Elements of Numerical Mathematical Economics with Excel

10.2. Nonlinear Hamiltonian and linear Hamiltonian (bang-bang control)

It is clear from the maximum principle conditions that the resolution of Eq. (10.1-1) must pass through the maximization of the Hamiltonian function H with respect to the control variable u(t).

Figure 10.2-1 (A) Nonlinear Hamiltonian and (B) linear Hamiltonian.

Now, essentially the following two cases arise in the OC theory for maximizing ℋ:

• 1. Hamiltonian function is nonlinear in u(t), and usually the control variable u(t) is unconstrained.
• 2. Hamiltonian ...