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

2020 ◽  
Author(s):  
Irina Bolodurina ◽  
Lyubov Zabrodina
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Optimization Algorithms ◽  
Evolutionary Optimization ◽  
Control Problems ◽  
Network Solution ◽  
The Neural Network ◽  
Evolutionary Optimization Algorithms

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

Machines ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 102
Author(s):  
Irina Bolodurina ◽  
Lyubov Zabrodina
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Necessary Optimality Conditions ◽  
Particle Swarm Algorithm ◽  
Control Problems ◽  
Mixed Constraints

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.

On fractional optimal control problems with an application in fractional chaotic systems using a Legendre collocation-optimization technique

2020 ◽  
pp. 014233122096958
Author(s):  
Safiye Ghasemi ◽  
Alireza Nazemi ◽  
Raziye Tajik ◽  
Marziyeh Mortezaee
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Minimum Principle ◽  
Control Problems ◽  
Back Propagation Algorithm ◽  
Functional Link ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems ◽  
Following Error

In this paper, an intelligence method based on single layer legendre neural network is proposed to solve fractional optimal control problems where the dynamic control system depends on Caputo fractional derivatives. First, with the help of an approximation, the Caputo derivative is replaced to integer order derivative. According to the Pontryagin minimum principle for optimal control problems and by constructing an error function, an unconstrained minimization problem is then defined. In the optimization problem, trial solutions are used for state, costate and control functions, where these trial solutions are constructed by using Legendre polynomial based functional link artificial neural network. In the following, error back propagation algorithm is used for updating the network parameters (weights). At the end, some illustrative examples are included to demonstrate the validity and capability of the proposed method. Three applicable examples about chaos control of Malkus waterwheel, finance fractional chaotic models and fractional-order geomagnetic field models are also considered.

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