tracking Control Research Articles

Adaptive fuzzy dynamic surface tracking control for a class of nonlinear systems with unknown distributed time delays and backlash-like hysteresis

In this article, an adaptive fuzzy backstepping dynamic surface control approach is developed for a class of nonlinear systems with unknown backlash-like hysteresis and unknown state discrete and distributed time-varying delays. Fuzzy logic systems are used to approximate the unknown nonlinear functions and a fuzzy state observer is designed for estimating the immeasurable states. Then, by combining the backstepping technique and the appropriate Lyapunov–Krasovskii functionals with the dynamic surface control approach, the output-feedback adaptive fuzzy tracking controller is designed. The main advantages of this article are (i) the existence of the state discrete and distributed time-varying delays such that the investigated systems are more general than that of the existing results, (ii) the proposed control scheme can eliminate the problem of “explosion of complexity” inherent in the backstepping design method, and (iii) for the nth nonlinear system, only one fuzzy logic system is used to approximate the unknown continuous time-varying delay functions since all of them are lumped into one unknown nonlinear function, which makes our design scheme easier to be implemented in practical applications. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error can converge to a small neighborhood of origin with an appropriate choice of design parameters. Finally, the simulation results demonstrate the effectiveness of the proposed approach.

Practical adaptive fuzzy tracking control for a class of perturbed nonlinear systems with backlash nonlinearity

This paper addresses the adaptive fuzzy tracking control problem for a class of perturbed nonlinear systems with backlash nonlinearity. In the proposed control scheme, fuzzy logic systems are used to approximate the unknown nonlinearity in each backstepping design, and the classic adaptive technique is employed to deal with some unknown parameters. The proposed fuzzy controller is developed by introducing some non-negative switching functions, and novel parameter adaptation learning laws are designed using the σ-modification method. It is emphasized that with the help of novel parameter adaptation laws, the high-gain phenomenon in the previous work can be avoided. In addition, by borrowing the property of the introduced non-negative functions and the inequality technique, an adaptive technique is employed to estimate the norm of the ideal weight vector such that the number of adaptation learning parameters online is reduced. By employing Barbalat’s lemma, it can be proved that all the signals in the closed-loop system remain semi-globally uniformly ultimately bounded, and, especially, that the tracking error converges to an accuracy predefined a priori. Two simulation examples are provided to verify the effectiveness of the proposed control scheme.

Adaptive fuzzy tracking control for a class of high-order switched uncertain nonlinear systems

In this paper, adaptive fuzzy tracking control is investigated for a class of high-order switched nonlinear systems. The considered systems possess the characteristic of completely unknown nonlinear functions and arbitrary switchings. An efficient fuzzy adaptive control method is established by combining the common Lyapunov function method with adding a power integrator approach. A common assumption that is widely used in high-order nonlinear systems with or without switching is removed. Because the unknown nonlinearities can be approximated by using fuzzy logic systems, our proposed method is more flexible and applicable. Furthermore, some effective parameters are introduced such that the obtained results can guarantee that the practical output tracking performance can be realized via easily tuning the controller design parameters. On the other hand, to solve the problem of over-parameterization, a result with only one adaptive law is given. Finally, simulation results are addressed to show the effectiveness of the theoretical approaches.

Adaptive Fuzzy Control of Stochastic Nonstrict-Feedback Nonlinear Systems With Input Saturation

This paper studies an adaptive fuzzy tracking control problem for nonlinear stochastic systems with input saturation and nonstrict-feedback form. We use fuzzy logic systems to approximate unknown nonlinear functions. A novel approach is introduced to tackle unknown functions with nonstrict-feedback structure in the design process. By introducing an auxiliary system, the input saturation problem can be solved. Moreover, based on backstepping control design approach, a novel adaptive fuzzy tracking controller is designed to guarantee all signals in the closed-loop system to be bounded, and the system output can be driven to track the trajectory of a given reference signal. Finally, some simulation results are given to confirm the effectiveness of the proposed approach.

