Premium
High‐order maximum principles for the stability analysis of positive bilinear control systems
Author(s) -
Hochma Gal,
Margaliot Michael
Publication year - 2015
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2224
Subject(s) - orthant , spectral radius , mathematics , eigenvalues and eigenvectors , bilinear interpolation , order (exchange) , linear system , legendre polynomials , lti system theory , invariant (physics) , matrix (chemical analysis) , control theory (sociology) , mathematical analysis , control (management) , computer science , mathematical physics , physics , statistics , finance , quantum mechanics , economics , artificial intelligence , materials science , composite material
Summary We consider a continuous‐time positive bilinear control system, which is a bilinear control system with Metzler matrices. The positive orthant is an invariant set of such a system, and the corresponding transition matrix is entrywise nonnegative for all time. Motivated by the stability analysis of positive linear switched systems under arbitrary switching laws, we define a control as optimal if it maximizes the spectral radius of the transition matrix at a given final time. We derive high‐order necessary conditions for optimality for both singular and bang–bang controls. Our approach is based on combining results on the second‐order derivative of a simple eigenvalue with the generalized Legendre‐Clebsch condition and the Agrachev–Gamkrelidze second‐order optimality condition. Copyright © 2015 John Wiley & Sons, Ltd.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom