Observer-Based Direct Adaptive Fuzzy-Neural Control for Nonaffine Nonlinear Systems

Guaranteeing Global Stability for Neuro-Adaptive Control of Unknown Pure-Feedback Nonaffine Systems via Barrier Functions

Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article presents a neuro-adaptive backstepping control approach by blending the mean value theorem (MVT), the barrier Lyapunov functions (BLFs), and the technique of neural approximation. Specifically, we first resort the MVT to acquire the intermediate and actual control inputs from the nonaffine structures directly. Then, neural networks (NNs) are adopted to approximate the unknown nonlinear functions, in which the compact sets for maintaining the approximation capabilities of NNs are predetermined actively through the BLFs. It is shown that, with the developed neuro-adaptive control scheme, global stability of the resulting closed-loop system is ensured. Simulations are conducted to verify and clarify the developed approach.

Reduced-Order Observer-Based Dynamic Event-Triggered Adaptive NN Control for Stochastic Nonlinear Systems Subject to Unknown Input Saturation

In this article, a dynamic event-triggered control scheme for a class of stochastic nonlinear systems with unknown input saturation and partially unmeasured states is presented. First, a dynamic event-triggered mechanism (DEM) is designed to reduce some unnecessary transmissions from controller to actuator so as to achieve better resource efficiency. Unlike most existing event-triggered mechanisms, in which the threshold parameters are always fixed, the threshold parameter in the developed event-triggered condition is dynamically adjusted according to a dynamic rule. Second, an improved neural network that considers the reconstructed error is introduced to approximate the unknown nonlinear terms existed in the considered systems. Third, an auxiliary system with the same order as the considered system is constructed to deal with the influence of asymmetric input saturation, which is distinct from most existing methods for nonlinear systems with input saturation. Assuming that the partial state is unavailable in the system, a reduced-order observer is presented to estimate them. Furthermore, it is theoretically proven that the obtained control scheme can achieve the desired objects. Finally, a one-link manipulator system and a three-degree-of-freedom ship maneuvering system are presented to illustrate the effectiveness of the proposed control method.

Asymptotic Fuzzy Neural Network Control for Pure-Feedback Stochastic Systems Based on a Semi-Nussbaum Function Technique

Most existing control results for pure-feedback stochastic systems are limited to a condition that tracking errors are bounded in probability. Departing from such bounded results, this paper proposes an asymptotic fuzzy neural network control for pure-feedback stochastic systems. The control goal is realized by proposing a novel semi-Nussbaum function-based technique and employing it in adaptive backstepping controller design. The proposed Nussbaum function is integrated with adaptive control technique to guarantee that the tracking error is asymptotically stable in probability.

Barrier Function-Based Neural Adaptive Control With Locally Weighted Learning and Finite Neuron Self-Growing Strategy

This paper presents a new approach to construct neural adaptive control for uncertain nonaffine systems. By integrating locally weighted learning with barrier Lyapunov function (BLF), a novel control design method is presented to systematically address the two critical issues in neural network (NN) control field: one is how to fulfill the compact set precondition for NN approximation, and the other is how to use varying rather than a fixed NN structure to improve the functionality of NN control. A BLF is exploited to ensure the NN inputs to remain bounded during the entire system operation. To account for system nonlinearities, a neuron self-growing strategy is proposed to guide the process for adding new neurons to the system, resulting in a self-adjustable NN structure for better learning capabilities. It is shown that the number of neurons needed to accomplish the control task is finite, and better performance can be obtained with less number of neurons as compared with traditional methods. The salient feature of the proposed method also lies in the continuity of the control action everywhere. Furthermore, the resulting control action is smooth almost everywhere except for a few time instants at which new neurons are added. Numerical example illustrates the effectiveness of the proposed approach.

