A STABLE SELF-LEARNING OPTIMAL FUZZY CONTROL SYSTEM

The issue of developing a stable self-learning optimal fuzzy control system is discussed in this paper. Three chief objectives are accomplished: 1) To develop a self-learning fuzzy controller based on genetic algorithms. In the proposed methodology, the concept of a fuzzy sliding mode is introduced to specify the system response, to simplify the fuzzy rules and to shorten the chromosome length. The speed of fuzzy inference and genetic evolution of the proposed strategy, consequently, is higher than that of the conventional fuzzy logic control. 2) To guarantee the stability of the learning control system. A hitting controller is designed to achieve this requirement. It works as an auxiliary controller and supports the self-learning fuzzy controller in the following manner. When the learning controller works well enough to allow the system state to lie inside a pre-defined boundary layer, the hitting controller is disabled. On the other hand, if the system tends to diverge, the hitting controller is turned on to pull the state back. The system is therefore stable in the sense that the state is bounded by the boundary layer. 3) To explore a fuzzy rule-base that can minimize a standard quadratic cost function. Based on the fuzzy sliding regime, the problem of minimizing the quadratic cost function can be transformed into that of deriving an optimal sliding surface. Consequently, the proposed learning scheme is directly applied to extract the optimal fuzzy rulebase. That is, the faster the hitting time a controller has and the shorter the distance from the sliding surface the higher fitness it possesses. The superiority of the proposed approach is verified through simulations.     

Fuzzy guaranteed cost control for nonlinear systems with time-varying delay

This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.     

A Combined Adaptive Law for Fuzzy Iterative Learning Control of Nonlinear Systems With Varying Control Tasks

To deal with the iterative control of uncertain nonlinear systems with varying control tasks, nonzero initial resetting state errors, and nonrepeatable mismatched input disturbance, a new adaptive fuzzy iterative learning controller is proposed in this paper. The main structure of this learning controller is constructed by a fuzzy learning component and a robust learning component. For the fuzzy learning component, a fuzzy system used as an approximator is designed to compensate for the plant nonlinearity. For the robust learning component, a sliding-mode-like strategy is applied to overcome the nonlinear input gain, input disturbance, and fuzzy approximation error. Both designs are based on a time-varying boundary layer which is introduced not only to solve the problem of initial state errors but also to eliminate the possible undesirable chattering behavior. A new adaptive law combining time- and iteration-domain adaptation is derived to search for suitable values of control parameters and then guarantee the closed-loop stability and error convergence. This adaptive algorithm is designed without using projection or deadzone mechanism. With a suitable choice of the weighting gain, the memory size for the storage of parameter profiles can be greatly reduced. It is shown that all the adjustable parameters as well as internal signals remain bounded for all iterations. Moreover, the norm of tracking state error vector will asymptotically converge to a tunable residual set even when the desired tracking trajectory is varying between successive iterations.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

图书馆机器人机械手参数自整定模糊PID控制器设计

采用PC/104系列板卡设计了一款嵌入式图书馆机器人气动机械手控制器,对机械手的参数自整定模糊PID控制算法进行了重点探讨,根据模糊子集的隶属度赋值表和模糊逻辑规则,查模糊矩阵表得出修正参数,完成对PID参数的在线自校正.用Microsoft eMbedded Visual C++(EVC)编程实现了图书取放气动机械手的智能控制,给出了控制软件算法流程及关键部分实现方法.用阶跃、正弦等典型输入信号做系统仿真,实验结果表明气动机械手能够快速、稳定、几乎无误差地跟踪系统给定值.所提出的系统设计方法对类似领域具有普遍适用性.     

模糊系统的稳定性分析与最优控制器设计

针对一类线性系统,首先设计了一种模糊控制器保证闭环系统的稳定性.根据得到的结果,如果只需满足稳定性条件,可以有很大的空间选择控制器参数.因此,本文根据Pontryagin最小值原理给出了一种最优模糊控制器的设计方法.     

Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors

In this paper, a fuzzy system-based adaptive iterative learning controller is proposed for a class of non-Lipschitz nonlinear plants which can repeat a given task over a finite time interval. The variable initial resetting state errors at the beginning of each trial is considered. To overcome the initial errors, a time-varying boundary layer is introduced to design an error function. Based on the error function, the main structure of this controller is constructed by a fuzzy iterative learning component and a feedback stabilization component. The fuzzy system is used as an approximator to compensate for the plant unknown nonlinearity. Since the optimal parameters for a good fuzzy approximation are in general unavailable, the adaptive algorithms are derived along the iteration axis to search for suitable parameter values and then guarantee the closed-loop stability and learning convergence. It is shown that all the adjustable parameters as well as internal signals remain bounded for all iterations. There even exist initial state errors, the norm of tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity and the learning speed can be easily improved if the learning gain is large.     

Guaranteed cost control analysis and iterative design for constrained Takagi–Sugeno systems

This paper presents a novel control design technique in order to obtain a guaranteed cost fuzzy controller subject to constraints on the input channel. This guaranteed cost control law is obtained via multi-parametric quadratic programming. The result is a piecewise fuzzy control law where the state partition is defined by fuzzy inequalities. The parameters of the Lyapunov function can be obtained previously using Linear Matrix Inequalities optimization.     

