Exact closed-form solution of generalized proportional navigation

Yuan, Pin-Jar; Hsu, Shau-Wei

doi:10.2514/3.21109

Cited by 32 publications

(6 citation statements)

References 11 publications

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“…Over the past decades PN has been extensively analyzed [1][2][3][4][5][6][7][8][9][10]. Guelman derived the closed-form solution of the true proportional navigation law [11], which was generalized for an arbitrary angle between the missile acceleration and the LOS [12][13][14]. The solution of the pure proportional navigation law has also been derived by Becker [15].…”

Section: Introductionmentioning

confidence: 99%

Optimality of Proportional Navigation Based on Nonlinear Formulation

Jeon

Lee

2010

IEEE Trans. Aerosp. Electron. Syst.

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Section: Introductionmentioning

confidence: 99%

Optimality of Proportional Navigation Based on Nonlinear Formulation

Jeon

Lee

2010

IEEE Trans. Aerosp. Electron. Syst.

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“…For two-dimensional (or navigation in the plane) PN guidance laws and homing systems, many research works on the proportional navigation use the two-dimensional dynamic models. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Some possible approaches have been introduced to design the three-dimensional PN. [17][18][19][20][21][22][23] Although PN schemes are quite simple to implement and well known as an optimal approach to intercept nonmaneuvering targets, its poor performance has been exhibited in intercepting maneuvering targets, and may be ineffective for some orientations between the missile and its target.…”

Section: Introductionmentioning

confidence: 99%

“…To account for maneuvering targets, all the PN results originated from two-dimensional space and the PN-variant guidance algorithms can be augmented to the case of maneuvering targets with known exact acceleration, including the true proportional navigation (TPN), 1,3,4 the realistic true proportional navigation (RTPN), [5][6][7] the ideal proportional navigation (IPN), 8,17 the general true proportional navigation (GTPN), 3,9,23 the general ideal proportional navigation (GIPN), 23 the pure proportional navigation (PPN), 2,17,19,24 the augmented proportional (APN), 10,11,[13][14][15] the augmented pure proportional navigation (APPN), 16 and the optimal guidance laws (OGL). [25][26][27][28] Unfortunately, the target information is usually hard to be measured or estimated as the target maneuvers change rapidly, and the complexity and the cost of the guidance system may be increased as more sensors and estimators are required.…”

Section: Introductionmentioning

confidence: 99%

Modified three‐dimensional true proportional navigation and its inverse optimal form

Liao

Zhang

2021

Optim Control Appl Methods

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A novel three-dimensional modified true proportional navigation (MTPN) guidance and its inverse optimal form are proposed for the interception of the nonmaneuvering and maneuvering targets, and the nonlinear dynamic characteristics of pursuit situations and target maneuvers are taken into full account.The proposed approach is feasible without knowing any prior information or estimate of the target maneuvers, which are regarded as the unknown disturbance input. Therefore, the TPN-type guidance is extended to intercept the maneuvering targets with bounded unknown accelerations. Moreover, the explicit physical significance is given for each component of the navigation gain expression of MTPN. The inverse optimal control approach and the input-to-state stability are introduced to the MTPN design. Using the MTPN, the homing missile can conduct the terminal homing guidance phase in any particular direction with respect to their nonmaneuvering or maneuvering targets through choosing an appropriate inertial reference coordinate system in practice. Using the proposed schemes, the line-of-sight (LOS) rate is globally exponentially stable for nonmaneuvering targets, and is input-to-state stability (ISS) for maneuvering targets with bounded unknown accelerations. Performed simulation results have confirmed the effectiveness of the proposed scheme. K E Y W O R D Sguidance and control, input-to-state stability, inverse optimal control, true proportional navigation

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“…The PNG law seeks to null the line-of-sight (LOS) rate by making the missile turn rate directly proportional to the LOS rate, and its characteristics against various targets have been broadly studied for a long time [1][2][3][4][5][6][7][8]. Guelman [9] proved that an ideal missile guided by the conventional PNG law can always intercept the target maneuvering with constant acceleration.…”

Section: Introductionmentioning

confidence: 99%