Robust adaptive self-structuring fuzzy control design for nonaffine,nonlinear systems

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L ₂ tracking performance to stabilise the closed-loop system. This L ₂ tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.     

分散混杂自适应模糊H∞控制器及其在自动化公路系统中的应用

本文针对一类SISO不确定非线性大系统,提出了一种混杂间接和直接自适应分散模糊H∞控制器.通过组合模糊系统和H∞跟踪技术开发的分散自适应模糊控制算法避免了控制设计中含有的符号函数.两种自适应模糊控制器的组合消除了它们各自均不能够同时融合被控对象知识与控制知识的局限.闭环大系统被证明是稳定的,且具有H∞跟踪性能.该算法应用于自动化公路系统中车辆的纵向跟随控制,仿真结果表明混杂自适应模糊H∞控制系统的跟踪性能更好而相应的控制幅值却更小.     

Robust decentralized adaptive fuzzy control for a class of large‐scale MIMO nonlinear systems

In this paper, a novel decentralized robust adaptive fuzzy control scheme is proposed for a class of large‐scale multiple‐input multiple‐output uncertain nonlinear systems. By virtue of fuzzy logic systems and the regularized inverse matrix, the decentralized robust indirect adaptive fuzzy controller is developed such that the controller singularity problem is addressed under a united design framework; no a priori knowledge of the bounds on lumped uncertainties are being required. The closed‐loop large‐scale system is proved to be asymptotically stable. Simulation results confirmed the validity of the approach presented. Copyright © 2011 John Wiley & Sons, Ltd.     

一类大系统的分散自适应模糊滑模控制

研究了一类具有未知函数控制增益的非线性大系统的分散模糊控制问题.基于滑模 控制原理和模糊集理论,提出了一种分散自适应模糊控制器的设计方法.通过理论分析,证明 了分散自适应模糊控制系统是全局稳定的,跟踪误差可收敛到零的一个领域内.     

Decentralised direct adaptive fuzzy control for a class of large-scale nonaffine nonlinear systems and application to AHS

A novel decentralised direct adaptive fuzzy controller design is presented for a class of large-scale nonaffine uncertain nonlinear systems in this article. By integrating a fuzzy logic system and H _∞ tracking technique, the designed controller is able to adaptively compensate for interconnections and disturbances with unknown bounds, but none of the control and adaptation laws contains a sign function so that control chattering can be shunned. The closed-loop large-scale system is guaranteed to be asymptotically stable and obtain good H _∞ tracking performance. The control approach developed is applied to the following control problem of a string of vehicles within an automated highway system (AHS) and simulation results verify its validity.     

一类MIMO非线性大系统基于H∞ 跟踪的分散自适应输出反馈模糊控制

针对一类状态不可测的MIMO不确定非线性大系统,提出一种基于H∞跟踪的分散自适应输出反馈模糊控制器.主要工作有:1)通过对观测误差向量进行滤波来确保严格正实条件成立,使得提出的反馈与自适应机制可以执行;2)利用模糊系统提出一种适用于一般非线性大系统基于H∞跟踪的分散自适应模糊控制方案;3)在统一的框架下处理了控制器奇异性.闭环大系统被证明足稳定的,且输出误差具有H∞跟踪性能.仿真结果验证了控制器设计的有效性.     

Robust Decentralized Adaptive Fuzzy Control of Large‐Scale Nonaffine Nonlinear Systems With Strong Interconnection and Application to Automated Highway Systems

A novel decentralized adaptive fuzzy controller is developed for a class of large‐scale uncertain nonaffine nonlinear systems in this paper. Incorporating the benefits of fuzzy systems, implicit function theorem, 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 implement 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.     

Decentralized robust H<Subscript>∞</Subscript> output feedback control for value bounded uncertain large-scale interconnected systems

In this paper, decentralized robust H_∞ output feedback control problem for large-scale interconnected system with value bounded uncertainties in the state, control input and interconnection matrices is investigated. A new bounded real lemma for the large-scale interconnected systems is derived by Lyapunov stability theory and linear matrix inequality method. Based on the new bounded real lemma, a sufficient condition expressed as matrix inequalities for the existence of a decentralized robust H_∞ output feedback controller is obtained. The controller which enables the closed-loop large-scale system robust stable and satisfies the given H_∞ performance is designed through a homotopy iterative method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

一类复杂控制系统分散自适应鲁棒控制器设计

基于模糊逻辑系统具有充分利用语言信息和逼近连续函数性质的思想,分析研究了一类非线性不确定复杂系统的自适应控制问题.利用系统的数学模型和模糊逻辑系统对不确定性的输出信息,设计出了复杂系统的分散自适应鲁棒控制器和模糊逻辑系统参数估计的自适应律,在较弱的假设条件下,证明了这种控制器使被控系统的状态及参数估计误差一致终极有界.仿真实例表明,所提出的方法是有效的.     

