Mixed H2/H∞ fuzzy output feedbackcontrol design for nonlinear dynamic systems: an LMI approach

This study introduces a mixed H₂/H_∞ fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H₂/H_∞ controller is developed to achieve the suboptimal H₂ control performance with a desired H_∞ disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H₂/H_∞ control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method     

Fuzzy tracking control design for nonlinear dynamic systems via T-Sfuzzy model

This study introduces a fuzzy control design method for nonlinear systems with a guaranteed H_∞ model reference tracking performance. First, the Takagi and Sugeno (TS) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be solved very efficiently using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method     

Multiobjective PID control design in uncertain robotic systemsusing neural network elimination scheme

A PID-type controller incorporating neural network elimination scheme and sliding-mode control action for different objectives including H₂ tracking performance, H_∞ tracking performance, and regional pole constraints is developed in robotic systems under plant uncertainties and external disturbances. The adaptive neural networks are used to compensate the plant uncertainties. The sliding-mode control action is included to eliminate the effect of approximation error via neural network approximation. The sufficient conditions are developed for different objectives in terms of linear matrix inequality (LMI) formulations. The interesting combinations of different objectives are considered in this paper, which include H_∞ PID tracking control design with regional pole constraints and mixed H₂/H_∞ PID tracking control design with regional pole constraints. These multiobjective PID control problems are characterized in terms of eigenvalue problem (EVP). The EVP can be efficiently solved by the LMI toolbox in Matlab. The proposed methods are simple and the PID control gain for different objectives can be obtained systematically     

一类离散非线性不确定互联系统的模糊分散控制

利用模糊控制方法研究一类离散非线性互联系统的分散控制问题.首先采用模糊(T-S)模型对离散非线性不确定互联系统进行模糊建模,应用并行分布补偿算法(PDC)给出状态反馈分散模糊控制方案,并基于李亚普诺夫函数方法证明了闭环系统的稳定性.然后当系统的状态不完全可测时,设计模糊分散观测器来估计各子系统的状态,从而给出基于观测器的状态反馈分散模糊控制设计的方法.因为该分散模糊控制设计问题是以线性矩阵不等式的形式给出,所以很容易用凸优化方法求解.仿真结果验证了所提出控制方法的有效性.     

A Novel Approach to $H_{bm infty}$ Decentralized Fuzzy-Observer-Based Fuzzy Control Design for Nonlinear Interconnected Systems

In general, due to the interactions among subsystems, it is difficult to design an $H_{infty }$-decentralized output-feedback controller for nonlinear interconnected systems. This study introduces $H_{infty }$-decentralized fuzzy-observer-based fuzzy control design, where the premise variables depend on the state variables estimated by a fuzzy observer, for nonlinear interconnected systems via T--S fuzzy models. The fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only. A novel decoupled method is proposed in this study to transform the non-linear matrix inequality (non-LMI) conditions into some LMI forms. By the proposed decoupled method, the problem of $H_{infty }$-decentralized fuzzy-observer-based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP) with five prespecified scalars for each subsystem. In general, it is a difficult task to solve the EVP with five prespecified scalars. Fortunately, this special EVP can be easily solved by using a genetic algorithm and an LMI-based optimization method. Finally, a simulation example is given to illustrate the design procedure and robust performance of the proposed methods.      

丢包网络化控制系统非脆弱量化H∞控制

针对非线性网络化控制（NCS）系统中控制器参数存在摄动的问题,考虑传感器—控制器和控制器—执行器均存在随机丢包和量化误差,提出了一种加性非脆弱量化H_∞控制器的设计方法．利用李亚普诺夫稳定性理论和线性矩阵不等式（LMI）方法,将该问题转化为线性矩阵不等式约束和线性目标函数的凸优化问题进行求解,给出了丢包下的非脆弱量化H_∞控制器存在的充分条件．所设计的控制器在容许的参数摄动、丢包概率和量化密度条件下,不仅能保证闭环NCS的稳定性和性能要求,而且是非脆弱的．数值仿真验证了所提方法的有效性．     

基于约束H∞输出反馈的四轮转向模型跟踪控制

以跟踪参考模型为控制策略,提出一种基于约束H_∞输出反馈控制的四轮转向（4WS）控制新方法．将前馈控制和反馈控制相结合,同时控制前、后轮转角,以实现实际车辆模型对参考模型的期望性能跟踪．兼顾抗干扰能力与执行机构输出饱和,将约束H_∞输出反馈控制应用于反馈控制器的设计．仿真实验表明所设计的4WS车辆系统可以很好地跟踪参考车辆模型,提高了车辆的操纵稳定性．     

分散自适应模糊滑模控制器的设计与分析

研究了一类具有函数控制增益的耦合大系统的分散自适应模糊控制问题 ,提出了能够利用专家的语言信息和数字信息的分散自适应模糊滑模控制器的设计方案 .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邻域内     

H∞ and positive-real control for linear neutraldelay systems

This note is concerned with the H_∞ and positive-real control problems for linear neutral delay systems. The purpose of H_∞ control is the design of a memoryless state feedback controller which stabilizes the neutral delay system and reduces the H_∞ norm of the closed-loop transfer function from the disturbance to the controlled output to a prescribed level, while the purpose of positive-real control is to design a memoryless state feedback controller such that the resulting closed-loop system is stable and the closed-loop transfer function is extended strictly positive real. Sufficient conditions for the existence of the desired controllers are given in terms of a linear matrix inequality (LMI). When this LMI is feasible, the expected memoryless state feedback controllers can be easily constructed via convex optimization     

