Direct Adaptive Fuzzy Control Research Articles

Fixed-time adaptive fuzzy control with prescribed tracking performances for flexible-joint manipulators

In this paper, we study the tracking control problem of flexible-joint manipulators with uncertain unstructured dynamics, and develop a prescribed fixed-time solution scheme by combining direct adaptive fuzzy control design with a class of smooth functions. With our scheme, only one adaptive law needs to be calculated online, and also there are no complicated terms, e.g., the partial derivatives of some multivariable functions, involved in virtual controllers and the actual control input, which show that the raised scheme is computationally attractive. Moreover, the boundedness of all closed-loop signals, and the fixed-time convergence of tracking error to a prescribed interval can be established through a rigorous proof, and the obtained results are further confirmed by simulation tests.

Direct Adaptive Fuzzy Control with Prescribed Tracking Accuracy for Orbit Adjustment of Satellites

In this paper, we investigate the orbit-adjustment problem of satellite systems in the presence of nonlinear uncertainties in kinematics and dynamics. We propose a novel direct adaptive fuzzy control scheme with prescribed tracking accuracy to address uncertain nonlinear dynamics by employing advanced fuzzy logic systems and integrating a class of sophisticated smooth functions, thereby ensuring convergence of the tracking error within a precisely defined interval. The ingeniously designed control scheme guarantees negative semi-definiteness of the Lyapunov function, ensuring boundedness for all variables. Moreover, our groundbreaking control approach requires only one adaptive law, completely eliminating any direct correlation with the number of nonlinear functions. Simulation results unequivocally validate the remarkable effectiveness and superiority of our innovative control approach.

Adaptive fuzzy controller for generalized chaotic Lorenz systems with hidden attractors based on Hamilton energy analysis

Control of the generalized chaotic systems’ dynamical behaviors is studied here, by which a direct adaptive fuzzy controller is proposed to control a chaotic dynamical system using their Hamilton energy level. A generalized chaotic Lorenz system with hidden attractors is used as the under-control system, and its Hamilton energy is formulated and analyzed. As a practical consideration, the system is requested to be in a specific desired energy level in each explicit situation. A model-based control is computed and an adaptive fuzzy control is proposed based on it to improve the control signal from the magnitude and smoothness points of view. Adaptation law is designed to adjust the fuzzy controller parameters optimally, based on the Lyapunov second law, and guarantee the system stability. Consequent parameters of the fuzzy rules are tuned based on the residual value between the system’s Hamilton energy and the desired level. Simulation results show superiority of the proposed controller based on tracking performance and control efficiency indices.

Fixed-time adaptive fuzzy control scheme with prescribed tracking accuracy for uncertain nonlinear hysteretic systems

When the Preisach operator, a commonly used hysteresis model, is coupled with uncertain unparametrizable nonlinear dynamics of systems, its tracking control problem in particular with the demands for prescribed tracking accuracy and finite convergence time is challenging, and has not yet been solved in the existing literature. In this study, we focus on the problem, and develop a fixed-time adaptive fuzzy control scheme as a solution to it, based upon a novel decomposition of the Preisach model, the design of a robust control framework, and the integration of a direct adaptive fuzzy control approach. With our scheme, it can be rigorously proved that the tracking error goes to a predefined interval around zero in a bounded convergence time, and all signals in the closed-loop system are bounded. Besides theoretical analysis, the obtained results are also confirmed by experimental tests based on a real-life piezoactuated positioner.

Decentralized direct adaptive fuzzy control scheme for state-constrained interconnected systems

This paper focuses on the problem of decentralized adaptive fuzzy tracking control for state-constrained interconnected systems. However, feasibility conditions on virtual controllers are imposed by barrier Lyapunov function (BLF) based approaches. To remove it, a nonlinear state-dependent barrier function (NSBF) is proposed, based on which the constrained interconnected system is equivalently transformed into a non-constrained one. Nonlinear interactions and uncertainties are approximated by fuzzy logic systems (FLS). A decentralized direct adaptive fuzzy control (DAFC) scheme is developed, in which a class of reduced-order smooth functions is fused with backstepping control design procedures, and only one adaptive law is used in each decentralized controller. With the proposed control scheme, not only the feasibility conditions but also the partial-derivative terms are not involved in virtual controllers, and the time derivative of the Lyapunov function is ensured negative semi-definite. It is shown that the proposed control scheme guarantees that the state constraints are not violated, and the tracking error converges to a predefined interval asymptotically. Two simulation examples confirm the effectiveness of the proposed control scheme.

