When does stabilizability imply the existence of infinite horizon optimal control in nonlinear systems?. (January 2023)

• Record Type: Journal Article
• Authors: Sakamoto, Noboru
• Is Part Of: Automatica. Volume 147(2023)
• Publication Date: 2023-01
• Subjects: Optimal control -- Stability -- Stabilizability -- Detectability -- Stable manifold -- Turnpike; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110706
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The paper addresses an existence problem for infinite horizon optimal control when the system under control is exponentially stabilizable or stable. Classes of nonlinear control systems for which infinite horizon optimal controls exist are identified in terms of stability, stabilizability, detectability and growth conditions. The result then applies to estimate the existence region of stable manifolds in the associated Hamiltonian systems. Applications of the results also include the analysis for turnpike property in nonlinear finite horizon optimal control problems by a geometric approach.