Examples for dynamic optimization in continuous time / optimal control
Three examples of dynamic optimization (optimal control) in continuous time, employing the maximum principle:
(1) the resulting system of differential equations (DE) for state and adjoint function can be solved separately (beginning at 7:05),
(2) the resulting system of DE must be solved jointly by way of eigenvalues and eigenvectors (beginning at 14:05),
(3) the resulting system of DE has time-varying coefficients (beginning at 33:10),
(3a) example (3) solved with the current-value Hamiltonian that eliminates the time-varying coefficients (beginning at 57:07).
I mention similarities to static optimization under constraints and of the Hamiltonian with the Lagrangian auxiliary function, where I refer to earlier videos:
• Examples for optimization subject to equal... (equality constraints)
• Examples for optimization subject to inequ... (inequality constraints)