Optimal fuzzy controller based on non-monotonic Lyapunov function with a case study on laboratory helicopter

This paper presents a new approach to design an observer-based optimal fuzzy state feedback controller for discrete-time Takagi–Sugeno fuzzy systems via LQR based on the non-monotonic Lyapunov function. Non-monotonic Lyapunov stability theorem proposed less conservative conditions rather than common quadratic method. To compare with optimal fuzzy feedback controller design based on common quadratic Lyapunov function, this paper proceeds reformulation of the observer-based optimal fuzzy state feedback controller based on common quadratic Lyapunov function. Also in both methodologies, the dependence of optimisation problem on initial conditions is omitted. As a practical case study, the controllers are implemented on a laboratory twin-rotor helicopter to compare the controllers' performance.     

Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems.

This correspondence studies the problem of finite-dimensional constrained fuzzy control for a class of systems described by nonlinear parabolic partial differential equations (PDEs). Initially, Galerkin's method is applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, a systematic modeling procedure is given to construct exactly a Takagi-Sugeno (T-S) fuzzy model for the finite-dimensional ODE system under state constraints. Then, based on the T-S fuzzy model, a sufficient condition for the existence of a stabilizing fuzzy controller is derived, which guarantees that the state constraints are satisfied and provides an upper bound on the quadratic performance function for the finite-dimensional slow system. The resulting fuzzy controllers can also guarantee the exponential stability of the closed-loop PDE system. Moreover, a local optimization algorithm based on the linear matrix inequalities is proposed to compute the feedback gain matrices of a suboptimal fuzzy controller in the sense of minimizing the quadratic performance bound. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.     

一类不确定时滞模糊系统的鲁棒H∞控制

对于一类不确定非线性时滞系统,研究使系统二次稳定的状态反馈控制方法。利用T—S模糊模型对时变时滞不确定非线性系统进行建模,采取分段光滑（PSQ）的Lyapunov函数和线性矩阵不等式方法给出使系统二次稳定的模糊状态反馈控制器存在的充分条件,避免并行补偿法中求解公共矩阵P的困难。仿真试验证明,通过该方法设计的控制器具有良好的鲁棒性,控制效果良好。     

基于可变学习率BP算法的空调控制系统的研究

通过分析控制器参数学习率和控制器性能之间的关系,设计一种基于可变学习速率反向传播算法VLRBP和模糊神经元网络的变频空调控制系统.该系统不仅可以通过反传误差信号训练控制器参数,而且可以根据网络的当前状态朝最优化方向调整控制器参数的学习率.实验结果表明,该控制系统不仅比传统的空调PID控制器和模糊控制器具有更好的控制性能,而且相比基于标准BP算法和动量BP算法的模糊神经网络控制系统,也具有更快的收敛速度和更好的控制精确度.     

Guaranteed‐cost fuzzy controller design for a self‐sustaining bicycle with practical constraints

This study presents a guaranteed‐cost fuzzy controller for a self‐sustaining bicycle. First, the nonlinear dynamics of the bicycle are exactly transformed into a T‐S fuzzy system with model uncertainty. The guaranteed‐cost fuzzy controller is then designed for the transformed T‐S fuzzy system. For practical considerations, the input/state constraints are also satisfied in the design. The main contribution of this study is the guaranteed‐cost control design for a T‐S fuzzy system with model uncertainty and input/state constraints. Finally, simulation results show the validity of the proposed controller design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于状态反馈线性二次型最优控制器的设计

基于状态反馈的线性二次型最优控制的研究已经取得了较好的效果,设计一款基于状态反馈的线性二次型最优控制器,并将它用在一个实际的状态方程中进行设计.该文所设计的控制系统结构简单,成本低,且易于实现.通过仿真实验以及性能指标的比较,仿真结果表明所设计的控制器是有效的,对系统的动态响应具有较好的跟踪效果,且抗扰能力较强.     

Reliable LQ fuzzy control for nonlinear discrete-time systems via LMIs.

This paper studies reliable linear quadratic (LQ) fuzzy regulator problem for nonlinear discrete-time systems with actuator faults. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. A sufficient condition expressed in linear matrix inequality (LMI) terms for the existence of reliable guaranteed cost (GC) fuzzy controllers is obtained. The fuzzy controller directly obtained from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system, while provide a guaranteed cost on the quadratic cost function of the system in the normal and actuator fault cases. Furthermore, an optimal reliable GC fuzzy controller in the sense of minimizing a bound on the worst or nominal case guaranteed cost is also given by means of an LMI optimization procedure. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Stable and optimal fuzzy control of linear systems

A number of stable and optimal fuzzy controllers are developed for linear systems. Based on some classical results in control theory, we design the structure and parameters of fuzzy controllers such that the closed-loop fuzzy control systems are stable, provided that the process under control is linear and satisfies certain conditions. It turns out that if stability is the only requirement, there is much freedom in choosing the fuzzy controller parameters. Therefore, a performance criterion is set to optimalize the parameters. Using the Pontryagin minimum principle, we design an optimal fuzzy controller for linear systems with quadratic cost function. Finally, the optimal fuzzy controller is applied to a ball-and-beam system     

A game-theoretic approach to a finite-time disturbance attenuationproblem

A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H _∞ norm bound     

Adaptive controller with fuzzy rules emulated structure and its applications

In this paper, the adaptive controller inspired by the neuro-fuzzy controller is proposed. Its structure, called fuzzy rules emulated network (FREN), is derived based on the fuzzy if–then rules. This structure not only emulates the fuzzy control rules but also allows the initial value of controller's parameters to be intuitively chosen. These parameters are further adjusted during system operation using a method similar to the steepest descent technique. The learning rate selection criteria based on Lyapunov's stability condition is also presented. FREN controller is applied to control various nonlinear systems, for examples, the single invert pendulum plant, the water bath temperature control, the high voltage direct current transmission system and the robotic system. Computer simulations results indicate that the proposed controller is able to control the target systems satisfactory.