基于模糊目标和模糊约束的满意控制

研究在预测控制框架下进行模糊决策问题,提出一种基于模糊目标和模糊约束的预测控制方法。其目标函数以决策者的控制要求和最终控制的满意度来表示,比传统的加权方差具有更多的自由度;与基于二次型性能指标的预测相比,该方法可使系统设计更加灵活。仿真结果表明了该方法的有效性。     

Approach to decision making in fuzzy environment

A general approach to solving a wide class of optimization problems with fuzzy coefficients in objective functions and constraints is described. It is based on a modification of traditional mathematical programming methods and consists in formulating and solving one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective function alone. This approach allows one to maximally cut off dominated alternatives from below as well as from above. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment. The approach is applied within the context of fuzzy discrete optimization models, that is based on a modification of discrete optimization algorithms. The results of the paper are of a universal character and are already being used to solve problems of the design and control of power systems and subsystems.     

Model predictive control using fuzzy decision functions

Fuzzy predictive control integrates conventional model predictive control with techniques from fuzzy multicriteria decision making, translating the goals and the constraints to predictive control in a transparent way. The information regarding the (fuzzy) goals and the (fuzzy) constraints of the control problem is combined by using a decision function from the theory of fuzzy sets. This paper investigates the use of fuzzy decision making (FDM) in model predictive control (MPG), and compares the results to those obtained from conventional MPG. Attention is also paid to the choice of aggregation operators for fuzzy decision making in control. Experiments on a nonminimum phase, unstable linear system, and on an air-conditioning system with nonlinear dynamics are studied. It is shown that the performance of the model predictive controller can be improved by the use of fuzzy criteria in a fuzzy decision making framework.     

Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

In this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.     

Multi-objective reliability-redundancy allocation problem using particle swarm optimization

This paper considers the multi-objective reliability redundancy allocation problem of a series system where the reliability of the system and the corresponding designing cost are considered as two different objectives. Due to non-stochastic uncertain and conflicting factors it is difficult to reduce the cost of the system and improve the reliability of the system simultaneously. In such situations, the decision making is difficult, and the presence of multi-objectives gives rise to multi-objective optimization problem (MOOP), which leads to Pareto optimal solutions instead of a single optimal solution. However in order to make the model more flexible and adaptable to human decision process, the optimization model can be expressed as fuzzy nonlinear programming problems with fuzzy numbers. Thus in a fuzzy environment, a fuzzy multi-objective optimization problem (FMOOP) is formulated from the original crisp optimization problem. In order to solve the resultant problem, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker regarding cost and reliability goals and then particle swarm optimization is applied to solve the resulting fuzzified MOOP under a number of constraints. The approach has been demonstrated through the case study of a pharmaceutical plant situated in the northern part of India.     

Identification and predictive control of a melter unit used in the sugar industry

This paper presents the real identification and non-linear predictive control of a melter unit; the unit is used in a sugar factory placed in Benavente (Spain). The proposed approach uses a specific recurrent neural network that allows us to identify a non-linear model of the process, providing a mathematical representation in the state space form. Output and state variables can be obtained from the inputs and measured disturbances acting on the system. The neural based predictive control is carried out through the optimization of a cost function that takes into account the output prediction errors from a reference trajectory and the future control efforts, by using the identified model as a prediction model for the system outputs. The solution to this problem provides the optimal set of future control actions, but only the first one is applied to the real process, and the optimization problem is solved again at time t + 1.The results show the good performance of neural predictive control and its suitability for applications in real systems, particularly in the process industry.     

An integrated expert system/operations research approach for the optimization of waste incinerator siting problems

This research aims at developing an integrated decision support system for the optimization of waste incinerator siting problems. In this integrated approach, both expert system and operations research techniques are used to model the siting problems of waste incinerator. Furthermore, an expert decision support system (EDSS) is implemented for the above problem and thus providing the decision makers a useful tool for decision-making. This EDSS is based on multi-criteria decision analysis in finding the best incinerator site by minimizing costs and environmental impacts. The proposed approach identifies a hierarchy of objectives for the siting problem. First of all, several potential sites need to be screened as a set of feasible alternative sites. Second, those alternative feasible sites will be further evaluated via the multi-criteria decision making methods. For the evaluation process, we solve a 0/1 combinatorial optimization problem at the upper level and proceed the multi-attribute utility function at the lower level to get the optimal solutions. An empirical application of a real world waste incinerator site selection existing in Taichung City, Taiwan is followed in the end. Computational results both of the cost minimization and of the whole systems are also provided.     

