Finite-horizon differential games for missile–target interception system using adaptive dynamic programming with input constraints

ABSTRACT

In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton–Jacobi–Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile–target interception system, assuming first-order dynamics for the interceptor and target.

KEYWORDS:

• Differential game
• finite-horizon
• adaptive dynamic programming
• input constraints
• missile–target interception

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61473147]; Funding of Jiangsu Innovation Program for Graduated Education [grant number KYLX16_0376]; and Funding for Outstanding Doctoral Dissertation in NUAA [grant number BCXJ16-02].

Notes on contributors

Jingliang Sun

Jingliang Sun was born in 1990. He received his BS degree in automation from Tianjin University of Technology, Tianjin, China. He is currently pursuing the PhD degree in control theory and control engineering at the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. His current research interests include optimal control, robust control, adaptive dynamic programming and differential games.

Chunsheng Liu

Chunsheng Liu was born in 1955. She received her BS, ME and PhD degrees from Huazhong University of Science & Technology, Xi'an Jiaotong University and Nanjing University of Aeronautics and Astronautics (NUAA), respectively. She is now a professor and PhD supervisor in automation engineering at NUAA. Her current research interests include optimal control, adaptive control, fault diagnosis and tolerant control with the application in aircraft.