Optimal Control with Salvage Term

[uberathlete]

Hi folks. Is anyone familiar with optimal control problems? How do you solve an optimal control problem that has a salvage term? Like for example,

max int F(t,X(t),U(t)) dt + S(X(t1)) subject to X'(t) = g(t,x,u) X(t0) = Xt0

Will the Hamiltonian be different from one from a normal OC problem? Also, do the necesary conditions change? Any enlightenment on this would be greatly appreciated. Thanks!

 

[JakeD]

Hi folks. Is anyone familiar with optimal control problems? How do you solve an optimal control problem that has a salvage term? Like for example,

max int F(t,X(t),U(t)) dt + S(X(t1)) subject to X'(t) = g(t,x,u) X(t0) = Xt0

Will the Hamiltonian be different from one from a normal OC problem? Also, do the necesary conditions change? Any enlightenment on this would be greatly appreciated. Thanks!

The Hamiltonian doesn't change but a transversality condition is added to the necessary conditions.