A hybrid solution approach for fuzzy multiobjective dual supplier and material selection problem of carton box production systems

A novel optimization problem of carton box manufacturing industries is introduced in this paper. A mixed integer linear formulation with multiple objective functions is developed in order to determine the value of some criteria of carton raw sheets such as size, amount, and supplier under simultaneous minimization of multiple goals such as purchasing cost of raw sheets under discount policy, wastage remained from raw sheets, and quantity of surplus of carton boxes. In order to cope with the unstable market of this sector, some parameters of the proposed formulation such as demand value of the products and price given for raw sheets are assumed to be fuzzy numbers. To tackle such fuzzy multiobjective problem, first, the fuzzy problem is converted to a crisp form using the concepts of necessity‐based chance‐constrained modelling approach. Then a new hybrid form of the fuzzy programming approach is proposed to solve the obtained crisp multiobjective problem effectively. Computational experiments on a real case given by a carton box factory show the superior result of the proposed solution approach compared with the well‐known multiobjective solution methods taken from the literature.     

Robust H2 guaranteed cost fuzzy control for uncertain discrete‐time fuzzy systems via poly‐quadratic Lyapunov functions

In this paper, new approaches regarding H₂ guaranteed cost stability analysis and controller synthesis problems for a class of discrete‐time fuzzy systems with uncertainties are investigated. The state‐space Takagi‐Sugeno fuzzy model with norm‐bounded parameter uncertainties is adopted. Based on poly‐quadratic Lyapunov functions, sufficient conditions for the existence of the robust H₂ fuzzy controller can be obtained in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design a suboptimal fuzzy controller which minimizes the upper bound on the quadratic cost function. The effectiveness of the proposed design approach is illustrated by two examples. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

动态不确定环境下广义控制问题的预测控制

通过对预测控制方法论思想的剖析,抒预测控制的基本原理从控制问题推广到一般的广义控制问题求解,并以机器人实时路径规划和ＦＭＳ实时加工调度为例说明了其应用,为动态不确定环境下基于优化的各类问题求解提供了新的思路。     

Fuzzy bilevel programming with multiple non-cooperative followers: model,algorithm and application

In centralized decision problems, it is not complicated for decision-makers to make modelling technique selections under uncertainty. When a decentralized decision problem is considered, however, choosing appropriate models is no longer easy due to the difficulty in estimating the other decision-makers’ inconclusive decision criteria. These decision criteria may vary with different decision-makers because of their special risk tolerances and management requirements. Considering the general differences among the decision-makers in decentralized systems, we propose a general framework of fuzzy bilevel programming including hybrid models (integrated with different modelling methods in different levels). Specially, we discuss two of these models which may have wide applications in many fields. Furthermore, we apply the proposed two models to formulate a pricing decision problem in a decentralized supply chain with fuzzy coefficients. In order to solve these models, a hybrid intelligent algorithm integrating fuzzy simulation, neural network and particle swarm optimization based on penalty function approach is designed. Some suggestions on the applications of these models are also presented.     

Evolutionary algorithms,simulated annealing and tabu search: a comparative study

Evolutionary algorithms, simulated annealing (SA), and tabu search (TS) are general iterative algorithms for combinatorial optimization. The term evolutionary algorithm is used to refer to any probabilistic algorithm whose design is inspired by evolutionary mechanisms found in biological species. Most widely known algorithms of this category are genetic algorithms (GA). GA, SA, and TS have been found to be very effective and robust in solving numerous problems from a wide range of application domains. Furthermore, they are even suitable for ill-posed problems where some of the parameters are not known before hand. These properties are lacking in all traditional optimization techniques. In this paper we perform a comparative study among GA, SA, and TS. These algorithms have many similarities, but they also possess distinctive features, mainly in their strategies for searching the solution state space. The three heuristics are applied on the same optimization problem and compared with respect to (1) quality of the best solution identified by each heuristic, (2) progress of the search from initial solution(s) until stopping criteria are met, (3) the progress of the cost of the best solution as a function of time (iteration count), and (4) the number of solutions found at successive intervals of the cost function. The benchmark problem used is the floorplanning of very large scale integrated (VLSI) circuits. This is a hard multi-criteria optimization problem. Fuzzy logic is used to combine all objective criteria into a single fuzzy evaluation (cost) function, which is then used to rate competing solutions.     

