Zero-sum differential game guidance law for missile interception engagement via neuro-dynamic programming

Abstract

In this paper, for solving the nonlinear control problem of the missile intercepting the maneuvering target, a novel nonlinear zero-sum differential game guidance law is proposed via the neuro-dynamic programming approach. First, the continuous-time nonlinear differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs (HJI) equation. Then, a critic neural network is designed to solve the corresponding nonlinear HJI equation. An adaptive weight tuning law for the critic weights is proposed, where an additional term is added to ensure the stability of the closed-loop nonlinear system. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic NN weights estimation error are proved with the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed differential game guidance law for nonlinear interception.

Keywords

Guidance law neuro-dynamic programming differential game nonlinear system Nash equilibrium

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References

Kumar

Ojha

Padhy

. Anticipated trajectory based proportional navigation guidance scheme for intercepting high maneuvering targets. Int J Control Autom Syst 2017; 15(3): 1351–1361.

Ghosh

Ghose

Raha

. Capturability of augmented pure proportional navigation guidance against time-varying target maneuver. J Guid Control Dynam 2014; 37(5): 780–787.

Yamasaki

Balakrishnan

Takano

. Modified command to line-of-sight intercept guidance for aircraft defense. J Guid Control Dynam 2013; 36: 901–905.

Cottrell

. Optimal intercept guidance for short-range tactical missiles. AIAA J 1971; 9(No. 7): 1414–1415.

Chen

Wang

. Optimal-control based guidance law to control both impact time and impact angle. Aero Sci Technol 2019; 84: 454–463.

Shima

. Optimal cooperative pursuit and evasion strategies against a homing missile. J Guid Control Dynam 2011; 34(2): 414–425.

Harl

Balakrishnan

. Impact time and angle guidance with sliding mode control. IEEE Trans Control Syst Technol 2012; 20(6): 1436–1449.

Re R

. Three-party differential game theory applied to missile guidance problem. Differential game theory with applications to missiles and autonomous systems guidance, vol. 102, 2017.

Wang

Jin

Liu

, et al. Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound. IEEE Trans Neural Network 2011; 22(1): 24–36.

10.

Vamvoudakis

Lewis

. Online solution of nonlinear two-player zero-sum games using synchronous policy iteration. In: Proceedings of the 2010 49th IEEE Conference on Decision and Control (CDC), IEEE, 15-17 December 2010, Atlanta, Georgia, USA, 2010.

11.

Dierks

Jagannathan

. Online optimal control of affine nonlinear discrete-time systems with unknown internal dynamics by using time-based policy update. IEEE Transact Neural Networks Learn Syst 2012; 23(7): 1118–1129.

12.

Yasini

Sistani

Karimpour

. Approximate dynamic programming for two-player zero-sum game related to H ∞ control of unknown nonlinear continuous-time systems. Int J Control Autom Syst 2015; 13(1): 99–109.

13.

Zhang

Han

. Three-dimensional finite-time guidance law based on sliding mode adaptive RBF neural network against a highly manoeuvering target. Aeronaut J 2022; 1–2.

14.

Xie

Liu

. Adaptive neural network model-based event-triggered attitude tracking control for spacecraft. Int J Control Autom Syst; 32020.

15.

Bardhan

Ghose

. Intercepting maneuvering target with specified impact angle by modified SDRE technique. In: Proceedings of the American Control Conference, Montréal., Canada, 27–29 June 2012, 2012, pp. 4613–4618.

16.

Nobahari

Nasrollahi

. A nonlinear robust model predictive differential game guidance algorithm based on the particle swarm optimization. J Franklin Inst 2020; 357: 15.

17.

Hao.

Finite-horizon near optimal design of nonlinear two-player zero-sum game in presence of completely unknown dynamics. Journal of Control, Automation and Electrical Systems 2015; 26.4:361-370.

18.

Wang

Cui

, et al. Deep reinforcement learning-based impact time control guidance law with constraints on the field-of-view. Aero Sci Technol 2022; 128: 107765.

19.

Vamvoudakis

Lewis

. Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 2010; 46(5): 878–888.

20.

Duan

Liu

Zhang

. Robust optimal control for finite-horizon zero-sum differential games via a plug-n-play event-triggered scheme. J Franklin Inst 2020; 357(10): 5989–6017.

21.

Bardhan

Ghose

. Nonlinear differential games-based impact-angle-constrained guidance law. J Guid Control Dynam 2015; 38(3): 384–402.