On the problem of optimal control synthesis in systems with distributed parameters

The design of an optimal control by the method of Lyapunov functions is considered for distributed systems described by linear partial differential equations. At first the original equations are reduced to a system of first-order equations. The optimal control is designed by minimizing an integral performance criterion, and it has the least value of the norm (a local criterion). Asymptotic stability of the closed-loop system is ensured in each case.