Observer-Based Adaptive Neural Network Control for Nonlinear Systems in Nonstrict-Feedback Form

This paper focuses on the problem of adaptive neural network (NN) control for a class of nonlinear nonstrict-feedback systems via output feedback. A novel adaptive NN backstepping output-feedback control approach is first proposed for nonlinear nonstrict-feedback systems. The monotonicity of system bounding functions and the structure character of radial basis function (RBF) NNs are used to overcome the difficulties that arise from nonstrict-feedback structure. A state observer is constructed to estimate the immeasurable state variables. By combining adaptive backstepping technique with approximation capability of radial basis function NNs, an output-feedback adaptive NN controller is designed through backstepping approach. It is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed-loop systems. Two examples are used to illustrate the effectiveness of the proposed approach.

Decomposed fuzzy systems and their application in direct adaptive fuzzy control

In this paper, a novel fuzzy structure termed as the decomposed fuzzy system (DFS) is proposed to act as the fuzzy approximator for adaptive fuzzy control systems. The proposed structure is to decompose each fuzzy variable into layers of fuzzy systems, and each layer is to characterize one traditional fuzzy set. Similar to forming fuzzy rules in traditional fuzzy systems, layers from different variables form the so-called component fuzzy systems. DFS is proposed to provide more adjustable parameters to facilitate possible adaptation in fuzzy rules, but without introducing a learning burden. It is because those component fuzzy systems are independent so that it can facilitate minimum distribution learning effects among component fuzzy systems. It can be seen from our experiments that even when the rule number increases, the learning time in terms of cycles is still almost constant. It can also be found that the function approximation capability and learning efficiency of the DFS are much better than that of the traditional fuzzy systems when employed in adaptive fuzzy control systems. Besides, in order to further reduce the computational burden, a simplified DFS is proposed in this paper to satisfy possible real time constraints required in many applications. From our simulation results, it can be seen that the simplified DFS can perform fairly with a more concise decomposition structure.

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.

Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics

This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.

Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems

This paper studies an adaptive tracking control for a class of nonlinear stochastic systems with unknown functions. The considered systems are in the nonaffine pure-feedback form, and it is the first to control this class of systems with stochastic disturbances. The fuzzy-neural networks are used to approximate unknown functions. Based on the backstepping design technique, the controllers and the adaptation laws are obtained. Compared to most of the existing stochastic systems, the proposed control algorithm has fewer adjustable parameters and thus, it can reduce online computation load. By using Lyapunov analysis, it is proven that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded in probability and the system output tracks the reference signal to a bounded compact set. The simulation example is given to illustrate the effectiveness of the proposed control algorithm.

Direct Adaptive Neural Control for a Class of Uncertain Nonaffine Nonlinear Systems Based on Disturbance Observer

In this paper, the direct adaptive neural control is proposed for a class of uncertain nonaffine nonlinear systems with unknown nonsymmetric input saturation. Based on the implicit function theorem and mean value theorem, both state feedback and output feedback direct adaptive controls are developed using neural networks (NNs) and a disturbance observer. A compounded disturbance is defined to take into account of the effect of the unknown external disturbance, the unknown nonsymmetric input saturation, and the approximation error of NN. Then, a disturbance observer is developed to estimate the unknown compounded disturbance, and it is established that the estimate error converges to a compact set if appropriate observer design parameters are chosen. Both state feedback and output feedback direct adaptive controls can guarantee semiglobal uniform boundedness of the closed-loop system signals as rigorously proved by Lyapunov analysis. Numerical simulation results are presented to illustrate the effectiveness of the proposed direct adaptive neural control techniques.

A NEW DIRECT ADAPTIVE REGULATOR WITH ROBUSTNESS ANALYSIS OF SYSTEMS IN BRUNOVSKY FORM

The direct adaptive regulation of unknown nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. Since the plant is considered unknown, we propose its approximation by a special form of a Brunovsky type neuro–fuzzy dynamical system (NFDS) assuming also the existence of disturbance expressed as modeling error terms depending on both input and system states plus a not-necessarily-known constant value. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. The existence and boundness of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating laws. Simulations illustrate the potency of the method and its applicability is tested on well known benchmarks, as well as in a bioreactor application. It is shown that the proposed approach is superior to the case of simple recurrent high order neural networks (HONN's).

