The interval turnpike property for adjoints. (English) Zbl 1500.49011
Summary: We derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further give stronger estimates for analytic semigroups and provide a numerical example with a boundary controlled semilinear heat equation to illustrate the results.
MSC:
49K20 | Optimality conditions for problems involving partial differential equations |
49K40 | Sensitivity, stability, well-posedness |
93B05 | Controllability |
93B07 | Observability |