Necessary conditions of optimality for a class of second-order hyperbolic systems with spatially dependent controls in the coefficients

In the paper, we consider the problem of parameter optimization for a class of second-order hyperbolic systems with distributional forcing terms. After necessary preparations in Sections 1 and 3, we develop in Section 4 the necessary conditions of optimality for the system with quadratic cost function. In Section 5, we extend these results to cover a wider class of controls; we also prove the existence of suboptimal policies. An example is presented indicating possible application to power system regulation problems.This work was supported in part by the National Science and Engineering Council of Canada under Grant No. 7109.The author would like to thank Professor L. Cesari for pointing out in a private communication that there are situations like the Lavrentiev phenomenon in which an approximation analogous to that given in Theorem 5.3 is not possible.