INDIRECT ADAPTIVE CONTROL OF UNKNOWN MULTI VARIABLE NONLINEAR SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTIES USING A NEW NEURO-FUZZY SYSTEM DESCRIPTION

The indirect adaptive regulation of unknown nonlinear dynamical systems with multiple inputs and states (MIMS) under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new neuro-fuzzy dynamical systems description, which uses the fuzzy partitioning of an underlying fuzzy systems outputs and high order neural networks (HONN's) associated with the centers of these partitions. Every high order neural network approximates a group of fuzzy rules associated with each center. The indirect regulation is achieved by first identifying the system around the current operation point, and then using its parameters to device the control law. Weight updating laws for the involved HONN's are provided, which guarantee that, under the presence of both parameter and dynamic uncertainties, both the identification error and the system states reach zero, while keeping all signals in the closed loop bounded. The control signal is constructed to be valid for both square and non square systems by using a pseudoinverse, in Moore-Penrose sense. The existence of the control signal is always assured by employing a novel method of parameter hopping instead of the conventional projection method. The applicability is tested on well known benchmarks.

ADAPTIVE CONTROL FOR MIMO UNCERTAIN NONLINEAR SYSTEMS USING RECURRENT WAVELET NEURAL NETWORK

Recurrent wavelet neural network (RWNN) has the advantages such as fast learning property, good generalization capability and information storing ability. With these advantages, this paper proposes an RWNN-based adaptive control (RBAC) system for multi-input multi-output (MIMO) uncertain nonlinear systems. The RBAC system is composed of a neural controller and a bounding compensator. The neural controller uses an RWNN to online mimic an ideal controller, and the bounding compensator can provide smooth and chattering-free stability compensation. From the Lyapunov stability analysis, it is shown that all signals in the closed-loop RBAC system are uniformly ultimately bounded. Finally, the proposed RBAC system is applied to the MIMO uncertain nonlinear systems such as a mass-spring-damper mechanical system and a two-link robotic manipulator system. Simulation results verify that the proposed RBAC system can achieve favorable tracking performance with desired robustness without any chattering phenomenon in the control effort.

ROBUST ADAPTIVE FUZZY CONTROLLER DESIGN FOR A CLASS OF UNCERTAIN NONLINEAR TIME-DELAY SYSTEMS

In this paper, the problems of stability and control for a class of uncertain nonlinear systems with unknown state time-delay are studied by using the fuzzy logic systems. Because the dynamic surface control technique is introduced to deal with the uncertain time-delay systems, the designed adaptive fuzzy controller can avoid the issue of "explosion of complexity", which comes from the traditional backstepping design procedure. Compared with the existing results in the literature, the robustness to the fuzzy approximation errors is improved by adjusting the estimations of the unknown bounds for the approximation errors. It is shown that the resulting closed-loop system is stable in the sense that all the signals are bounded and the system output track the reference signal in a small neighborhood of the origin by choosing design parameters appropriately. Three simulation examples are given to demonstrate the effectiveness of the proposed techniques.

Self-Structured Organizing Single-Input CMAC Control for Robot Manipulator

This paper represents a self-structured organizing single-input control system based on differentiable cerebellar model articulation controller (CMAC) for an n-link robot manipulator to achieve the high-precision position tracking. In the proposed scheme, the single-input CMAC controller is solely used to control the plant, so the input space dimension of CMAC can be simplified and no conventional controller is needed. The structure of single-input CMAC will also be self-organized; that is, the layers of single-input CMAC will grow or prune systematically and their receptive functions can be automatically adjusted. The online tuning laws of single-input CMAC parameters are derived in gradient-descent learning method and the discrete-type Lyapunov function is applied to determine the learning rates of proposed control system so that the stability of the system can be guaranteed. The simulation results of robot manipulator are provided to verify the effectiveness of the proposed control methodology.

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.

