Duality in the optimal control for damped hyperbolic systems with positive control (Q1811943)

The paper considers a linear-quadratic optimal control problem governed by a hyperbolic equation. Assuming that the optimality system (necessary optimality conditions) has a solution, the authors show that the dual problem (formulated for the adjoint equation) has a solution and the same cost as the original problem. Comparing with the previous work by \textit{J. Y. Park} and \textit{M. J. Lee} [``Duality in the optimal control for damped hyperbolic systems with positive control'', Nonlinear Anal. Forum 4, 105--117 (1999; Zbl 1037.49034)], the only difference is that now there are imposed some positiveness constraints on the initial value of the state.