I have a nonlinear dynamical model that is described by 12 system of ordinary differential equation in the form of

x'(t)= f(x,u); where x is the states variable  and u is the control variable.

- I have constraints on the state and the control variables

- I would like to use optimal control theory to find the cost effective control mechanism for disease control.

- I am using the Pontryagin Minimun Principle to characterize an optimal solution.

- I already defined my cost function, Hamiltonian, and the co-state dynamical equations.

-  Since they are very complex,they cannot be solved analytically

- I have Initial and final conditions on the states variables

- I do have final time.

- I was apply  Runge-Kutta fourth order method for optimal control problem  using matlab to solve the problem. But since the dynamics is complex that became so lengthy and difficult to manage.

Therefore,  I am looking for numerical algorithms  that can help to solve my problem efficiently.