= Free-terminal-time transversality condition
{title2=$\min_u H(T,x(T),u,p(T))+\Phi_T(T,x(T))=0$}
For a smooth normal <optimal control> problem with freely variable terminal time, fixed terminal state independent of that time and terminal cost $\Phi$, the optimized <Hamiltonian of an optimal-control problem> at completion satisfies $H(T)+\Phi_T=0$. It follows by varying the terminal time in the augmented objective; restrictions on terminal time or a moving endpoint introduce additional terms or inequalities.
Back to article page
