Combining ode45 and optimization solvers

Hi,

I am strugging to solve ode45 with an optimization paramter that is time varying. Let's take an example

where is known vector and x is scalar (assume ). To solve the system by ode45, I will need to use interp1 command because varies with time. The output of the ode45 will be a vector which includes the solution of the ode. With that being said, I want to find the optimal

such that it is almost the same as u. My objective function will be . But when I use interp1 command, it does not work because will not be double type. If I use for example cvx toolbox, will be cvx type and not double !!

How can I fix this?

[Star Strider]

What sort of optimisation do you want to do?

Do any of the MATLAB Toolboxes (Such as the Optimization Toolbox or Global Optimization Toolbox) have the functions that perform that sort of optimisation?

[Fahad Aljehani]

I prefer using CVX. But I am open to use any buildin function that can do the job, fmincon, fminunc,etc.