ABSTRACT

A numerical method using neural network for solving infinite-horizon time-delayed optimal control problems is studied. The problem is first transformed, using a Páde approximation, to one without a time-delayed argument. By a suitable change of variable, the obtained non-delay infinite-horizon optimal control problem is converted to a finite-horizon nonlinear optimal control problem. We try to approximate the solution of Hamiltonian conditions based on the Pontryagin minimum principle (PMP). For this purpose, we introduce an error function that contains all PMP conditions. We then minimize the error function where weights and biases associated with all neurons are unknown. Substituting the optimal values of the weights and biases in the trial solutions, we obtain the optimal solution of the original problem. Several examples are given to show the efficiency of the method.

摘要

研究了一种利用神经网络求解无限视距时滞最优控制问题的数值方法。首先使用 Páde 近似将问题转换为没有时间延迟参数的问题。通过适当改变变量，将得到的无时滞无限范围最优控制问题转化为有限范围非线性最优控制问题。我们尝试基于庞特里亚金最小原理（PMP）来近似哈密顿条件的解。为此，我们引入了一个包含所有 PMP 条件的误差函数。然后我们最小化误差函数，其中与所有神经元相关的权重和偏差都是未知的。代入试验解中权重和偏差的最优值，我们得到原问题的最优解。