A fuzzy adaptive tracking control for a class of uncertain strick-feedback nonlinear systems with dead-zone input

This paper addresses the problem of fuzzy adaptive tracking control for a class of uncertain strick-feedback nonlinear systems with dead-zone input and unknown bounded disturbances. Dead-zone actuators and unknown disturbances are considered at the same time. The generalized fuzzy hyperbolic model (GFHM) is used to approximate the unknown nonlinear functions. Then, the dynamic surface control (DSC) technique is employed to avoid the problem of ‘explosion of complexity’, and just one adaptive law in the design of controller makes the system more simple and the computational burden lighter. Lyapunov stability analysis shows that all the signals in the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB). Finally, two simulation examples validate the effectiveness of the proposed scheme.

Prescribed Performance Switched Adaptive Dynamic Surface Control of Switched Nonlinear Systems With Average Dwell Time

In this paper, the problem of adaptive fuzzy tracking control is investigated for a class of switched nonlinear systems. A new switched adaptive output feedback control method is presented where the changes of plant can be considered explicitly. Mode-dependent fuzzy logic systems are employed to approximate the switching nonlinear functions in system. To reduce the conservativeness caused by adoption of a common adaptive law for all subsystems, the switching optimal weight vectors are directly estimated via switched adaptive laws at each step of backstepping. However, the difficulties are how to ensure the estimation performance subject to persistent switchings, and how to design common virtual controls based on switching parameters. Further, based on the estimation of optimal weight vectors, the switched fuzzy state observer can be also applied to obtain the unmeasured states. By designing a novel Lyapunov function, the improved dynamic surface control incorporated by prescribed performance technique guarantees all the total state tracking errors, not partial ones, within predefined performance bounds. Simulation results are provided to demonstrate the effectiveness of the proposed method.

Adaptive Fuzzy Backstepping Tracking Control for Strict-Feedback Systems With Input Delay

This paper investigates the problem of adaptive fuzzy tracking control for nonlinear strict-feedback systems with input delay and output constraint. Input delay is handled based on the information of Pade approximation and output constraint problem is solved by barrier Lypaunov function. Some adaptive parameters of the controller need to be updated online through considering the norm of membership function vector instead of all sub-vectors. A novel adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed-loop systems are semiglobally uniformly ultimately bounded, and the tracking error can be adjusted around the origin with a small neighborhood. The stability of the closed-loop systems is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.

Command-Filtered-Based Fuzzy Adaptive Control Design for MIMO-Switched Nonstrict-Feedback Nonlinear Systems

The adaptive fuzzy tracking control design problem for multi-input and multi-output uncertain switched nonstrict-feedback nonlinear systems with arbitrary switchings is investigated in this paper. Fuzzy logic systems are introduced to identify the unknown nonlinear functions (for state measurable case) and model the uncertain nonlinear systems (for state immeasurable case). Both state feedback and observer-based output feedback control design schemes are developed based on combined command filter and adaptive fuzzy control technique. The proposed adaptive fuzzy controllers not only solve the “explosion of complexity” problem existing in conventional backstepping control schemes, but as well as avoid the calculation of partial derivatives. Furthermore, the stability of the fuzzy control systems under arbitrary switchings is proven based on the common Lyapunov function method. Two simulation examples are presented to further demonstrate the effectiveness of the proposed control strategies.

Approximation-based adaptive fuzzy tracking control for a class of switched nonlinear pure-feedback systems

ABSTRACTIn this paper, the problem of adaptive fuzzy tracking control is investigated for switched nonlinear pure-feedback systems under arbitrary switching. By utilising mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Compared with the existing results, a priori knowledge of control directions is not required. On the other hand, differing from the existing literatures, the piecewise switched adaptive laws are designed to replace the common adaptive laws, which can reduce the conservativeness. Furthermore, the difficulties from how to deal with the unknown control directions and design common virtual control are overcome. Based on the backstepping technique and the common Lyapunov functions, an adaptive fuzzy control scheme is developed to guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded with the tracking error converging to a neighbourhood of the origin. Simulation results are provided to demonstrate the effectiveness of the proposed techniques.

Synthetic adaptive fuzzy tracking control for MIMO uncertain nonlinear systems with disturbance observer

In this paper, a synthetic adaptive fuzzy tracking control method is studied for a class of multi-input multi-output (MIMO) uncertain nonlinear systems with time-varying disturbances. The unknown nonlinear functions are approximated by employing generalized fuzzy hyperbolic model. A synthetic adaptive fuzzy control is designed by dynamic surface control, serial-parallel estimation model and the disturbance observer. Then by using Lyapunov stability theory, it is guaranteed that all the variables of the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB). Finally, a satisfactory tracking performance with faster and higher accuracy can be obtained by adjusting the parameters appropriately. A practical example simulation can demonstrate the effectiveness and applicability of the proposed control approach.

