
The author studies state constrained optimal control problems with parabolic evolution equations. Optimality conditions are derived where the state and control expressions have been decoupled. The approach used is to consider a family of problems where deviation of the dynamics from feasibility is penalized through a parameter \(\varepsilon\). Decoupled optimality conditions are determined for each of these problems. Using Slater-like assumptions the limit of these optimality conditions provide optimality conditions for the original problem and the existence of Lagrange multipliers. The method is demonstrated on a distributed control problem with a Dirichlet boundary condition, and a boundary control problem with a Neumann boundary condition.
optimal control, optimality conditions, Lagrange multipliers, Dirichlet boundary condition, Neumann boundary condition, Initial value problems for linear higher-order PDEs, Optimality conditions for problems involving partial differential equations, parabolic evolution equations, Higher-order parabolic equations
optimal control, optimality conditions, Lagrange multipliers, Dirichlet boundary condition, Neumann boundary condition, Initial value problems for linear higher-order PDEs, Optimality conditions for problems involving partial differential equations, parabolic evolution equations, Higher-order parabolic equations
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