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Evolutionary Design of NN-ANARX Model for Closed Loop Control Using Genetic Algorithms

This study outlines a genetic algorithm-based approach for optimizing closed loop control systems using Neural Networks, specifically focusing on the NN-ANARX model. It explores principles such as initial population, fitness function evaluation, chromosome evolution through crossover and mutation, and the iterative selection process for the best model. The aim is to address challenges in system structure identification and control system optimization through genetic algorithms. The proposed method enhances model quality by systematically evaluating control accuracy, model order, and correlation metrics.

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Evolutionary Design of NN-ANARX Model for Closed Loop Control Using Genetic Algorithms

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  1. Evolutionary Design of the Closed Loop Controlon the Basis of NN-ANARX Model UsingGeneticAlgoritm

  2. Principles of Genetic Algorithms Initial Population – a set of strings called Chromosomes [0 1 0 1 1 0 1 0 … 0 1 1 1 0 1] [0 0 0 0 1 1 1 0 … 1 1 0 1 0 1] … [0 1 0 0 0 0 10 … 1 1 1 1 0 1] Calculation of fitness function, sort Chromosomes and choose the best ones

  3. Principles of Genetic Algorithms Formation of new generation: 1. Crossover [0 1 0 1 1 0 1 0 … 0 1 0 1 0 1] [1 0 0 0 0 1 1 0 … 1 0 1 1 1 1] at random places [0 1 0 1 1 0 1 0 … 0 0 1 1 1 1] [1 0 0 0 0 1 1 0 … 1 1 0 1 0 1] 2. Mutation [0 1 1 1 1 0 1 0 … 0 1 1 1 0 1] at random places (~1%) [0 1 0 1 1 0 0 0 … 0 1 1 1 0 1] “Best Parents” are used in crossover and mutation more frequently 3. “New Blood” – some absolutely new chromosomes

  4. Principles of Genetic Algorithms Initial Population Mutation, Crossover Selection Repeat until a Chromosome with a best fitness is found Formation of new generation

  5. Principles of Genetic Algorithms for selection of Neural Network’s Structure Fitness function – for example, MSE

  6. NARX (Nonlinear Autoregressive Exogenous) model: ANARX (Additive Nonlinear Autoregressive Exogenous) model: or ANARX model

  7. 1st sub-layer is a sigmoid function n-th sub-layer NN-based ANARX model (NN-ANARX)

  8. NN-ANARX model ANARX model ANARX Model based Dynamic Output Feedback Linearization Algorithm NN

  9. NN-based ANARX model Parameters (W1, …, Wn, C1, …, Cn) NN-ANARX Model based Control of Nonlinear Systems Controller u(t) Nonlinear System y(t) Dynamic Output Feedback Linearization Reference signal v(t)

  10. Problems to be solved • A little or no knowledge about structure of the system is given a priori • A set of neural networks must be trained to find an optimal structure • Quality of the model depends on the choice of initial parameters • Quality of the model should be evaluated in the closed loop • These problems can be solved using GA.

  11. GA for structural identification NN-ANARX structure may be easily coded as a gene. Consider an example (custom structure model):

  12. Dynamic controller based on custom structure model Gene:

  13. Fitness function • Model structure optimization is based on fitness function consisting of 3 parameters: • Error of the closed-loop control system • Order of the model • Correlation test • All of the criteria are normalized

  14. Numerical evaluation of the criteria Correlation between the following three parameters is checked: Further the parameter Q is the mean of the means of the means of cross correlation coefficients computed for three parameters mentioned above. Evaluation function: with

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