Asymptotics of a Solution to an Optimal Boundary Control Problem with Performance Index Defined on the Boundary

Key Points

• The study aims to explore the asymptotic behavior of solutions to an optimal control problem involving elliptic equations.
• Analyzed the optimal control problem with performance index defined on the boundary.
• Examined a flow through the domain boundary using the Laplace operator.
• Implemented constraints via an integral relation on the control.
• Derived a complete asymptotic expansion based on a small parameter.
• Achieved a thorough asymptotic expansion of the solution in relation to the small parameter.
• Established the impact of the Laplace operator and zero-order operator on performance.
• Outlined the dependence of the control performance on the state deviation at the boundary.