Tracking Control of Uncertain High-Order Nonlinear Systems with Odd Rational Powers and the Dead-Zone Input: A Direct Fuzzy Adaptive Control Method

Tracking Control of Uncertain High-Order Nonlinear Systems with Odd Rational Powers and the Dead-Zone Input: A Direct Fuzzy Adaptive Control Method

Adaptive Fuzzy Fault-Tolerant Control for a Class of Nonlinear Systems under Actuator Faults: Application to an Inverted Pendulum

This work investigates a fuzzy direct adaptive fuzzy fault-tolerant Control (FFTC) for a class of perturbed single input single output (SISO) uncertain nonlinear systems. The designed controller consists of two sub-controllers. One is an adaptive unit, and the other is a robust unit, whereas the adaptive unit is devoted to getting rid of the dynamic uncertainties along with the actuator faults, while the second one is developed to deal with fuzzy approximation errors and exogenous disturbances. It is proved that the proposed approach ensures a good tracking performance against faults occurring, uncertainties, and exogenous disturbances, and the stability study of the closed-loop is proved regarding the Lyapunov direct method in order to prove that all signals remain bounded. Simulation results are presented to illustrate the accuracy of the proposed technique.

Direct Adaptive Fuzzy Control Scheme With Guaranteed Tracking Performances for Uncertain Canonical Nonlinear Systems

In our recent work, we propose an indirect adaptive fuzzy control scheme for uncertain unparametrizable nonlinear systems, which ensures that the number of adaptive laws does not increase with the number of fuzzy rules, and the time derivative of the chosen Lyapunov function is negative semidefinite. However, the scheme involves a class of high-order smooth functions and their time derivatives, which can make the controller structure become sophisticated especially when the relative degree of system is quite large. To overcome this problem, in the article, we propose a new direct adaptive fuzzy control scheme based on a class of reduced-order smooth functions. With the scheme, no partial-derivative term is involved in controller and virtual controllers, only one adaptive law is used regardless of the increase of fuzzy rules, and also the time derivative of Lyapunov function can be ensured negative semidefinite. It is proved that all closed-loop signals are bounded, and the output tracking error converges to a prescribed interval asymptotically. The transient tracking performance and robustness of the proposed control scheme are also considered. The effectiveness of the obtained results is illustrated by two practical control systems.

Direct Adaptive Fuzzy Tracking Control of Non-affine Stochastic Nonlinear Time-Delay Systems

In this research, the problem of direct adaptive fuzzy control based on state feedback for a class of non-affine stochastic nonlinear systems with time delay is considered. Fuzzy logic systems (FLSs) and mean value theorem are utilized to overcome the design difficulties appeared in the unknown nonlinearities and non-affine structure, respectively. With the utilization of adaptive control and backstepping design framework, a direct adaptive fuzzy control method is developed. Through Lyapunov analysis, the presented controller can guarantee that the variables in the closed-loop system are all bounded in the fourth-moment, in the mean time, the output signal can track the given reference signal by appropriately selecting the design parameters. Simulation results are provided to illustrate the correctness of the theoretical results.

A novel disturbance rejection factor based stable direct adaptive fuzzy control strategy for a class of nonlinear systems

AbstractThis paper proposes a unique disturbance rejection factor (DRF) based design of direct stable adaptive fuzzy logic controllers (AFLCs) for a class of non‐linear systems with large and fast disturbances. The proposed AFLCs are realized by employing hybrid combinations of Lyapunov theory based local adaptation and harmony search algorithm based global optimization technique. These hybrid AFLCs are designed with the objective of optimizing both the structure and free parameters of it with guaranteed stability and, at the same time, simultaneously achieving satisfactory tracking performance and disturbance rejection. The novelty of the proposed work lies in the fact that, in a bid to perform the disturbance rejection, the nature of the disturbance itself is used in designing the tracking control law. The proposed DRF based hybrid stable AFLCs are implemented for several benchmark case studies and extensive performance evaluations demonstrate their usefulness.

Combined indirect & direct adaptive fuzzy decentralised control of large-scale systems with strong interconnection and its application

To achieve better adaptation properties, the proposed controller is a weighted combination of indirect and direct adaptive fuzzy controls such that both fuzzy descriptions and control rules can be incorporated under a united controller design at the same time. By using fuzzy systems and robust control technique, the interconnections between subsystems are extended to general unknown nonlinear functions. No a priori knowledge of lower and upper bounds on lumped uncertainties is required to construct each local controller. The resulting closed-loop large-scale system is proved to be asymptotically stable. The controller design is applicable to an automated highway system, and simulation results confirm its practical usefulness.