Adaptive-Fourier-neural-network-based control for a class of uncertain nonlinear systems

An adaptive Fourier neural network (AFNN) control scheme is presented in this paper for the control of a class of uncertain nonlinear systems. Based on Fourier analysis and neural network (NN) theory, AFNN employs orthogonal complex Fourier exponentials as the activation functions. Due to the clear physical meaning of the neurons, the determination of the AFNN structure as well as the parameters of the activation functions becomes convenient. One salient feature of the proposed AFNN approach is that all the nonlinearities and uncertainties of the dynamical system are lumped together and compensated online by AFNN. It can, therefore, be applied to uncertain nonlinear systems without any a priori knowledge about the system dynamics. Derived from Lyapunov theory, a novel learning algorithm is proposed, which is essentially a frequency domain method and can guarantee asymptotic stability of the closed-loop system. The simulation results of a multiple-input-multiple-output (MIMO) nonlinear system and the experimental results of an X - Y positioning table are presented to show the effectiveness of the proposed AFNN controller.

Self-Organizing Adaptive Fuzzy Neural Control for a Class of Nonlinear Systems

This paper proposes a self-organizing adaptive fuzzy neural control (SAFNC) via sliding-mode approach for a class of nonlinear systems. The proposed SAFNC system is comprised of a computation controller and a supervisory controller. The computation controller including a self-organizing fuzzy neural network (SOFNN) identifier is the principal controller. The SOFNN identifier is used to online estimate the controlled system dynamics with the structure and parameter learning phases of fuzzy neural network (FNN), simultaneously. The structure learning phase possesses the ability of online generation and elimination of fuzzy rules to achieve optimal neural structure, and the parameter learning phase adjusts the interconnection weights of neural network to achieve favorable approximation performance. The supervisory controller is used to achieve the L2-norm bound tracking performance with a desired attenuation level. Moreover, all the parameter learning algorithms are derived based on Lyapunov function candidate, thus the system stability can be guaranteed. Finally, simulation results show that the SAFNC can achieve favorable tracking performances.

RCMAC Hybrid Control for MIMO Uncertain Nonlinear Systems Using Sliding-Mode Technology

A hybrid control system, integrating principal and compensation controllers, is developed for multiple-input-multiple-output (MIMO) uncertain nonlinear systems. This hybrid control system is based on sliding-mode technique and uses a recurrent cerebellar model articulation controller (RCMAC) as an uncertainty observer. The principal controller containing an RCMAC uncertainty observer is the main controller, and the compensation controller is a compensator for the approximation error of the system uncertainty. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. The Taylor linearization technique is employed to increase the learning ability of RCMAC and the adaptive laws of the control system are derived based on Lyapunov stability theorem and Barbalat's lemma so that the asymptotical stability of the system can be guaranteed. Finally, the proposed design method is applied to control a biped robot. Simulation results demonstrate the effectiveness of the proposed control scheme for the MIMO uncertain nonlinear system.

Adaptive Wavelet Neural Network Control With Hysteresis Estimation for Piezo-Positioning Mechanism

An adaptive wavelet neural network (AWNN) control with hysteresis estimation is proposed in this study to improve the control performance of a piezo-positioning mechanism, which is always severely deteriorated due to hysteresis effect. First, the control system configuration of the piezo-positioning mechanism is introduced. Then, a new hysteretic model by integrating a modified hysteresis friction force function is proposed to represent the dynamics of the overall piezo-positioning mechanism. According to this developed dynamics, an AWNN controller with hysteresis estimation is proposed. In the proposed AWNN controller, a wavelet neural network (WNN) with accurate approximation capability is employed to approximate the part of the unknown function in the proposed dynamics of the piezo-positioning mechanism, and a robust compensator is proposed to confront the lumped uncertainty that comprises the inevitable approximation errors due to finite number of wavelet basis functions and disturbances, optimal parameter vectors, and higher order terms in Taylor series. Moreover, adaptive learning algorithms for the online learning of the parameters of the WNN are derived based on the Lyapunov stability theorem. Finally, the command tracking performance and the robustness to external load disturbance of the proposed AWNN control system are illustrated by some experimental results.