On the existence of an optimal element for the neutral optimal problem with delay in controls. (English) Zbl 1513.49001
Summary: For an optimal control problem involving neutral differential equation
\[
\dot{x}(t) = A(t)\dot{x}(t-\sigma) + f(t,x(t), x(t-\tau), u(t))+g(t, x(t), x(t-\tau), u(t-\theta)), t\in[t_0, t_1]
\]
existence theorems of an optimal element are provided. Under element we imply the collection of delay parameters \(\sigma\) and \(\tau\), the initial moment and vector, control and finally moment.
MSC:
49J15 | Existence theories for optimal control problems involving ordinary differential equations |
34K35 | Control problems for functional-differential equations |
34K40 | Neutral functional-differential equations |