Decentralised direct adaptive output feedback fuzzy controller for a class of large-scale nonaffine nonlinear systems and its applications

A novel cooperation-based decentralised direct adaptive fuzzy control via output feedback is developed for a class of large-scale nonaffine uncertain nonlinear systems using a direct adaptive fuzzy approach in this article. Under assumption that all the controllers share their prior information about the subsystem reference models, the interconnections between subsystems are relaxed to arbitrarily strong nonlinearities without matching conditions. The assumption on input gains is extended from typical positive constants to highly nonlinear functions. The feedback and adaptation mechanisms require neither the typical observation error filtering nor the famous strictly positive-real condition. Based on Lyapunov's direct method, the tracking errors of the closed-loop large-scale system are guaranteed to converge to tunable neighbourhoods of the origin. The proposed algorithm is applied to controlling two mechanical large-scale systems and simulation results substantiate its effectiveness.     

Decentralized adaptive tracking control of nonaffine nonlinear large-scale systems with time delays

This paper addresses the problem of decentralized tracking control of large-scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time-varying delays. Based on Lyapunov-Krasovskii functional approach and implicit function theorem, a delay-independent decentralized tracking controller is proposed. Due to functional approximation capability of fuzzy logic systems (FLS), neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time-varying delays is required in our control design. Furthermore, transient performance of the resulting closed-loop system is also addressed under an analytical framework. Finally, two numerical examples are provided to show the effectiveness of the proposed controller.     

Fixed-structure robust controller synthesis via decentralized static output feedback

This paper describes and illustrates a unified methodology for robust, fixed-structure controller synthesis. The approach is based upon direct fixed-structure controller synthesis using a decentralized static output feedback formulation as a general framework for representing a large class of controller structures. Scaled Popov bounds for the real structured singular value are used to account for real parameter uncertainty and provide the means for optimizing a worst-case ℋ︁₂ cost bound with respect to the free parameters of the controller. Quasi-Newton optimization algorithms are used to solve the resulting numerical optimization problem. Initial stability multiplier and scaling matrices needed in scaled Popov synthesis are obtained by solving an LMI feasibility problem. Using both centralized and decentralized controller structures, numerical results are obtained for a 16th-order acoustic duct model with uncertain damped natural frequencies and for a two-dimensional beam-spring model with uncertain actuator locations. © 1998 John Wiley & Sons, Ltd.     

Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

基于观测器的可重构机械臂分散自适应模糊控制

提出一种基于观测器的可重构机械臂分散自适应模糊控制方案.将可重构机械臂的动力学描述为一个交联子系统的集合,子系统控制器由自适应模糊系统和鲁棒控制项组成.基于状态观测器观测值构建的自适应模糊系统用于逼近子系统动力学模型和交联项,鲁棒控制项用于抵消模糊逼近误差对轨迹跟踪的影响.数值仿真证明了所提出的分散控制方案的有效性.     

Decentralized adaptive backstepping stabilization of interconnected systems with dynamic input and output interactions

So far there is still no result available for backstepping based decentralized adaptive stabilization of unknown systems with interactions directly depending on subsystem inputs, even though such interactions commonly exist in practice. In this paper, we provide a solution to this problem by considering both input and output dynamic interactions. To clearly illustrate our approaches, we will start with linear systems and then extend the results to nonlinear systems. Each local controller, designed simply based on the model of each subsystem by using the standard adaptive backstepping technique without any modification, only employs local information to generate control signals. It is shown that the designed decentralized adaptive backstepping controllers can globally stabilize the overall interconnected system asymptotically. The L₂ and L_∞ norms of the system outputs are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters.     

