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Principles of Genetic Algorithms

Evolutionary Design of the Closed Loop Control on the Basis of NN-ANARX Model Using Genetic Algoritm. Principles of Genetic Algorithms. Initial Population – a set of strings called C hromosomes. [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] …

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Principles of 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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