Solving infinite-horizon optimalcontrol problems of the time-delayedsystems by a feed forward neural network model

Area of Science:

• Control Theory
• Computational Mathematics
• Artificial Intelligence

Background:

• Optimal control problems with time delays are challenging due to their infinite dimensionality.
• Existing numerical methods often struggle with convergence and computational efficiency for such problems.
• The Pontryagin Minimum Principle (PMP) provides necessary conditions for optimality but can be difficult to solve analytically.

Purpose of the Study:

• To develop a robust and efficient numerical method for solving infinite-horizon time-delayed optimal control problems.
• To leverage neural networks for approximating solutions to the Hamiltonian conditions derived from the PMP.
• To demonstrate the effectiveness of the proposed method through various examples.

Main Methods:

• Transformation of the time-delayed optimal control problem into a non-delayed equivalent using Páde approximation.
• Conversion of the non-delayed infinite-horizon problem into a finite-horizon nonlinear optimal control problem via a change of variables.
• Approximation of the PMP's Hamiltonian conditions by defining and minimizing an error function using neural networks.
• Optimization of neural network weights and biases to satisfy all PMP conditions.

Main Results:

• The proposed neural network-based method successfully approximates the optimal solutions for infinite-horizon time-delayed optimal control problems.
• The method effectively handles the complexities introduced by time delays and infinite horizons.
• Numerical examples validate the efficiency and accuracy of the developed technique.

Conclusions:

• The neural network approach offers a powerful tool for solving a class of optimal control problems previously difficult to address numerically.
• This method provides a viable alternative for researchers and engineers dealing with time-delayed control systems.
• Further research can explore extensions of this method to more complex control scenarios.