• International Journal of Aeronautical and Space Sciences
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• 제7권2호
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• pp.1-13
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• 2006

The Lyapunov stability theory has been known inadequate to prove capturability of guidance laws because the equations of motion resulted from the guidance laws do not have the equilibrium point. By introducing a proper transformation of the range state, the original equations of motion for a stationary target can be converted into nonlinear equations with a specified equilibrium subspace. Physically, the equilibrium subspace denotes the direction of missile velocity to the target. By using a single Lyapunov function candidate, capturability of several PN laws for a stationary target is then proved for examples. In this approach, there is no assumption of the constant speed missile. The proposed method is expected to provide a unified and simplified scheme to prove the capturability of various kinds of guidance laws.

• International Journal of Control, Automation, and Systems
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• 제5권4호
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• pp.397-409
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• 2007

In this paper, we propose a nonlinear guidance law for missiles against maneuvering targets. First, we derive the equations of motion described in the line-of-sight reference frame and then we define the equilibrium subspace of the nonlinear system to guarantee target interception within a finite time. Using Sontag's formula, we derive a nonlinear guidance law that always delivers the state to the equilibrium subspace. If the speed of the missile is greater than that of the target, the proposed law has global capturability in that, under any initial launch conditions, the missile can intercept the maneuvering target. The proposed law also minimizes the integral cost of the control energy and the weighted square of the state. The performance of the proposed law is compared with the augmented proportional navigation guidance law by means of numerical simulations of various initial conditions and target maneuvers.

• 한국항공우주학회지
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• 제44권3호
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• pp.203-211
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• 2016

BTT 미사일은 STT 미사일과 달리 피치와 롤 채널이 동역학적으로 결합되어 있기 때문에 유도 법칙 개발 시 3차원 추적 기하학을 고려하여야 한다. 기존 연구결과들과는 달리 본 논문에서는 3차원 추적 기하학뿐만 아니라 자동조종장치의 피치와 롤 채널 동역학을 모두 고려한 BTT 미사일의 최적 종말 유도 법칙을 제안한다. 그 결과, 제안하는 유도 법칙은 상대적으로 느린 자동조종장치 동역학에서도 시간 지연 효과로 인한 성능 하락 없이 작은 요격 오차의 높은 요격 성능을 보장한다. 또한, 제안하는 최적 유도 법칙은 잔여 비행시간의 함수를 계수로 하는 궤환 형태로 구해진다. 끝으로 다양한 요격 상황에서의 모의실험을 통해 그 성능을 입증한다.