Solutions of generalized proportional navigation with maneuvering and nonmaneuvering targets

Yuan, Pin-Jar; Hsu, Shau-Wei

doi:10.1109/7.366329

Cited by 40 publications

(7 citation statements)

References 14 publications

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“…Based on the preceding finite time stability theory, we can prove sufficient conditions for the finite time convergence of the guidance system (5).…”

Section: Finite Time Convergent Guidance Lawsmentioning

confidence: 99%

“…Theorem 1: Consider the guidance system (5). If there exists a control u such that the system state satisfies…”

Section: Finite Time Convergent Guidance Lawsmentioning

confidence: 99%

“…we obtain the results presented in the following theorem. Theorem 2: Consider the guidance system (5). The guidance law (19) nullifies the LOS angular rate in infinite time.…”

Section: Finite Time Convergent Guidance Lawsmentioning

confidence: 99%

“…Then, by appropriate modification of the guidance law (19), we obtain the results presented in following theorem. Theorem 3: Consider the guidance system (5). The following guidance law…”

Section: Finite Time Convergent Guidance Lawsmentioning

confidence: 99%

“…Simulation results show that the guidance laws are highly effective. P ROPORTIONAL navigation (PN) and its variants have been widely used as homing guidance laws because they are highly efficient and easy for implementation [1][2][3][4][5][6][7][8][9][10]. The PN guidance law has the required accuracy to intercept a nonmaneuvering target or a weakly maneuvering target.…”

mentioning

confidence: 99%

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Guidance Laws with Finite Time Convergence

Zhou

Sun

Teo

2009

Journal of Guidance, Control, and Dynamics

242

235

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Conventional guidance laws are designed based on Lyapunov theorems on asymptotic stability or exponential stability. They will guide the line-of-sight angular rate to converge to zero or its small neighborhood, however, only as time approaches infinity. In this paper, new guidance laws with finite convergent time are proposed. The guidance laws are obtained based on new sufficient conditions derived in this paper for the finite time convergence of the line-of-sight angular rate. It is proved that, with the guidance laws, the line-of-sight angular rate will converge to zero or a small neighborhood of zero before the final time of the guidance process. Furthermore, such guidance laws will ensure finite time convergence and finite time stability in both the planar and three-dimensional environments. Simulation results show that the guidance laws are highly effective. Nomenclature a Mr , a M , a M = missile acceleration along the line-of-sight axes a r , a , a = relative acceleration along line-of-sight axes a Tr , a T , a T = target acceleration along line-of-sight axes N = navigation ratio q = line-of-sight angle _ q = derivative of q with respect to time q = second-order derivative of q with respect to time r = relative range _ r = derivative of r with respect to time r = second-order derivative of r with respect to time t = time u = missile acceleration normal to line of sight u r = missile acceleration along line of sight V M = missile velocity V T = target velocity w = target acceleration normal to line of sight w r = target acceleration along line of sight x M , y M , z M = position coordinates of missile in inertial frame x T , y T , z T = position coordinates of target in inertial frame = azimuth = elevation ' M = flight-path angle of missile ' T = flight-path angle of target M = heading angle of missile T = heading angle of target

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“…Based on the preceding finite time stability theory, we can prove sufficient conditions for the finite time convergence of the guidance system (5).…”

Section: Finite Time Convergent Guidance Lawsmentioning

confidence: 99%

“…Theorem 1: Consider the guidance system (5). If there exists a control u such that the system state satisfies…”

Section: Finite Time Convergent Guidance Lawsmentioning

confidence: 99%

“…we obtain the results presented in the following theorem. Theorem 2: Consider the guidance system (5). The guidance law (19) nullifies the LOS angular rate in infinite time.…”

Section: Finite Time Convergent Guidance Lawsmentioning

confidence: 99%

“…Then, by appropriate modification of the guidance law (19), we obtain the results presented in following theorem. Theorem 3: Consider the guidance system (5). The following guidance law…”

Section: Finite Time Convergent Guidance Lawsmentioning

confidence: 99%

mentioning

confidence: 99%

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Guidance Laws with Finite Time Convergence

Zhou

Sun

Teo

2009

Journal of Guidance, Control, and Dynamics

242

235

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Missile Guidance

Rodriguez¹

2007

Wiley Encyclopedia of Electrical and Electronics Engineering

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The future of missile guidance depends to a large extent on the ongoing reinterpretation of the ABM treaty between the United States and the former Soviet Union. After 9–11, work was initiated on the development of mini‐nukes for underground bunkers. The need for guided missiles that permit precision strikes with minimal collateral damage was also reaffirmed. A Brief History: From 1944 to the Present Missile Guidance, Navigation, and Control Subsystems Classification of Missiles, Targets, Guidance Systems, Navigation Methods, and Target‐Sensing Methods Guidance Algorithms Future Developments Acknowledements

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Missile Guidance

Rodriguez

2015

Wiley Encyclopedia of Electrical and Electronics Engineering

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Solutions of generalized proportional navigation with maneuvering and nonmaneuvering targets

Cited by 40 publications

References 14 publications

Guidance Laws with Finite Time Convergence

Guidance Laws with Finite Time Convergence

Missile Guidance

Missile Guidance

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