Open AccessClosed‐form solution of discrete‐time optimal control and its convergence
Author(s) -
Zhang Hehong,
Xie Yunde,
Xiao Gaoxi,
Zhai Chao
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0749
Subject(s) - control theory (sociology) , convergence (economics) , sequence (biology) , optimal control , discrete time and continuous time , backstepping , mathematics , state (computer science) , bang–bang control , control (management) , adaptive control , computer science , mathematical optimization , algorithm , statistics , artificial intelligence , biology , economics , genetics , economic growth
The convergence of a new closed‐form solution for the discrete‐time optimal control is presented. First, a new time optimal control law with simple structure is constructed in the form of the state feedback for a discrete‐time double‐integral system by using the state backstepping approach. The control signal sequence in this approach is determined by the linearised criterion according to the position of the initial state point on the phase plane. This closed‐form non‐linear state feedback control law clearly shows that time optimal control in discrete time is not necessarily the bang‐bang control. Second, the convergence of the time optimal control law is proved by demonstrating the convergence path of the state point sequence driven by the corresponding control signal sequence. Finally, numerical simulation results demonstrate the effectiveness of this new discrete‐time optimal control law.