Pulse and Point Optimal Control of Linear Hyperbolic Integro-Differential Systems with Mixed Boundary Conditions

Abstract

We investigate an optimal control problem for a linear hyperbolic integrodifferential equation, subject to Robin-type boundary conditions. The control operates as an operator on the equation’s right-hand side, integrating Dirac delta functions concerning temporal or spatial variables. A priori inequalities in negative norms are established for the boundary value problem (BVP) operator. From these findings, we derive theorems on the problem’s well-posedness and the existence of optimal control across multiple scenarios, subject to specific assumptions regarding the admissible control set and the quality criterion.

Keywords

• integro-differential equation
• linear hyperbolic equation
• volterra operator
• viscoelastic media
• optimal control
• pulse control