A minimal energy control problem for second-order linear hyperbolic systems with two independent variables

In this paper, we investigate controllability and minimal energy optimal control for GoursatDarboux problem for the second-order linear hyperbolic systems with two independent variables. The equation describes a relation between functions u: D?Rm and z: D?Rn. We get an integral representation of the GoursatDarboux problem by means of Riemann's matrix. The first half of the paper considers conditions under which there exists a control u for which the solution z of dynamics satisfies z(x1, y1) = p for any given p. The studied problem is reduced to the moments problem. The optimal control was found in a closed analytic form. Further, degeneracy of the matrix constructed by means of Riemann's matrix is shown to be a necessary and sufficient condition of controllability. Copyright (c) 2011 John Wiley & Sons, Ltd.