Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi–Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.     

A new approach for dynamic fuzzy logic parameter tuning in Ant Colony Optimization and its application in fuzzy control of a mobile robot

Ant Colony Optimization is a population-based meta-heuristic that exploits a form of past performance memory that is inspired by the foraging behavior of real ants. The behavior of the Ant Colony Optimization algorithm is highly dependent on the values defined for its parameters. Adaptation and parameter control are recurring themes in the field of bio-inspired optimization algorithms. The present paper explores a new fuzzy approach for diversity control in Ant Colony Optimization. The main idea is to avoid or slow down full convergence through the dynamic variation of a particular parameter. The performance of different variants of the Ant Colony Optimization algorithm is analyzed to choose one as the basis to the proposed approach. A convergence fuzzy logic controller with the objective of maintaining diversity at some level to avoid premature convergence is created. Encouraging results on several traveling salesman problem instances and its application to the design of fuzzy controllers, in particular the optimization of membership functions for a unicycle mobile robot trajectory control are presented with the proposed method.     

Design of variable structure control for fuzzy nonlinear systems

In this paper, the variable structure control problem is presented for Takagi–Sugeno fuzzy systems with uncertainties and external disturbances. The sliding surfaces for the T–S fuzzy system are proposed by using a Lyapunov function and a fuzzy Lyapunov function, respectively. And we design the variable structure controllers such that the global T–S fuzzy system confined on the sliding surfaces is asymptotically stable. Two examples are given to illustrate the effectiveness of our proposed methods.     

Optimal fuzzy controller design: local concept approach

In this paper, we present a global optimal and stable fuzzy controller design method for both continuous- and discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory. The stability of the entire closed-loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant feedback continuous fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties     

Structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear PID control with variable gains

The popular linear PID controller is mostly effective for linear or nearly linear control problems. Nonlinear PID controllers, however, are needed in order to satisfactorily control (highly) nonlinear plants, time-varying plants, or plants with significant time delay. This paper extends our previous papers in which we show rigorously that some fuzzy controllers are actually nonlinear PI, PD, and PID controllers with variable gains that can outperform their linear counterparts. In the present paper, we study the analytical structure of an important class of two- and three-dimensional fuzzy controllers. We link the entire class, as opposed to one controller at a time, to nonlinear PI, PD, and PID controllers with variable gains by establishing the conditions for the former to structurally become the latter. Unlike the results in the literature, which are exclusively for the fuzzy controllers using linear fuzzy sets for the input variables, this class of fuzzy controllers employs nonlinear input fuzzy sets of arbitrary types. Our structural results are thus more general and contain the existing ones as special cases. Two concrete examples are provided to illustrate the usefulness of the new results.     

Robust H-infinity fuzzy control for uncertainMarkovian jump nonlinear singular systems withwiener process

This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear singular system. The purpose of the robust stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties. In the robust H-infinity control problem, in addition to the stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequality (LMI) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.     

A fast recursive algorithm based on fuzzy 2-partition entropy approach for threshold selection

The fuzzy c-partition entropy approach for threshold selection is an effective approach for image segmentation. The approach models the image with a fuzzy c-partition, which is obtained using parameterized membership functions. The ideal threshold is determined by searching an optimal parameter combination of the membership functions such that the entropy of the fuzzy c-partition is maximized. It involves large computation when the number of parameters needed to determine the membership function increases. In this paper, a recursive algorithm is proposed for fuzzy 2-partition entropy method, where the membership function is selected as S-function and Z-function with three parameters. The proposed recursive algorithm eliminates many repeated computations, thereby reducing the computation complexity significantly. The proposed method is tested using several real images, and its processing time is compared with those of basic exhaustive algorithm, genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO) and simulated annealing (SA). Experimental results show that the proposed method is more effective than basic exhaustive search algorithm, GA, PSO, ACO and SA.     

Position tracking of a 3-PSP parallel robot using dynamic growing interval type-2 fuzzy neural control

Parallel robots have complicated structures as well as complex dynamic and kinematic equations, rendering model-based control approaches as ineffective due to their high computational cost and low accuracy. Here, we propose a model-free dynamic-growing control architecture for parallel robots that combines the merits of self-organizing systems with those of interval type-2 fuzzy neural systems. The proposed approach is then applied experimentally to position control of a 3-PSP (Prismatic–Spherical–Prismatic) parallel robot. The proposed rule-base construction is different from most conventional self-organizing approaches by omitting the node pruning process while adding nodes more conservatively. This helps preserve valuable historical rules for when they are needed. The use of interval type-2 fuzzy logic structure also better enables coping with uncertainties in parameters, dynamics of the robot model and uncertainties in rule space. Finally, the adaptation structure allows learning and further adapts the rule base to changing environment. Multiple simulation and experimental studies confirm that the proposed approach leads to fewer rules, lower computational cost and higher accuracy when compared with two competing type-1 and type-2 fuzzy neural controllers.     

