The interval turnpike property for adjoints

2020/05/25 by Timm Faulwasser, Faulwasser, Timm, Lars Grüne +5 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #49K20 #49K40 #93B05 #93B07 #93D20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.2005.12120

openalex publication_date 2020/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work 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.

Citations

• Exact Controllability, Stabilization and Perturbations for Distributed Systems

Cited by

• Turnpike property for hierarchical optimal control problems: from particle systems to hydrodynamic equations
• Dissipativity and optimal control

Related

• Linear turnpike theorem
• Turnpike property of linear quadratic control problems with unbounded control operators
• The turnpike property in finite-dimensional nonlinear optimal control
• The turnpike property in nonlinear optimal control -- A geometric approach
• Turnpike in optimal control and beyond: a survey