Decentralized global disturbance attenuation for a class of large-scale uncertain nonlinear systems

This paper studies the problem of global robust disturbance attenuation via decentralized state feedback for a class of large-scale nonlinear systems with parameter and interconnection uncertainties. The parameter uncertainty is from a compact set and the uncertain interconnections are bounded by higher-order polynomials of state variables. The problem that we address is to design a robust decentralized controller such that the closed-loop large-scale nonlinear system is input-to-state stable and the L₂ gain from the disturbance input to the controlled output is below a prescribed value for all admissible uncertain parameters and interconnections. A Lyapunov-based recursive design approach is developed to construct the decentralized controller explicitly. As a special case, the problem of almost disturbance decoupling via decentralized state feedback is also solved.     

Intelligent complementary sliding-mode control with dead-zone parameter modification

This paper proposes an intelligent complementary sliding-mode control (ICSMC) system which is composed of a computed controller and a robust controller. The computed controller includes a neural dynamics estimator and the robust compensator is designed to prove a finite L₂-gain property. The neural dynamics estimator uses a recurrent neural fuzzy inference network (RNFIN) to approximate the unknown system term in the sense of the Lyapunov function. In traditional neural network learning process, an over-trained neural network would force the parameters to drift and the system may become unstable eventually. To resolve this problem, a dead-zone parameter modification is proposed for the parameter tuning process to stop when tracking performance index is smaller than performance threshold. To investigate the capabilities of the proposed ICSMC approach, the ICSMC system is applied to a one-link robotic manipulator and a DC motor driver. The simulation and experimental results show that favorable control performance can be achieved in the sense of the L₂-gain robust control approach by the proposed ICSMC scheme.     

Nonlinear fractional‐order power system stabilizer for multi‐machine power systems based on sliding mode technique

This paper presents two novel nonlinear fractional‐order sliding mode controllers for power angle response improvement of multi‐machine power systems. First, a nonlinear block control is used to handle nonlinearities of the interconnected power system. In the second step, a decentralized fractional‐order sliding mode controller with a nonlinear sliding manifold is designed. Practical stability is achieved under the assumption that the upper bound of the fractional derivative of perturbations and interactions are known. However, when an unknown transient perturbation occurs in the system, it makes the evaluation of perturbation and interconnection upper bound troublesome. In the next step, an adaptive‐fuzzy approximator is applied to fix the mentioned problem. The fuzzy approximator uses adjacent generators relative speed as own inputs, which is known as semi‐decentralized control strategy. For both cases, the stability of the closed‐loop system is analyzed by the fractional‐order stability theorems. Simulation results for a three‐machine power system with two types of faults are illustrated to show the performance of the proposed robust controllers versus the conventional sliding mode. Additionally, the fractional parameter effects on the system transient response and the excitation voltage amplitude and chattering are demonstrated in the absence of the fuzzy approximator. Finally, the suggested controller is combined with a simple voltage regulator in order to keep the system synchronism and restrain the terminal voltage variations at the same time. Copyright © 2014 John Wiley & Sons, Ltd.     

Decentralized adaptive fuzzy sliding mode control for reconfigurable modular manipulators

A stable decentralized adaptive fuzzy sliding mode control scheme is proposed for reconfigurable modular manipulators to satisfy the concept of modular software. For the development of the decentralized control, the dynamics of reconfigurable modular manipulators is represented as a set of interconnected subsystems. A first‐order Takagi–Sugeno fuzzy logic system is introduced to approximate the unknown dynamics of subsystem by using adaptive algorithm. The effect of interconnection term and fuzzy approximation error is removed by employing an adaptive sliding mode controller. All adaptive algorithms in the subsystem controller are derived from the sense of Lyapunov stability analysis, so that resulting closed‐loop system is stable and the trajectory tracking performance is guaranteed. The simulation results are presented to show the effectiveness of the proposed decentralized control scheme. Copyright © 2009 John Wiley & Sons, Ltd.     

A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems

This paper investigates the robust H_∞ control and non-fragile control problems for Takagi-Sugeno (T-S) fuzzy systems with linear fractional parametric uncertainties. The robust H_∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H_∞ performance of the resulting closed-loop system is ensured. And the non-fragile H_∞ control problem is to design a state feedback controller with parameter uncertainties. Based on the linear matrix inequality (LMI) approach, new sufficient conditions for the solvability of the two problems are obtained. It is shown that the desired state feedback fuzzy controller can be constructed by solving a set of LMIs. Numerical examples are also provided to demonstrate the effectiveness of the proposed design method.