Finite-Time Fuzzy Adaptive Consensus for Heterogeneous Nonlinear Multi-Agent Systems

This paper deals with the finite-time consensus control problem for a class of nonlinear strict-feedback multi-agent systems with heterogeneous dynamics. Due to the existence of unknown nonlinear dynamics of the system, this paper adopts the excellent approximation ability of fuzzy logic systems to design the consensus control protocol. Moreover, fuzzy logic systems and adaptive method are used to approximate the unknown system dynamics in the design of virtual controllers for different orders of the subsystems. The proposed direct adaptive fuzzy tracking controller for every agent is constructed via a backstepping design process. The proposed adaptive fuzzy controller can ensure that the outputs of all agents can track a common desired trajectory in finite time. Finally, the performance of the proposed fuzzy adaptive consensus control algorithm is demonstrated by two numerical studies of MASs including both homogeneous and heterogeneous dynamics of the interacting agents.

Direct adaptive fuzzy position controller for an electropneumatic actuator: Design and experimental evaluation

This paper proposes a direct adaptive fuzzy position controller for an electropneumatic actuator. This control approach is based on the estimation of an ideal inverse dynamic control, which is capable of satisfying the control objectives in terms of tracking desired trajectories and stability. For this purpose, a fuzzy system is used to approximate as best as possible this ideal inverse dynamic control. The adjustable parameters of the used fuzzy system are updated online with a stable adaptation law. This latter is developed in order to minimize the error between the unknown ideal inverse dynamic control and the used fuzzy controller. The general non-affine model of the controlled actuator is used to develop the control law and its adaptation mechanism, meaning that the presented adaptive fuzzy position controller does not rely on a physical model of the pneumatic actuator. The stability of the closed-loop system is performed using a Lyapunov approach. Finally, real-time experimental results are presented to show the performances of the proposed position controller.

Stability analysis of brain emotional intelligent controller with application to electrically driven robot manipulators

This study discusses stability analysis of the brain emotional learning-based intelligent controller (BELBIC) for model-free tracking control of a class of uncertain non-linear systems. Due to the unique adaptation laws for the controller gains, stability analysis of these controllers is a challenging task. This issue constructs the motivation of this study to undertake this task. Similar to direct adaptive fuzzy control, the BELBIC plays the role of a direct intelligent controller. Thus, the stability of the BELBIC can be guaranteed based on the stability analysis of direct adaptive fuzzy control. The main objective of this study is that the stability of the BELBIC in tracking control of a class of uncertain non-linear systems is guaranteed. Based on the proposed stability analysis and Barbalat's lemma, BELBIC can yield in the asymptotic convergence of the tracking error to zero. In comparison with the existing works in the literature, the proposed approach has fewer tuning parameters. Therefore, the developed approach has a simple structure. The simulation results on an articulated manipulator actuated by permanent magnet DC motors and comparison with other model-free approaches are presented to show the superiority of the proposed approach.

Adaptive Fuzzy Control for Multivariable Nonlinear Systems with Indefinite Control Gain Matrix and Unknown Control Direction

Abstract In this paper, we focus on the direct adaptive fuzzy control design for a class of uncertain MIMO nonlinear systems with indefinite control gain matrix and unknown control direction. The control design is based on the approximation of an unknown ideal control law that can meet the control objective by using fuzzy systems. The adjustable parameters of the used fuzzy systems are adjusted online using the error between the unknown ideal controller and the fuzzy controller. In this paper, unlike most existing works, the Nussbaum gain technique is not used to overcome the obstacle of the unknown control direction. In fact, with the help of a matrix decomposition technique, the unknown control direction is redefined as an unknown constant vector, which is estimated online by a suitable update law. The stability of the closed-loop system is studied using the Lyapunov direct approach. Numerical simulation results are provided to illustrate the effectiveness of the proposed control design approach.

Direct Adaptive Fuzzy Control of Nonlinear Descriptor Systems

This paper deals with direct adaptive fuzzy control for uncertain affine nonlinear descriptor systems. Two cases are considered: in the first one, it is assumed that the control gain is known, while in the second one, it is an unknown-but-bounded symmetric positive definite matrix. To account for uncertainties in the system dynamics, a fuzzy system is employed to directly approximate the unknown ideal controller. The adjustable parameters of the fuzzy system are updated by either a Lyapunov-based adaptative law in the first case, or a gradient descent algorithm minimizing a suitable quadratic cost function in the second case. Furthermore, an auxiliary compensating signal is designed to guarantee that the tracking error asymptotically vanishes in both cases. Simulation results show how the proposed methods exhibit satisfactory performance thus demonstrating their effectiveness.