A general technique for deriving analytical structure of fuzzy controllers using arbitrary trapezoidal input fuzzy sets and Zadeh AND operator

Deriving the analytical structure of fuzzy controllers is very important as it creates a solid foundation for better understanding, insightful analysis, and more effective design of fuzzy control systems. We previously developed a technique for deriving the analytical structure of the fuzzy controllers that use Zadeh fuzzy AND operator and the symmetric, identical trapezoidal or triangular input fuzzy sets. Many fuzzy controllers use arbitrary trapezoidal/triangular input fuzzy sets that are asymmetric. At present, there exists no technique capable of deriving the analytical structure of these fuzzy controllers. Extending our original technique, we now present a novel method that can accomplish rigorously the structure derivation for any fuzzy controller, Mamdani type or TS type, that employs the arbitrary trapezoidal input fuzzy sets and Zadeh fuzzy AND operator. The new technique contains our original technique as a special case. Given the importance of PID control, we focus on Mamdani fuzzy PI and PD controllers in this paper and show in detail how to use the new technique for different configurations of the fuzzy PI/PD controllers. The controllers use two arbitrary trapezoidal fuzzy sets for each input variable, four arbitrary singleton output fuzzy sets, four fuzzy rules, Zadeh fuzzy AND operator, and the centroid defuzzifier. This configuration is more general and complicated than the Mamdani fuzzy PI/PD controllers in the current literature. It actually contains them as special cases. We call this configuration the generalized fuzzy PI/PD controller.     

基于MATLAB环境下模糊控制参数的优化设计与仿真

该文提出了一种基于MATLAB环境下，利用优化工具箱和模糊逻辑工具箱以及M函数文件，使用单纯形法对模糊控制器中的量化因子和比例因子进行自寻优，可获得一个基于一定性能指标的次优或最优模糊控制器。以二阶系统为例进行了计算机仿真，仿真结果表明该方法具有良好的收敛性，使系统的动态性能得到明显的改善。     

动态不确定非线性系统直接自适应模糊backstepping控制

对一类单输入单输出动态不确定非线性系统,提出一种直接自适应模糊backstepping和小增益相结合的控制方法.设计中,首先用模糊逻辑系统逼近虚拟控制器:其次把自适应模糊控制和backstepping控制设计技术相结合.给出了直接自适应模糊控制设计方法.最后基于Lyapunov函数和小增益方法证明了整个闭环系统的稳定性.仿真实例进一步验证了所提方法的有效性.     

Interval type-2 fuzzy expert system for prediction of carbon monoxide concentration in mega-cities

This paper presents an indirect approach to interval type-2 fuzzy logic system modeling to forecaste the level of air pollutants. The type-2 fuzzy logic system permits us to model the uncertainties among rules and the parameters related to data analysis. In this paper, we propose an indirect method to create an interval type-2 fuzzy logic system from a historical data, where Footprint of Uncertainties of fuzzy sets are extracted by implementation of an interval type-2 FCM algorithm and based on an upper and lower value for the level of fuzziness m in FCM. Finally, the proposed model is applied for prediction of carbon monoxide concentration in Tehran air pollution. It is shown that the proposed type-2 fuzzy logic system is superior in comparison to type-1 fuzzy logic systems in terms of two performance indices.     

Hybrid Fuzzy Modelling for Model Predictive Control

Model predictive control (MPC) has become an important area of research and is also an approach that has been successfully used in many industrial applications. In order to implement a MPC algorithm, a model of the process we are dealing with is needed. Due to the complex hybrid and nonlinear nature of many industrial processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between the proposed modern intelligent (fuzzy) approach and a classic (linear) approach was made. It was established that the MPC algorithm employing the proposed hybrid fuzzy model clearly outperforms the approach where a hybrid linear model is used, which justifies the usability of the hybrid fuzzy model. The hybrid fuzzy formulation introduces a powerful model that can faithfully represent hybrid and nonlinear dynamics of systems met in industrial practice, therefore, this approach demonstrates a significant advantage for MPC resulting in a better control performance.     

