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Operations research, linear programming, control theory, systems theory, optimal control, game theory

1 vote
0 answers
165 views

Pontryagin principle for optimal control problem with a terminal cost involving the control

Let $T >0$ and consider the problem of minimizing $$ P(v(.)) \triangleq \int_0^T l(x_t,v_t) d t + h(x_T) $$ over a broad class of control $v(.)$ where \begin{equation} \dot x_t = f(x_t,v_t), \quad x …
megaproba's user avatar
  • 375
1 vote
1 answer
213 views

how to impose a terminal condition in a minimisation problem?

Consider the problem of minimising $$ J(u(.)) \triangleq \int_0^T l(x(t),u(t)) d t + \phi(x(T)), \: T> 0 $$ over a space of controls $\mathcal{U}$ with the constraint $$ \dot x(t) = f(x(t),u(t)), \: …
megaproba's user avatar
  • 375