Closed-Form Solution of RTPN Guidance Law using Adomian Decomposition

Garai, Tanushree; Mukhopadhyay, S.; Ghose, Debasish

doi:10.1109/iciinfs.2008.4798491

Cited by 1 publication

(2 citation statements)

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“…Substituting the Adomian polynomials A n in equation (26), the solution of the differential equation (15) may be obtained from equation (17). Likewise, for coupled and multi-variable non-linear differential equations, multiple Adomian polynomials may be evaluated for the solution of the individual variables [19].…”

Section: Adomian Decomposition Methodsmentioning

confidence: 99%

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Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Garai

Mukhopadhyay

Ghose

2009

Proceedings of the Institution of Mechanical Engineers, Part G:

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Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

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Section: Adomian Decomposition Methodsmentioning

confidence: 99%

“…The convergence of the Adomian polynomials is not being dealt here; it has been reported in the literature [21]. The authors have presented the approximated closed-form solutions of the dynamics under TPN guidance law in reference [26]. The non-linear equations of motion are completely different under the TPN and RTPN guidance laws.…”

Section: Introductionmentioning

confidence: 99%