Investigation of Optimization Algorithms for Neural Network Solutions of Optimal Control Problems with Mixed Constraints

Abstract

In this paper, we consider the problem of selecting the most efficient optimization algorithm for neural network approximation—solving optimal control problems with mixed constraints. The original optimal control problem is reduced to a finite-dimensional optimization problem by applying the necessary optimality conditions, the Lagrange multiplier method and the least squares method. Neural network approximation models are presented for the desired control functions, trajectory and conjugate factors. The selection of the optimal weight coefficients of the neural network approximation was carried out using the gravitational search algorithm and the basic particle swarm algorithm and the genetic algorithm. Computational experiments showed that evolutionary optimization algorithms required the smallest number of iterations for a given accuracy in comparison with the classical gradient optimization method; however, the multi-agent optimization methods were performed later for each operation. As a result, the genetic algorithm showed a faster convergence rate relative to the total execution time.

Keywords

• optimal control problem
• evolutionary optimization
• neural network approach