Adaptive dynamic surface control for uncertain nonlinear systems with interval type-2 fuzzy neural networks

Observer-based finite-time adaptive fuzzy back-stepping control for MIMO coupled nonlinear systems

An attempt is made in this paper to devise a finite-time adaptive fuzzy back-stepping control scheme for a class of multi-input and multi-output (MIMO) coupled nonlinear systems with immeasurable states. In view of the uncertainty of the system, adaptive fuzzy logic systems (AFLSs) are used to approach the uncertainty of the system, and the unmeasured states of the system are estimated by the finite-time extend state observers (FT-ESOs), where the state of the observer is a sphere around the state of the system. The accuracy and efficiency of the control effect are ensured by combining the back-stepping and finite-time theory. It is proved that all the states of the closed-loop adaptive control system are semi-global practical finite-time stability (SGPFS) by the finite-time Lyapunov stability theorem, and the tracking errors of the system states converge to a tiny neighborhood of the origin in a finite time. The validity of this scheme is demonstrated by a simulation.

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H_∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example.

Prescribed Performance Control with Sliding-Mode Dynamic Surface for a Glue Pump Motor Based on Extended State Observers

The actuator of a particleboard glue-dosing system, the glue pump motor, is affected by external disturbances and unknown uncertainty. In order to achieve accurate glue-flow tracking, in this paper, a glue pump motor compound control method was designed. First, the prescribed performance control method is used to improve the transient behaviors, and the error of the glue flow tracking is guaranteed to converge to a preset range, as a result of the design of an appropriate performance function. Second, two extended state observers were designed to estimate the state vector and the disturbance, in order to improve the robustness of the controlled system. To further strengthen the steady-state performance of the system, the sliding-mode dynamic surface control method was introduced to compensate for uncertainties and disturbances. Finally, a Lyapunov stability analysis was conducted, in order to prove that all of the signals are bounded in a closed-loop system, and the effectiveness and feasibility of the proposed method were verified through numerical simulation.

Admissibility Analysis for Interval Type-2 Fuzzy Descriptor Systems Based on Sliding Mode Control

This paper is concerned with the sliding mode control of nonlinear singular systems in terms of the interval type-2 (IT2) fuzzy model. To better approximate the nonlinear systems, the modeling errors are considered in the IT2 fuzzy model. The uncertainties in membership functions are expressed based on their boundedness. Admissibility conditions are obtained via a linear matrix inequalities approach. A new reaching law-based sliding controller is presented by choosing a typical sliding surface to analyze the sliding motion, such that all of the input gains are allowed to be different and the chattering of the system can be minimized with a guaranteed H_∞ performance. The feasibility of the proposed control method is verified by simulation results.

Interval Type-2 Fuzzy Neural Networks for Chaotic Time Series Prediction: A Concise Overview

Chaotic time series widely exists in nature and society (e.g., meteorology, physics, economics, etc.), which usually exhibits seemingly unpredictable features due to its inherent nonstationary and high complexity. Thankfully, multifarious advanced approaches have been developed to tackle the prediction issues, such as statistical methods, artificial neural networks (ANNs), and support vector machines. Among them, the interval type-2 fuzzy neural network (IT2FNN), which is a synergistic integration of fuzzy logic systems and ANNs, has received wide attention in the field of chaotic time series prediction. This paper begins with the structural features and superiorities of IT2FNN. Moreover, chaotic characters identification and phase-space reconstruction matters for prediction are presented. In addition, we also offer a comprehensive review of state-of-the-art applications of IT2FNN, with an emphasis on chaotic time series prediction and summarize their main contributions as well as some hardware implementations for computation speedup. Finally, this paper trends and extensions of this field, along with an outlook of future challenges are revealed. The primary objective of this paper is to serve as a tutorial or referee for interested researchers to have an overall picture on the current developments and identify their potential research direction to further investigation.

Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks

This paper investigates the controllability and synchronization problems for identical-hierarchy mixed-valued logical control networks. The logical network considered is hierarchical, and Boolean network is a special case of logical network. Here, identical-hierarchy means that there are identical number of nodes in each layer of logical network and corresponding nodes have the same dimension for any two layers of logical networks. Meanwhile, in each layer of logical networks, the dimensions of nodes are distinct, and it is called a mixed-valued logical network. First, the controllability problem is investigated and two notions of controllability are presented, i.e., group-controllability and simultaneously-controllability. By resorting to Perron-Frobenius theorem, some necessary and sufficient criteria are obtained to guarantee group-controllability and simultaneously-controllability, respectively. Second, based on the algebraic representation of the studied model, synchronization problems are analytically discussed for two types of controls, i.e., free control sequences and state-output feedback control. Finally, two numerical examples are presented to show the validness of our main results.

