Abstract
A modified finite-time impact angle control guidance (IACG) law is developed. First, based on the biased proportional navigation guidance (PNG) approach, the finite-time convergent impact-angle error dynamic is deduced from the guidance model. Then, a modified IACG law considering finite-time convergence is designed by inserting a time-to-go term into the dominator of the biased term. Furthermore, the finite-time stability and the explicit settling time of the impact-angle error dynamic is derived via utilizing the approach of Lyapunov analysis. Unlike the conventional IACG laws achieving finite-time convergence, the advantage of this modified guidance law is that the settling time for the impact-angle error is always smaller than the final time. Hence, under different initial impact-angle errors, the modified guidance law assures achieving the impact-angle error convergence before interception. Besides, it is convenient to adjust parameters. Finally, some numerical simulations under various scenarios are provided to confirm the properties of the modified finite-time convergent guidance law.
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References
Kim, B.S., Lee, J.G., Han, H.S.: Biased PNG law for impact with angular constraint. IEEE Trans. Aerosp. Electron. Syst. 34(1), 277–288 (1998)
Erer, K.S., Osman, M.: Indirect impact-angle-control against stationary targets using biased pure proportional navigation. J. Guid. Control. Dyn. 35(2), 700–704 (2012)
Lee, C.-H., Kim, T.-H., Tahk, M.-J.: Interception angle control guidance using proportional navigation with error feedback. J. Guidance Control Dyn. 36(5), 1556–1561 (2013)
Ryoo, C.-K., Cho, H., Tahk, M.-J.: Optimal guidance laws with terminal impact angle constraint. J. Guid. Control. Dyn. 28(4), 724–732 (2005)
Wang, C., Dong, W., Wang, J., Shan, J.: Nonlinear suboptimal guidance law with impact angle constraint: an SDRE-based approach. IEEE Trans. Aerosp. Electron. Syst. 56(6), 4831–4840 (2020)
Haimo, V.T.: Finite time controllers. SIAM J. Control. Optim. 24(4), 760–770 (1986)
Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control. Optim. 38(3), 751–766 (2000)
Levant, A.: Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence. IEEE Trans. Autom. Control 46(9), 1447–1451 (2001)
Hong, Y.G., Huang, J., Xu, Y.S.: On an output feedback finite time stabilization problem. IEEE Trans. Autom. Control 46(2), 305–309 (2001)
Orlov, Y.: Finite time stability and robust control synthesis of uncertain switched systems. SIAM J. Control. Optim. 43(4), 1253–1271 (2004)
Zuo, Z., Han, Q.-L., Ning, B.: Fixed-time Cooperative Control of Multi-Agent Systems. Springer International Publishing, Cham, Switzerland (2019)
Gurfil, P., Jodorkovsky, M., Guelman, M.: Finite time stability approach to proportional navigation systems analysis. J. Guid. Control. Dyn. 21(6), 853–861 (1998)
Zhou, D., Sun, S., Teo, K.L.: Guidance laws with finite time convergence. J. Guid. Control. Dyn. 32(6), 1838–1846 (2009)
Zhang, Y., Sun, M., Chen, Z.: Finite-time convergent guidance law with impact angle constraint based on sliding-mode control. Nonlinear Dyn. 70(1), 619–625 (2012)
Xiong, S., Wang, W., Liu, X., Wang, S., Chen, Z.: Guidance law against maneuvering targets with intercept angle constraint. ISA Trans. 53(4), 1332–1342 (2014)
Kumar, S.R., Rao, S., Ghose, D.: Nonsingular terminal sliding mode guidance with impact angle constraints. J. Guid. Control. Dyn. 37(4), 1114–1130 (2014)
Zhao, J., Zhou, J.: Strictly convergent nonsingular terminal sliding mode guidance law with impact angle constraints. Optik 127(22), 10971–10980 (2016)
Wang, C., Dong, W., Wang, J., Shan, J., Xin, M.: Guidance law design with fixed-time convergent error dynamics. J. Guid. Control. Dyn. 44(7), 1389–1398 (2021)
Kumar, S.R., Ghose, D.: Three-dimensional impact angle guidance with coupled engagement dynamics. Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng. 231(4), 621–641 (2016)
Si, Y., Song, S.: Three-dimensional adaptive finite-time guidance law for intercepting maneuvering targets. Chin. J. Aeronaut. 30(6), 1985–2003 (2017)
Wang, C., Dong, W., Wang, J., Xin, M.: Impact-angle-constrained cooperative guidance for salvo attack. J. Guidance, Control, Dyn. 45, 1–20 (2021)
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Wang, J., Tao, X., Dong, W., Wang, H., Wang, C. (2023). A Modified Finite-Time Guidance Law with Impact Angle Constraint. In: Yan, L., Duan, H., Deng, Y. (eds) Advances in Guidance, Navigation and Control. ICGNC 2022. Lecture Notes in Electrical Engineering, vol 845. Springer, Singapore. https://doi.org/10.1007/978-981-19-6613-2_682
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DOI: https://doi.org/10.1007/978-981-19-6613-2_682
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