THE LINEAR PROGRAMMING APPROACH TO DETERMINISTIC OPTIMAL CONTROL PROBLEMS

Given a deterministic optimal control problem (OCP) with value function, say J ∗ , we introduce a linear program (P) and its dual (P ∗ ) whose values satisfy sup(P ∗ ) ≤ inf(P) ≤ J ∗ (t, x). Then we give con- ditions under which (i) there is no duality gap, i.e. sup(P ∗ ) = inf(P), and (ii) (P) is solvable and it is equivalent to the (OCP) in the sense that min(P) = J ∗ (t, x).