Hybrid parametric minimum principle. (August 2020)

• Record Type: Journal Article
• Authors: Lin, Jia-Jiang; Luo, Xiong-Lin
• Is Part Of: Nonlinear analysis. Volume 37(2020)
• Publication Date: 2020-08
• Subjects: Hybrid systems -- Pontryagin maximum principle -- Optimal control problem -- Discrete control -- Hybrid minimum principle; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100902
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper discusses a special kind of hybrid system, named hybrid parametric system, which subsystem is characterized by parameters of model function. The parameters of model function represent the batch operation (discrete control). The joint optimization of both continuous and discrete control variables is named hybrid parametric optimal control problem. The corresponding necessary optimality conditions are established in the form of the hybrid parametric minimum principles, which are proposed and proved in this paper. The first principle, i.e. single stage hybrid parametric minimum principle, is proved based on the similar technique used by the proof of the classical Pontryagin maximum principle, and the second principle, multistage hybrid parametric minimum principle, is proved by reducing it into a nominal case of first principle. Moreover, in the virtue of the continuity of parameter space, the hybrid parametric minimum principle only requires a prescribed number of switching times.