Saturated Adaptive Hierarchical Fuzzy Attitude-Tracking Control of Rigid Spacecraft With Modeling and Measurement Uncertainties

The problem of the attitude-tracking control of spacecraft subject to additive measurement uncertainty, control saturation, parametric uncertainty, and unknown external disturbances is studied in this paper. Because of the mismatched disturbance generated by measurement uncertainty in attitude kinematics, the normwise adaptive estimations for the bounds of the mismatched disturbance are involved in the kinematical controller; then, a saturated adaptive hierarchical fuzzy controller for attitude dynamics is developed in the backstepping design, where an antiwindup compensator is used to deal with the effect of control saturation, elementwise adaptive estimations are used to compensate parametric uncertainty, and direct adaptive hierarchical fuzzy control is designed to compensate the lumped disturbances in attitude dynamics. It is proved via Lyapunov analysis that the attitude-tracking errors eventually converge to adjustable small neighborhoods of zero. Simulation results validate the effectiveness and performance of the proposed control approach.

Synchronization and identification of nonlinear systems by using a novel self-evolving interval type-2 fuzzy LSTM-neural network

Nonlinear systems widely exist in the real world. Researches on the synchronization and identification of nonlinear systems have both theoretical and practical interests. However, since the pseudo-random and parameter sensitivity, some nonlinear dynamics, such as chaotic systems, are difficult to achieve the required regression approximation. By means of the fuzzy-neural structure and long short-term memory (LSTM) mechanism, this paper proposes a novel inference structure of the self-evolving interval type-2 fuzzy LSTM-neural network (eIT2FNN-LSTM) for the synchronization and identification of nonlinear dynamics. In order to tackle with the time-dependency data generated by nonlinear systems, recurrent neural fuzzy systems with LSTM structure is introduced into type-2 fuzzy neural networks, where, by means of gate mechanism, a recurrent structure in the time dimension by feeding the rule firing strength of each rule back to itself is implemented. Besides, an online rule generation algorithm based on dynamic density clustering is utilized to achieve structural updates, which can meet the need of high frequency data process in reality. By incorporating direct adaptive interval type-2 LSTM fuzzy control scheme and sliding mode approach, two chaotic systems with external disturbance noise or/and random-varying parameters can be synchronized based on Lyapunov stability criterion, where two methods, i.e., the gradient training and particle swarm optimization (PSO) algorithm are used. In order to further verify the universality of the proposed scheme, besides nonlinear system, real-life datasets are also utilized to verify the effectiveness of the proposed fuzzy-neural inference system.

Adaptive fuzzy output feedback control for nonlinear systems based on event-triggered mechanism

Approaches of considering event-triggered fuzzy control for nonlinear output feedback systems are restricted to a conservative result that only a tunable unknown tracking error is obtained. This work proposes a new fuzzy control strategy to remove this restriction. Technically, a new idea contributes to the design of the Lyapunov function, which is constructed with a series of smooth functions rather than chosen in a quadratic form as regular. With this idea, a new direct adaptive fuzzy controller is then developed to avoid the possible chattering phenomenon in addition to achieve the asymptotic stability. Besides the chattering-free property, the proposed scheme is performance-oriented in the sense that the relationship between the design parameters and tracking performance is established in an explicit way, which allows the users to make design decisions accordingly. Through Lyapunov analysis, it is proven that besides the system stability, the tracking error will ultimately approach to a user-defined interval. Simulation studies are performed to demonstrate the theoretical results.

Adaptive-Fuzzy Control Compensation Design for Direct Adaptive Fuzzy Control

For direct adaptive fuzzy control of perturbed uncertain nonlinear systems, proportional-integral-derivative control compensation usually has to be used to guarantee $H_{{{\infty }}}$ tracking performance or $L_{2}$ -gain property of the closed-loop system. One common problem is that the control compensation often introduces unwanted high gain at the control input. This paper proves that classical direct adaptive fuzzy control with adaptive-fuzzy control compensation not only is capable of solving the problem of high gain, but also can guarantee $L_{2}$ -gain property of the closed-loop system. A sliding-surface-based adaptive fuzzy control is designed for control compensation. By using a class of triangular membership functions nearest to the origin and a simple adaptive law, the adaptive fuzzy control term is converted to an equivalence control term, which is used to facilitate stability analysis. Moreover, the system output can track not only the constant-period periodic signals but also the constant signal. Compared with previous direct adaptive fuzzy control approaches that can guarantee $H_{{{\infty }}}$ tracking performance or $L_{2}$ -gain property, in addition to the $L_{2}$ -gain property of common tracking error rather than modified tracking error, the major advantages of our approach are that the assumptions on control gain function are relaxed and a less conservative control design on robustness is achieved. Simulation results are given to demonstrate the effectiveness of the proposed approach.