RESEARCH PAPER NULL CONTROLLABILITY OF FRACTIONAL DYNAMICAL SYSTEMS WITH CONSTRAINED CONTROL Rajagopal Joice Nirmala 1 , Krishnan Balachandran 2 , Juan J. Trujillo 3 Abstract This paper concerns the null controllability of fractional dynamical sys- tems with constrained control. We assume that the linear system is con- trollable with square integrable control and provide sufficient conditions for the null controllability with constrained control. Further, sufficient condi- tions for the null controllability of nonlinear system also are established. Examples are provided to illustrate the theory. MSC 2010 : Primary 34A08, 93B05 Key Words and Phrases: fractional dynamical system, null controlla- bility, constrained control, proper, asymptotic stability 1. Introduction The main objective of the study is to establish sufficient conditions for the null controllability of fractional dynamical system with limited control. It plays fundamental role in the solution of the time optimal control prob- lems. Though the importance of this problem of optimization of systems with control constraints has long been recognized most researchers have worked on controllability of systems with limited control. Ordinary and partial differential equations of fractional orders have been the focus of many studies due to their frequent appearance in various c  2017 Diogenes Co., Sofia pp. 553–565 , DOI: 10.1515/fca-2017-0029 Brought to you by | University of Sydney Library Authenticated Download Date | 6/3/17 1:34 PM