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We describe the use of Ant Colony Optimization (ACO) for the ball and beam control problem, in particular for the problem of tuning a fuzzy controller of Sugeno type. In our case study, the controller has four inputs, each of them with two membership functions, we consider the interpolation point for every pair of membership function as the main parameter and their individual shape as secondary ones in order to achieve the tuning of the fuzzy controller by using an ACO algorithm [15]. Simulation results show that using ACO and coding the problem with just three parameters instead of six, allows us to find an optimal set of membership function parameters for the fuzzy control system with less computational effort needed.

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We describe in this paper a new method for adaptive model-based control of non-linear dynamic plants using Neural Networks, Fuzzy Logic and Fractal Theory. The new neuro-fuzzy-fractal method combines Soft Computing (SC) techniques with the concept of the fractal dimension for the domain of Non-Linear Dynamic Plant Control. The new method for adaptive model-based control has been implemented as a computer program to show that our neuro-fuzzy-fractal approach is a good alternative for controlling non-linear dynamic plants. We illustrate in this paper our new methodology with the case of controlling biochemical reactors in the food industry. For this case, we use mathematical models for the simulation of bacteria growth for several types of food. The goal of constructing these models is to capture the dynamics of bacteria population in food, so as to have a way of controlling this dynamics for industrial purposes. IntroductionWe describe in this paper a new method for adaptive control of non-linear dynamic plants based on the use of Neural Networks, Fuzzy Logic and Fractal Theory. Production processes in real world plants are often highly non-linear and dif®cult to control [1]. The problem of controlling them using conventional controllers has been widely studied [2]. Much of the complexity in controlling any process comes from the complexity of the process being controlled. This complexity can be described in several ways. Highly non-linear systems are dif®cult to control, particularly when they have complex dynamics (such as instabilities to limit cycles and chaos). Dif®culties can often be presented by constraints, either on the control parameters or in the operating regime. Lack of exact knowledge of the process, of course, makes control more dif®cult. Optimal control of many processes also requires systems, which make use of predictions of future behavior. The mathematical models for the plants are assumed to be systems of differential equations. The goal of having these models is to capture the dynamics of production processes, so as to have a way of controlling this dynamics for industrial purpose [3].We need a mathematical model of the non-linear dynamic plant to understand the dynamics of the processes involved in production. For a speci®c case, this may require testing several models before obtaining the appropriate mathematical model for the process [4]. For real world plants with complex dynamics, we may even need several models for different sets of parameter values to represent all of the possible behaviors of the plant. The general mathematical model of a plant can be expressed as follows: dx=dt f 1 x; D; a À bf 2 x; D; a dp=dt bf 2 x; D; a where x P R n is a vector of state variables, p P R m is a vector of products, b P R is a constant measuring the ef®ciency of the conversion process, D P 0; 3 is the fractal dimension of the process, and a P R is a selection parameter. The fractal dimension is used to characterize the production process, for example in the case of biochemical reactors D represents ...

This paper describes an optimization of interval type-2 and type-1 fuzzy integrators in ensembles of ANFIS models with genetic algorithms (GAs), this with emphasis on its application to the prediction of chaotic time series, where the goal is to minimize the prediction error. The Mackey-Glass time series was considered to validate the proposed ensemble approach. The methods used for the integration of the ensembles of ANFIS are: type-1 and interval type-2 Mamdani fuzzy inference systems (FIS). Genetic Algorithms are used for optimization of the membership function parameters of the FIS in each integrator. In the experiments we changed the type of the membership functions for each type-1 and interval type-2 FIS, thereby increasing the complexity of the training, The output (Forecast) generated by each integrator is calculated with the RMSE (root mean square error) to minimize the prediction error, therefore we compared the performance obtained by each FIS.

Stability is one of the more important aspects in the traditional knowledge of Automatic Control. Type-2 Fuzzy Logic is an emerging and promising area of application to Intelligent Control (in this case, Fuzzy Control). We present a design methodology based on the Margaliot work [10] for the design of Stable Mamdani Type-2 Fuzzy Logic Controllers.