We consider a general example for an optimal control problem subject to coupled differential equations (CDEs). As CDEs we define a coupled system of partial differential equations (PDEs) and ordinary differential equations (ODEs). All differential equations here represent a time evolution and are fully coupled. An averaging or evaluation operator, resp., is applied to PDE states entering into an ODE such that the ODE has no spatial dependency. Following a first-optimize-then-discretize method, we derive the adjoint equations by means of the necessary first-order optimality conditions. We prove that the coupling structure of the CDE problem in the adjoint system is reversed. This feature is observed and exploited in (continuous as well as discretized) optimal control problems in real-world applications.    «

We consider a general example for an optimal control problem subject to coupled differential equations (CDEs). As CDEs we define a coupled system of partial differential equations (PDEs) and ordinary differential equations (ODEs). All differential equations here represent a time evolution and are fully coupled. An averaging or evaluation operator, resp., is applied to PDE states entering into an ODE such that the ODE has no spatial dependency. Following a first-optimize-then-discretize method, w...    »