How to solve optimal control problem with delay?

[Song921012]

Hello, can Infiniteopt.jl solve optimal control problem with delay? For example,

$$\left\{\begin{array}{l} \min\int_0^T e^{-\beta t}\left(C_E \frac{u(t)^3}{x(t)}-p u(t)\right) d t+0.1 T^2 \\\ \dot{x}=a x(t)\left(1-\frac{x(t-h)}{b}\right)-u(t) \\\ x(t)=2 \forall t \in[-h, 0] \quad, \quad x(t) \geq 2 \forall t \in[0, T] \\\ u(t) \geq 0 \forall t \in[0, T] \\\ T \text{ free. } \end{array}\right.$$

[pulsipher]

InfiniteOpt does not directly support problems where the limits of an infinite parameter (e.g., time) are decision variables (i.e., T in this case). However, such problems can often be reformulated into standard dynamic optimization problems (with a fixed horizon) as demonstrated on some of the other discussions on the forum and as is common in optimal control literature. In this case, I suspect this can be reformulated in like manner to minimum time problems since I beleive the final time T is a variable and the initial time -h is fixed.