Observer-based adaptive fuzzy quantized tracking DSC design for MIMO nonstrict-feedback nonlinear systems

This paper concerned with the problem of observer-based adaptive fuzzy quantized tracking dynamic surface control (DSC) is investigated for the uncertain multi-input and multi-output (MIMO) nonstrict-feedback nonlinear systems, which contain unknown nonlinear functions, input quantization, and unmeasured states. By using fuzzy logic systems to identify the uncertain MIMO nonstrict-feedback nonlinear systems, a fuzzy state observer is introduced to estimate the immeasurable states. By transforming the hysteretic quantized input into a new nonlinear decomposition, and utilizing the DSC backstepping design method, a novel and less conservative fuzzy adaptive quantized tracking control approach is developed. It is shown that the proposed control scheme can guarantee the stability of the closed-loop system, and also that the system outputs can track the given desired trajectories. The simulation results are provided to verify the effectiveness of the proposed control strategy.

Adaptive tracking control for a class of switched uncertain nonlinear systems under a new state-dependent switching law

This paper deals with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and the adaptive backstepping and dynamic surface control techniques are adopted. First, a new state-dependent switching method is proposed. By introducing convex combination technique and designing a state-dependent switching law, only the solvability of the adaptive tracking control problem for a convex combination of the subsystems is necessary. Second, a new common Lyapunov function with switched adaptive parameters is constructed to reduce the conservatism. Third, to avoid Zeno behavior, a modified state-dependent switching law with dwell time is proposed. It is shown that under the proposed control and switching laws, all the signals of the closed-loop system are bounded and all the state tracking errors can converge to a priori accuracy, even if some subsystems are uncontrollable. Finally, the effectiveness of the proposed method is illustrated through two simulation examples.

Fuzzy adaptive control for SISO nonlinear uncertain systems based on backstepping and small-gain approach

With the combination of the adaptive backstepping technique and small-gain approach, the adaptive fuzzy tracking control for a class of uncertain single-input and single-output (SISO) nonlinear systems with unmodeled dynamics, dynamic disturbances, unknown dead zone output and unmeasurable states is studied. The designed controller guarantees that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the output of the closed-loop system converges to a small neighborhood of the desired output. In addition, only three adaptive parameters need to be updated online, which simplifies the structure of the controller and promotes the implementation of the proposed scheme in engineering. A Nussbaum-type function is introduced to overcome the difficulty caused by the non-sensitivity of the output in the dead band. A simulation example is given to show the effectiveness of the proposed algorithm.

Adaptive fuzzy tracking control for nonlinear strict-feedback systems with unmodeled dynamics via backstepping technique

This paper considers an output tracking control problem with unmodeled dynamics for a class of nonlinear strict-feedback systems, which possess unstructured uncertainties and dynamic disturbances. Uncertain nonlinearities contain both unmeasured states and measurable output. A direct tracking controller is obtained on the basic of the backstepping and fuzzy logic system. By the use of small-gain approach, the discussed closed-loop system is proved to be input-to-state practically stable (ISpS) and all the parameter signals are semi-globally uniformly ultimately bounded. There are three adaptive parameters in the fuzzy controller. Finally, simulation examples are given to illustrate the efficiency of the proposed approach.

Robust adaptive fuzzy control of a three-phase active power filter based on feedback linearization

In this paper, a robust adaptive fuzzy control system using feedback linearization is proposed for a three-phase active power filter (APF). The APF system is divided into two separate loops: the current dynamic inner loop and the DC voltage dynamic outer loop. Adaptive fuzzy tracking control using feedback linearization is employed for the current dynamic inner loop to overcome the drawbacks of the conventional method. The proposed controller can ensure proper tracking of the reference current and impose desired dynamic behavior, giving robustness and insensitivity to parameter variations. Adaptive fuzzy proportional-integral control is applied to the DC voltage dynamics outer loop to improve the dynamic response and reduce the error of the stable state. Simulation results demonstrate the high performance of the proposed adaptive fuzzy control strategies.

