• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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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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• v.5 no.4
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.3
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• pp.203-211
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• 2016

In contrast with STT missiles, the guidance law design for BTT missiles should be based on 3-dimensional pursuit kinematics, since the pitch and roll channels of BTT missiles are coupled dynamically. More generally than the prior works, the dynamics of pitch and roll channels, as well as 3-dimensional pursuit kinematics are considered in the design of our terminal-phase optimal guidance law for BTT missiles proposed in this paper. Thereby, the proposed optimal guidance law guarantees high capturability with small miss distance without significant performance degradation due to time-lag effect even in case of relatively slow autopilot dynamics. Moreover, the resulting optimal guidance law is expressed explicitly in feedback-form with the coefficients given as the functions of time-to-go. The effectiveness and practicality of our work is demonstrated through various simulation results.