摘要
The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.
The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution. These equations(if solvable) can be solved numerically by using the terminal value and the backward iteration. To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game. The main contributions of this paper are as follows.First, the existence of Nash equilibrium controls for the discretetime formation control problem is shown. Second, a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.
作者简介
Corresponding author:JOND Hossein Barghi was born in 1986.He received his B.S.degree in computer software engineering and M.S.degree in mechatronics engineering from University of Applied Science&Technology and Islamic Azad University in 2009 and 2011 both from Iran,respectively.Currently,he is working towards his Ph.D.degree in the Department of Computer Engineering,Karadeniz Technical University,Trabzon,Turkey.He spent one year during 2016–2017 in the Department of Applied Mathematics,VSB-Technical University of Ostrava,Czech Republic,within the Erasmus+exchange program.His research interests include multi-agent systems,optimal control theory,differential game theory,formation control,and trajectory planning.E-mail:barghi@ktu.edu.tr;NABIYEV Vasif was born in 1963.He received his B.S.and M.S.degrees in the Faculty of Computer Engineering and Automation from St.Petersburg Electro Technical University in 1985,and his Ph.D.degree in the Department of Computer Science from Moscow Technical University in 1990.From 2005,he has been a professor in Computer Science Department from Karadeniz Technical University,Turkey,where he still lectures.His research interests are in artificial intelligence,biometry,data security,human computer interaction,operational research,discrete and applied mathematics,combinatorial algorithms,and game theory.E-mail:vasif@ktu.edu.tr。