Adaptive fuzzy tracking control for non-affine nonlinear yaw channel of unmanned aerial vehicle helicopter

The article deals with the problem of the yaw control of the unmanned aerial vehicle helicopter which is non-affine nonlinear by use of a novel projection-based adaptive fuzzy control approach. First, principle model and control design model of the yaw channel of the unmanned aerial vehicle helicopter are described. Then, a dynamic approximation technique is introduced to approach the non-affine model of the unmanned aerial vehicle helicopter into an affine model with variable parameters, which is applied to facilitate the design of nonlinear control scheme. Next, in the proposed controller, fuzzy controller is designed to deal with the unknown uncertainties and disturbances. Meanwhile, the projection-based adaptive law applied in fuzzy controller bounds the parameter estimation function and can also guarantee the robustness of the designed control scheme against uncertain disturbances. Moreover, the convergence and stability of the designed controller are proved by Lyapunov stability theory. Finally, the simulation results of the yaw channel of an unmanned aerial vehicle helicopter are performed to illustrate that the designed controller has good tracking performance, stability, and robustness under the condition of the time-vary uncertain disturbances.

Precision laser tracking servo control system for moving target position measurement

Laser tracking and servo control is essential for the laser tracker to accurately measure coordinates and trajectories of dynamic targets in the space. It has demanding requirements for tracking performance of the servo system in terms of dynamic response properties, controlling accuracy and stability. The currently used servo controlling system in the laser tracker usually adopts the traditional proportional, integral and differential (PID) controlling methods While measuring the dynamic coordinates, the target lens move randomly in a greatly dynamic way; the system’s tracking speed faces a delay in adapting to it, resulting in frequent miss or loss of the target. Based on the requirements of the laser tracing and servo system to quickly track targets moving in a very random and dynamic manner, this paper studies the controlling properties of the laser tracking servo system and the modelling of the controlled objects, proposing a hybrid controlling structure and method which incorporates multi-loop feedback control as well as fuzzy prediction and control-based correction. The deviation signal of the photoelectric location is extracted and fuzzified. Fuzzy rules and controlling strategies are formulated. A fuzzy adaptive PID tracking control algorithm is also presented. A platform for testing the servo tracking system is constructed. The proposed controlling strategies and algorithms are applied to the single-axis laser tracking and rapid prototype tracking tests. Test results show that the angular acceleration of the dynamic tracking servo exceeds 200°/s2, proving great improvements in the system’s random dynamic tracking performance and stability.

Adaptive Fuzzy Tracking Control Design for SISO Uncertain Nonstrict Feedback Nonlinear Systems

This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods.

Adaptive fuzzy tracking control for a class of pure-feedback nonlinear systems with time-varying delay and unknown dead zone

This paper investigates the problem of adaptive fuzzy tracking control for a category of pure-feedback nonlinear systems with time-varying delay and unknown dead zone. Fuzzy logic systems are used to identify unknown functions existing in systems. Mean-value theorem is introduced to overcome the difficulty arising from the pure-feedback structure in designing controller. Based on the information of dead-zone slopes, dead zone is handled. Only one adaptive parameter needs updating online by considering the norm of membership function vectors rather than all sub-vectors. Moreover, utilizing the adaptive backstepping technique, a novel adaptive fuzzy tracking control scheme is developed to guarantee all signals of the closed-loop systems are semi-globally uniformly ultimately bounded, and the tracking error can be regulated to the origin with a small neighborhood. The stability of the closed-loop system is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.

Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation

This paper studies the problem of adaptive output tracking control for a class of nonlinear systems subject to unknown time delay and input saturation. To address the delay and the input saturation, some reasonable assumptions and an auxiliary system are introduced. The fuzzy logic approach is employed to approximate the unknown functions in the system. An observer is designed to estimate the unavailable system states. The dynamic surface control (DSC) technique is utilized to avoid the problem of “explosion of complexity”. By combining the backstepping and DSC methods, a bounded control input is designed to ensure that all signals of the closed-loop system are bounded and the tracking error can fluctuate around the origin within a small neighborhood. Finally, two examples are presented to demonstrate the effectiveness and potential of the proposed new design techniques.