Investigation of the Evolutionary Optimization Algorithms for the Neural Network Solution of the Optimal Control Problems

Abstract

In this paper, we consider the neural network approach to solving optimal control problems with mixed constraints at the stage of optimization of the functional approximations through evolutionary algorithms. Based on the necessary optimality conditions and the Lagrange multiplier method, the initial optimal control problem is reduced to a nonlinear optimization problem and the corresponding approximation model of the neural network for the control function and the trajectory is presented. The convergence of the neural network approach using a genetic algorithm, a population-based gravitational search algorithm, and a basic particle swarm algorithm was studied. Also, the results obtained are compared with the operation of the gradient descent algorithm. Computational experiments have shown that evolutionary algorithms for optimizing functions use the least number of iterations to achieve a given accuracy, but multi-agent methods of gravitational search and particle swarming show the longest execution time per iteration. The genetic optimization algorithm showed the fastest convergence rate relative to the total execution time of the algorithm.