Analytical solutions to a guidance problem

Cochran, John E.; No, T. S.; Thaxton, D. G.

doi:10.2514/6.1988-4222

Cited by 4 publications

(6 citation statements)

References 6 publications

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“…as shown in As a guidance law, we define the generalized commanded relative acceleration A c = k±R (4) where ki and k% are navigation constants. In Cochran's analysis [2], k% = 0 while the navigation constant ki takes on the values 3 and 4 for the integrable cases. Here, however, both parameters ki and fe are real and arbitrary.…”

Section: Guidance Lawmentioning

confidence: 99%

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Optimal Interception of a Maneuvering Long-range Missile

2001

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In a Newtonian central force field, the minimumfuel interception of a satellite, or a ballistic missile, in elliptic trajectory can be obtained via Lawden's theory of primer vector. To secure interception when the target performs evasive maneuvers, a new control law, with explicit solutions, is implemented. It is shown that by a rotation of coordinate system, the problem of three-dimensional interception is reduced to a planar problem. The general case of planar interception of a long range ballistic missile is then studied. Examples of interception at a specified time, head-on interception and minimum-fuel interception are presented. In each case, the requirement for the thrust acceleration is expressed explicitly as a function of time.

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Section: Guidance Lawmentioning

confidence: 99%

“…To secure interception, it is proposed in this paper to use an improved guidance law, first discussed by Cochran in Ref. [2], and later generalized and solved in closed form by the present authors in Ref.fll].…”

Section: Introductionmentioning

confidence: 99%

Optimal Interception of a Maneuvering Long-range Missile

2001

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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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“…In the area of homing guidance,

{scriptℋ}_{\infty}

(from keywords) the proportional navigation (PN) has been used widely , such as true PN (TPN) , realistic TPN , and ideal PN . However, its poor performance in intercepting maneuvering targets has been exhibited.…”

Section: Introductionmentioning

confidence: 99%

A novel three‐dimensional guidance law implementation using only line‐of‐sight azimuths

Liao

Xie

2014

Intl J Robust & Nonlinear

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Summary A novel three‐dimensional guidance law using only line‐of‐sight azimuths based on input‐to‐state stability and robust nonlinear scriptℋ∞ observer is proposed for interception of maneuvering targets. The proposed guidance law does not need any prior information of unknown bounded target maneuvers and uncertainties. Since in practice the line‐of‐sight rate is difficult for a pursuer to measure accurately, a nonlinear robust scriptℋ∞ observer is introduced to estimate it. A three‐dimensional guidance law with bearing only measurement is obtained for interception of maneuvering targets. The presented algorithm is tested using computer simulations against a maneuvering target. Copyright © 2014 John Wiley & Sons, Ltd.

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Analytical solutions to a guidance problem

Cited by 4 publications

References 6 publications

Optimal Interception of a Maneuvering Long-range Missile

Optimal Interception of a Maneuvering Long-range Missile

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

A novel three‐dimensional guidance law implementation using only line‐of‐sight azimuths

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