Decentralized adaptive control of a class of large-scaleinterconnected nonlinear systems

Decentralized adaptive control design for a class of large-scale interconnected nonlinear systems with unknown interconnections is considered. The motivation behind this work is to develop decentralized control for a class of large-scale systems which do not satisfy the matching condition requirement. To this end, large-scale nonlinear systems transformable to the decentralized strict feedback form are considered. Coordinate-free geometric conditions under which any general interconnected nonlinear system can be transformed to this form are obtained. The interconnections are assumed to be bounded by polynomial-type nonlinearities. Global stability and asymptotic regulation are established using classical Lyapunov techniques. The controller is shown to maintain robustness for a wide class of systems obtained by perturbation in the dynamics of the original system. Furthermore, appending additional subsystems does not require controller redesign for the original subsystems. Finally, the scheme is extended to the model reference tracking problem when global uniform boundedness of the tracking error to a compact set is established     

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.     

H∞ state feedback control for discrete singularsystems

Deals with the problem of state feedback H_∞ control for discrete singular systems. It is not assumed that the singular system under consideration is necessarily regular. The problem we address is the design of a state feedback controller, such that the resulting closed-loop system is not only regular, causal, and stable, but also satisfies a prescribed H_∞-norm-bound condition. In terms of certain matrix inequalities, a necessary and sufficient condition for the solution to this problem is obtained, and a suitable state feedback-control law is also given     

H∞ multiple objective robust controllers forinfinite-horizon single measurement single control input problems

A graphical method is introduced that solves the robust infinite horizon H_∞ multiple-objective control problem for single measurement, single control input systems. The solution is obtained by describing boundaries on the Nichols chart. Each boundary defines the set of all admissible gain and phase values for the loop transmission at a given frequency. These boundaries are obtained by using the well-known parameterization of all the solutions for a single objective H_∞ control problem. The new method links between the theories of H_∞ and quantitative feedback theory (QFT). It can be used to design robust H_∞ controllers with almost no overdesign, and it provides a convenient solution of H_∞ multiple-objective problems that are difficult to solve by the standard four-block setting. It also extends the methods of SISO QFT to deal with a vector of disturbances. The latter may affect the controlled plant through any input coupling matrix and not necessarily through the controller input, or the measurement output     

Model reference output feedback fuzzy tracking control design for nonlinear discrete-time systems with time-delay

In this study, a model reference fuzzy tracking control design for nonlinear discrete-time systems with time-delay is introduced. First, the Takagi and Sugeno (TS) fuzzy model is employed to approximate a nonlinear discrete-time system with time-delay. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy observer-based controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be efficiently solved using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method.     

Robust decentralized direct adaptive output feedback fuzzy control for a class of large-sale nonaffine nonlinear systems

In the previous work of Huang et al., a decentralized direct adaptive fuzzy H_∞ tracking controller of large-scale nonaffine nonlinear systems is obtained predicated upon the assumption that the mismatching error dynamics stay squared integrable. In this note, we focus in the absence of the conservative assumption upon developing a robust decentralized direct adaptive output feedback fuzzy controller. By combination of a state observer, a fuzzy inference system and robust control technique, the previous controller design is modified and no a priori knowledge of bounds on lumped uncertainties is required. All the signals of the closed-loop large-scale system are proved to be uniformly ultimately bounded. The effectiveness of the developed scheme is demonstrated through the simulation results of interconnected inverted pendulums.     

基于分散反馈控制的时滞混沌大系统

研究一类具有时滞关联的时滞大系统的混沌现象和分散反馈控制问题。应用线性矩阵不等式（LMI）方法,基于李雅普诺夫定理,分别得到了系统存在分散时滞反馈控制器和分散标准反馈控制器的充分条件,并利用分散时滞反馈控制器对系统中存在的不稳定周期轨道的追踪控制问题进行研究。仿真结果表明控制器具有很强的鲁棒性。     

Adaptive fuzzy output feedback decentralized control of pure‐feedback nonlinear large‐scale systems

In this paper, an adaptive fuzzy decentralized output feedback control approach is presented for a class of uncertain nonlinear pure‐feedback large‐scale systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the immeasurable states. On the basis of the adaptive backstepping recursive design technique, an adaptive fuzzy decentralized output feedback is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded (SUUB), and that the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

一类切换模糊时滞组合系统的分散镇定

提出了切换模糊时滞组合系统模型,并研究了状态和互联项具有时滞情况下的分散镇定问题.当每个互联子系统中的每个切换子系统具有有限个备选的状态反馈控制器,且单一控制器均不能保证系统稳定的情况下,利用多Lyapunov函数方法给出了时滞相关的矩阵不等式条件和分散切换律设计方法,使系统在所提出的分散切换律和分散控制器下渐近稳定.仿真结果表明了所提出方法的有效性.     

Nonlinear H∞ control and its application to rigidspacecraft

The problem of H_∞ control of a rigid spacecraft with three control torques and disturbances is addressed. The Hamilton-Jacobi-Isaacs inequality for H_∞ feedback design is solved. An H_∞ suboptimal feedback is given, and the stability properties of the closed-loop system are studied     

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.