# Genetic algorithm for instruction of a neural network for vertikalizatsii ekzoskeleta with one criterion of optimisation

For management of dynamic installations use neural networks [23, 60, 91, 98]. Working out of HECTARES for instruction of NANOSECOND for a control system vertikalizatsii ekzoskeleta we will begin for one optimised criterion on classical HECTARE.

The block diagramme of this NANOSECOND is presented in drawing 3.10. The circuit design is the simplified copy of the circuit design nejroseti, presented on drawing 2.11. At adjustment of such network the hybrid algorithm which provides a combination of algorithms of genetic type and variation algorithm of adjustment of NANOSECOND is used.We assume, that in the course of work G it is necessary to gain the maximum values of parametres pи qнейронных networks NET1и NET2и the weight

Factors on an entry of neural network NET3 w_{1} w_{2} w_{3}.

Rice unok 3.10 - the Block diagramme synthesised nejroseti with one optimised criterion

As the neural network (nejrokontroller) in this case models the PID-REGULATOR the PID-REGULATOR model is realised by means of a recurrent neural network with delay elements on an entry and on an exit. Dynamics of model of this neural network is presented by a following equation:

y (n +1) = F (y (n)..., y (N - q +1), x (n)... χ (N - p +1)), (3.25)

Where y (n), y (n-1)..., y (n - q +1) - values of a starting signal during the previous moments of a time on which the model exit y (n +1) depends; x (n)... χ (n - p +1) - current and previous value of an arrival signal; F-some nonlinear function of the arguments.

For implementation of model (3.25) by means of NANOSECOND in the elementary configuration, that is in the form of single-layer perseptrona with an activation linear function, it is necessary to define weight numbers single-layer perseptrona, that is assemblage

The NANOSECOND is adjusted by some criterion which is necessary for minimising. In the capacity of such criterion the minimum of a root-mean-square error, for example, deviations of a real path vertikalizatsii ekzoskeleta from set or optimum can be accepted:

Where N-number of discrete readout on a path vertikalizatsii ekzoskeleta.

Thus, the problem consists in definition of concrete values of elements of the arranged in sequence assemblage (3.26) which would minimise funktsional (3.27). This problem can be solved by means of classical G in which (3.27) it is used in the capacity of fitness functions, and in the capacity of genes of chromosomes of population weight numbers of assemblage (3.26) are used. Weight numbers are coded either a bit pattern, or a Gray code. Having generated initial population from casual combinations allelej elements of assemblage (3.26), and by formation of new populations by means of genetic operators of crossing and a mutation, the chromosome providing minimisation funktsionala (3.37) is defined.

However it is fair provided that powers of subsets of assemblage (3.26) are known. But at synthesis in recurrent NANOSECOND, as a rule, are not known neither r, nor q.Следовательно, variation HECTARE for synthesis

nejrokontrollerov on the basis of recurrent NANOSECONDS to use it is not obviously possible.

Let's observe the hybrid HECTARE offered by us which allows to overcome these difficulties.

On the first step we will generate population by random sampling of parametres of a recurrent network p, qи w_{0}. It is possible to present this population in the form of table 3.2. Besides, it is necessary to choose admissible parametres of optimised criterion. It is necessary for selection poluchemyh as a result of use of genetic operators of individuals.

Table 3.2 - the Format of initial population of genetic algorithm

Table 3.2 is written down for Nобразцов (individuals) in initial population. Number of the individual in population is coded by a subscript. azhdaja the individual of initial population gives the derived initial population. In table 3.3 derived initial population for the individual №1 of table 3.2 is presented.

Table 3.3 is written down for Mобразцов (individuals) in initial derived population. Number of the individual in population is coded by a superscript.

Table 3.3 - the Format of initial derived population for the individual №1 from initial population of table 3.2

For every line table 3.2 the derived initial population is formed. In last column of table 3.3 value of function of fitness for the matching individual who pays off according to (3.27) registers.

For each derived initial population the variation HECTARE [77, 85] is realised. Result of work of this algorithm is creation

Parental pool. The parental pool is characterised by three parametres of function of fitness: the minimum value of function

Fitness J_{min}, the maximum value of function of fitness J_{max} and an average quadratic deviation σJфункции fitness in parental pools of derived populations. These values register in last three columns of table 3.2 for the matching individual which derived population are individuals of table 3.2.

The person, the making solution (LYRES), analyses the third columns of a parental pool of table 3.2 and by results of this analysis forms of them the base pool which each individual is optimised by means of hybrid G.Sushchnost of hybrid HECTARE consists in the following. Optimised criterion JJ is formed of three parametres of function of fitness, for example,

90

Where a_{1}, a_{2}, a_{3} - empirically selected positive factors.

After that get down to a consecutive variation of parametres of individuals from a base pool of table 3.2 in the following sequence. The parametre variation pпервой the base individual and transition to variation G according to a derived parental pool of table 3.3 is carried out. naliziruetsja criterion JJродительской of derived population of the first individual. If a variation pприводит to increase (decrease) of criterion JJ its variation towards increase (decrease) of this criterion proceeds.

Process of cyclic application variation G and a parametre variation pповторяются while the variation of this parametre leads to increase in criterion JJ. If criterion JJбольше does not increase, in matching columns parametres Jmin_{1} register, Jmax_{1}, σJ_{1}и analogous procedures «variation genetic algorithm» for parametres qи w_{0} are carried out. After that we are refunded to procedure «a variation plus classical genetic algorithm» for parametre pи so until variations of these three parametres will stop to call increase (decrease) JJ. Then we carry out transition to the following individual of table 3.2. The algorithm is finished after in table 3.2 there will be only one individual.

To realise hybrid G it is possible in the various ways. Ways differ rules of escalating of usages of delays in neural networks NET1 and NET2. In drawing 3.11 the circuit design of the hybrid HECTARE, a realising way of escalating of delays by a rule «is presented while the result is not becomes worse».

Drawing 3.11 - the Circuit design of hybrid genetic algorithm (beginning)

Drawing 3.11 - the Circuit design of hybrid genetic algorithm (continuation)

Drawing 3.11 - the Circuit design of hybrid genetic algorithm (termination)

The essence of this rule consists that arrival signal delays are spliced until the optimised criterion does not stop to improve. Then start to splice starting signal delays until the optimised criterion does not stop to improve. Then are switched to escalatings of delays in an arrival signal and so are switched until the demanded criteriaon of performance will be attained or the permissible limit of delays will not be settled.

The algorithm drawing 3.11 works as follows. In blocks 1-4 initial parametres of performance of algorithm are set. And a priori we assume, that the minimum quantity of delays on an entry and on an exit is equal to unit. In blocks 5, 6 it is formed parental pools of NANOSECOND NET1и NET2, and in the block 7 from parental pools choose NANOSECOND with optimum structure. The block 8 implements a process vertikalizatsii. On its exit we gain value of optimised criterion. This criterion is compared to previous criterion. If it has changed in the "correct" party it is compared it to admissible criterion, and if it less admissible optimisation process is stopped (блок12). If the criterion has not attained demanded value transition to the block 13 is carried out. Blocks 13-16 are carried out in a scraper until then,

While the criterion will not attain demanded value, or will not change in «not correct» the party. In this case the space on a step back (the block 17) and transition to increase in delays on a starting signal is carried out. Blocks 18-26 for a starting signal are analogous to blocks 13-17 and 8-10 for an arrival signal.

3.3

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