Optimal Control of Nonsymmetric Hyperbolic Systems in <i>n</i> Variables on the Half-Space

Abstract

We study a quadratic control problem on the finite time interval with respect to the system of hyperbolic partial differential equations \[\begin{gathered} \frac{{\partial y}}{{\partial i}} = \sum_t {A_i \frac{{\partial y}}{{\partial x_i }}} + f, \hfill \\ My_{\partial \Omega } = u, \hfill \\ y(0) = y_0 , \hfill \\ \end{gathered} \] on the spatial domain $\Omega = \{ x \in \mathbb{R}^n | {x_1 } . > 0\} $. For a special case it is shown that the control u may be synthesized in feedback form. The nonlinear operator equations involved in this synthesis are shown to have unique solutions within an appropriate class of functions.