Command Filter-Based Adaptive Neural Tracking Controller Design for Uncertain Switched Nonlinear Output-Constrained Systems

In this paper, a new adaptive approximation-based tracking controller design approach is developed for a class of uncertain nonlinear switched lower-triangular systems with an output constraint using neural networks (NNs). By introducing a novel barrier Lyapunov function (BLF), the constrained switched system is first transformed into a new system without any constraint, which means the control objectives of the both systems are equivalent. Then command filter technique is applied to solve the so-called "explosion of complexity" problem in traditional backstepping procedure, and radial basis function NNs are directly employed to model the unknown nonlinear functions. The designed controller ensures that all the closed-loop variables are ultimately boundedness, while the output limit is not transgressed and the output tracking error can be reduced arbitrarily small. Furthermore, the use of an asymmetric BLF is also explored to handle the case of asymmetric output constraint as a generalization result. Finally, the control performance of the presented control schemes is illustrated via two examples.

Deriving and Analyzing Analytical Structures of a Class of Typical Interval Type-2 TS Fuzzy Controllers

A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.

Adaptive Neural Network Control for the Trajectory Tracking of the Furuta Pendulum

The purpose of this paper is to introduce a novel adaptive neural network-based control scheme for the Furuta pendulum, which is a two degree-of-freedom underactuated system. Adaptation laws for the input and output weights are also provided. The proposed controller is able to guarantee tracking of a reference signal for the arm while the pendulum remains in the upright position. The key aspect of the derivation of the controller is the definition of an output function that depends on the position and velocity errors. The internal and external dynamics are rigorously analyzed, thereby proving the uniform ultimate boundedness of the error trajectories. By using real-time experiments, the new scheme is compared with other control methodologies, therein demonstrating the improved performance of the proposed adaptive algorithm.

Adaptive Fuzzy Tracking Control for a Class of MIMO Nonlinear Systems in Nonstrict-Feedback Form

This paper focuses on the problem of fuzzy adaptive control for a class of multiinput and multioutput (MIMO) nonlinear systems in nonstrict-feedback form, which contains the strict-feedback form as a special case. By the condition of variable partition, a new fuzzy adaptive backstepping is proposed for such a class of nonlinear MIMO systems. The suggested fuzzy adaptive controller guarantees that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors eventually converge to a small neighborhood around the origin. The main advantage of this paper is that a control approach is systematically derived for nonlinear systems with strong interconnected terms which are the functions of all states of the whole system. Simulation results further illustrate the effectiveness of the suggested approach.

A New Framework for Analysis on Stability and Bifurcation in a Class of Neural Networks With Discrete and Distributed Delays

This paper studies the stability and Hopf bifurcation in a class of high-dimension neural network involving the discrete and distributed delays under a new framework. By introducing some virtual neurons to the original system, the impact of distributed delay can be described in a simplified way via an equivalent new model. This paper extends the existing works on neural networks to high-dimension cases, which is much closer to complex and real neural networks. Here, we first analyze the Hopf bifurcation in this special class of high dimensional model with weak delay kernel from two aspects: one is induced by the time delay, the other is induced by a rate parameter, to reveal the roles of discrete and distributed delays on stability and bifurcation. Sufficient conditions for keeping the original system to be stable, and undergoing the Hopf bifurcation are obtained. Besides, this new framework can also apply to deal with the case of the strong delay kernel and corresponding analysis for different dynamical behaviors is provided. Finally, the simulation results are presented to justify the validity of our theoretical analysis.

Adaptive Neural Stabilizing Controller for a Class of Mismatched Uncertain Nonlinear Systems by State and Output Feedback

In this paper, first, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is proposed. By using a radial basis function NN (RBFNN), a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. Then, an observer-based adaptive controller based on RBFNN is designed to stabilize uncertain nonlinear systems with immeasurable states. The state-feedback and observer-based controllers are based on Lyapunov and strictly positive real-Lyapunov stability theory, respectively, and it is shown that the asymptotic convergence of the closed-loop system to zero is achieved while maintaining bounded states at the same time. The presented methods are more general than the previous approaches, handling systems with no restriction on the dimension of the system and the number of inputs. Simulation results confirm the effectiveness of the proposed methods in the stabilization of mismatched nonlinear systems.