Generation of an optimal architecture of neuro force controllers for robot manipulators in unknown environments using genetic programming with fuzzy fitness evaluation

 In this paper, we have applied genetic programming to generate an optimal architecture of neuro force controllers for robot manipulators in any environment. In order to perform precise force control in unknown environments, the optimal structured neuro force controller is generated using genetic programming with fuzzy fitness evaluation. After the architecture of the neuro controller has been optimized for any kinds of environments, it can be applied for a robot contact task with an unknown environment in on-line manner using its own adaptation ability. An effective crossover operation is proposed for the efficient evolution of the controllers. The simulation has been carried out to evaluate the effectiveness of the proposed robot force controller.     

H2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty

This paper presents a design method of H₂ guaranteed cost (GC) fuzzy controllers for discrete-time nonlinear systems with parameter uncertainties. The Takagi and Sugeno (T-S) fuzzy model with parameter uncertainties is employed to represent an uncertain discrete-time nonlinear system. A sufficient condition for the existence of H₂ GC fuzzy controllers is presented in terms of linear matrix inequalities (LMIs). The resulting fuzzy controllers not only guarantee that the closed-loop fuzzy system is quadratically stable, but also provide a guaranteed cost on the H₂ performance index. Furthermore, an optimal H₂ GC fuzzy controller in the sense of minimizing a bound on the guaranteed cost is provided by means of an LMI optimization procedure. Finally, it is also demonstrated, through numerical simulations on the backing up control of a truck-trailer, that the proposed design method is effective.     

Risk assessment in control of fractional-order coronary artery system in the presence of external disturbance with different proposed controllers

In this study, different controllers for control of fractional-order coronary artery system in the presence of external disturbance are designed. Using sliding mode, the proposed type 1 and type 2 fuzzy methods, the suitable controllers are proposed. In sliding mode control, a fractional sliding surface is presented and the control signal is modified to prevent chattering in the control system. With mathematical analysis, a type of membership function is suggested which has better performance in the fractional order system. Also, a rule-base is presented which leads to better results in type 1 and type 2 fuzzy controllers. The risk of the proposed controllers in different conditions is analyzed. Finally, according to the other analyzing methods, it is shown that this analyzing method has more accurate results.     

相对运动小推力的模糊控制

在航天器交会对接和轨道保持问题中，一般都基于相对运动方程进行控制，然而在某些情况下，用极大值原理有时并不能求得问题的解，而且对控制屡有噪声干扰时，控制律难以设计，该文讨论了在相对运动方程下对追踪飞行器进行模糊控制的方法。文中提出基于模糊逻辑规则构造控制器，仿真结果验证了模糊控制器的可行性，而且验证了在噪声干扰下控制器的鲁棒性。     

Intelligent adaptive model-based control of robotic dynamic systems with a hybrid fuzzy-neural approach

We describe in this paper a new method for adaptive model-based control of robotic dynamic systems using a new hybrid fuzzy-neural approach. Intelligent control of robotic systems is a difficult problem because the dynamics of these systems is highly nonlinear. We describe an intelligent system for controlling robot manipulators to illustrate our fuzzy-neural hybrid approach for adaptive control. We use a new fuzzy inference system for reasoning with multiple differential equations for model selection based on the relevant parameters for the problem. In this case, the fractal dimension of a time series of measured values of the variables is used as a selection parameter. We use neural networks for identification and control of robotic dynamic systems. We also compare our hybrid fuzzy-neural approach with conventional fuzzy control to show the advantages of the proposed method for control.     

PD型模糊学习控制及其在可重复轨迹跟踪问题中的应用

针对可重复轨迹跟踪问题,提出了一种PD型模糊学习算法.该算法集成两种控 制:作为基础的PD型模糊逻辑算法和改善系统性能的学习算法.模糊学习控制在模糊控制 基础上引入迭代学习算法,使得模糊PD控制器可以精确地跟踪可重复轨迹以及消除周期性 扰动.本文在能量函数和泛函分析的基础上,通过严格的推导表明PD型模糊学习算法可达 到:1)系统跟踪误差一致收敛到零;2)学习控制序列几乎处处收敛到理想的控制信号.     

基于Fuzzy推理的自调整PID控制器*

本文提出一衙 新的基于Ｆｕｚｚｙ推理的ＰＩＤ自整定控制器。