Soft computing based procurement planning of time-variable demand in manufacturing systems

Procurement planning with discrete time varying demand is an important problem in Enterprise Resource Planning (ERP).It can be described using the non-analytic mathematical programming model proposed in this paper.To solve the model we propose to use a fuzzy decision embedded genetic algorithm.The algorithm adopts an order strategy selection to simplify the original real optimization problem into binary ones.Then,a fuzzy decision quantification method is used to quantify experience from planning experts.Thus,decision rules can easily be embedded in the computation of genetic operations.This approach is applied to purchase planning problem in a practical machine tool works,where satisfactory results have been achieved.     

Embedded MPC Controller Based on Interior‐Point Method with Convergence Depth Control

To allow the implementation of model predictive control on the chip, we first propose a primal–dual interior point method with convergence depth control to solve the quadratic programming problem of model predictive control. Compared with algorithms based on traditional termination criterion, the proposed method can significantly reduce the computation cost while obtaining an approximate solution of the quadratic programming problem with acceptable optimality and precision. Thereafter, an embedded model predictive controller based on the quadratic programming solver is designed and implemented on a digital signal processor chip and a prototype system is built on a TMDSEVM6678LE digital signal processor chip. The controller is verified on two models by using the hardware in loop frame to mimic real applications. The comparison shows that the whole design is competitive in real‐time applications. The typical computation time for quadratic programming problems with 5 decision variables and 110 constraints can be reduced to less than 2 ms on an embedded platform.     

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete‐time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi‐Sugeno (T‐S) fuzzy model to represent a discrete‐time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on‐line optimization paradigm that utilizes the closed‐loop state feedback controller and is solved using the standard semi‐definite programming (SDP). To reduce the on‐line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Decision models for sustainable groundwater planning and control

An integrated approach to the sustainable planning and control of groundwater resources is presented. Physical/chemical models describing the groundwater system (i.e., the water flows and physical and chemical behavior of the pollutants) are embedded as constraints in the optimization problem. Two main kinds of decision problems are considered: control problems, conditioned by real time information, and planning problems. A specific case study relevant to the application of a receding-horizon control scheme, with the objective of optimizing water extraction from a set of wells, is presented, considering different demand scenarios.     

Optimal guaranteed cost control for an uncertain discrete T-S fuzzy system with time-delay

This paper considers the guaranteed cost control problem for a class of uncertain discrete T-S fuzzy systems with time delay and a given quadratic cost function. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequalities （LMI） approach by constructing a specific nonquadratic Lyapunov-Krasovskii functional and a nonlinear PDC-like control law. A convex optimization problem is also formulated to select the optimal guaranteed cost controller that minimizes the upper bound of the closed-loop cost function. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approaches.     

基于满意优化的非线性预测控制

对多约束的非线性系统建立T—S模糊模型,采用局部线性化方法在每个采样点对非线性系统进行线性化,从而得到系统的线性化模型。针对传统的优化方法无法直接处理带有一定模糊不确定性的优化问题,该文在广义预测控制滚动优化的机制下把具有模糊边界约束的有限预测时域的优化问题,转化为等价的确定性规划问题,通过模糊规划方法来求解多约束的目标函数,从而用满意优化取代传统的二次型性能指标来求解模糊约束条件的预测控制。仿真结果表明了该方法的有效性。     

模糊动态环境下复杂系统的满意优化控制

提出一种在满意控制框架下进行模糊决策的方法,将控制目标和系统约束模糊化,形 成多目标的优化问题,通过模糊规划方法求解,与基于二次型性能指标的预测控制相比,该方法 可使得系统设计更灵活.