Advances in optimal control of differential systems with the state suprema

This paper deals with a further development of analytic techniques for Optimal Control Problems (OCPs) involving differential systems with the state suprema. Differential equations evolving with state suprema (maxima) provide a useful modelling framework for various real-world applications, namely, in electrical engineering and in biology. The corresponding dynamic models lead to Functional Differential Equations (FDEs) in the presence of state-dependent delays. We study some particular (but important) cases of optimal control processes governed by systems with sup-operator in the right hand sides of the differential equations and obtain constructive characterizations of optimal solutions. The constrained OCPs we examine are formulated assuming the (linear) feedback-type control law. The case study presented in this article constitutes a formal extension of the concept of positive dynamic systems to differential systems with the state suprema. © 2017 IEEE.

• Fecha de publicación: 2018
• Institución: Universidad de Medellín
• Repositorio: Repositorio UDEM
• Idioma: eng
• OAI Identifier: oai:repository.udem.edu.co:11407/4886
• Acceso en línea: http://hdl.handle.net/11407/4886
• Palabra clave: Differential equations; Optimal control systems; Analytic technique; Differential systems; Functional differential equations; Modelling framework; Optimal control problem; Optimal controls; Optimal solutions; State dependent delay; Equations of state
• License: http://purl.org/coar/access_right/c_16ec