Bank-to-Turn Guidance Law Using Lyapunov Function and Nonzero Effort Miss

No, Tae Soo; Cochran, John E.; Kim, Eul Gon

doi:10.2514/2.4736

Cited by 23 publications

(19 citation statements)

References 9 publications

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“…In the following sections, we denote the nonlinear guidance laws (27), (34), and (43) as NLG1, NLG2, and NLG3, respectively. The rates of the states in the guidance system converging to the sliding manifold are determined by c 1 and c 2 which could be chosen as relatively large constants from within ½5 30.…”

Section: Three-dimensional Nonlinear Guidance Law Without Target Accementioning

confidence: 99%

“…A nearoptimal solution is obtained in Aggrawal and Moore 26 using multiple timescale techniques. By defining a Lyapunov function in terms of nonzero effort miss, a guidance law that directly computes the pitch acceleration and roll angle commands is presented in No et al 27 The sliding-mode control has also been applied to the integrated design of guidance law and autopilot. With a single sliding surface defined using the zero-effort miss distance, a sliding-mode controller is derived for an integrated missile autopilot and guidance loop in Shima et al 28 An adaptive nonlinear guidance law is proposed in Chaw and Chol 29 to compensate for the uncertainties in both target acceleration and control loop dynamics.…”

Section: Introductionmentioning

confidence: 99%

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A generalized design method for three-dimensional guidance laws

Zhou

Teo

2016

Proceedings of the Institution of Mechanical Engineers, Part G:

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The true proportional navigation guidance law, the augmented proportional navigation guidance law, or the adaptive sliding-mode guidance law, is designed based on the planar target-to-missile relative motion dynamics. By a proper construction of a nonlinear Lyapunov function for the line-of-sight angular rates in the three-dimensional guidance dynamics, it is shown that the three guidance laws mentioned above are able to ensure the asymptotic convergence of the angular rates as they are directly applied to the three-dimensional guidance environment. Furthermore, considering the missile autopilot dynamics as a first-order lag, we design three-dimensional nonlinear guidance laws by using the backstepping technique for three cases: (1) the target does not maneuver; (2) the information of target acceleration can be acquired; and (3) the target acceleration is not available but its bound is known a priori. In the first step of the backstepping design of the control law, there is no need to cancel the nonlinear coupling terms in the three-dimensional guidance dynamics in such way that the final expressions of the proposed guidance laws are significantly simplified. Thus, the proposed nonlinear Lyapunov function for the line-of-sight angular rates is a generalized function for designing three-dimensional guidance laws. Simulation results of a missile interception mission show that the proposed guidance laws are highly effective.

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Section: Three-dimensional Nonlinear Guidance Law Without Target Accementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A generalized design method for three-dimensional guidance laws

Zhou

Teo

2016

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…Let us define the impact time error as s =t f − t d (4) wheret f and t d denote the estimated impact time and the desired impact time, respectively. The desired impact time of each missile is set by considering the given mission, salvo attack or simultaneous attack.…”

Section: B Two-dimensional Lyapunov-based Itcg Lawmentioning

confidence: 99%

“…Guidance laws based on Lyapunov theory, one of the famous nonlinear system theories, were proposed [1][2][3]. A bank-to-turn guidance law was proposed by introducing nonzero effort miss using Lyapunov stability theory [4]. A sliding mode control scheme and a back-stepping controller were also applied to develop nonlinear guidance laws [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov-based impact time control guidance laws against stationary targets

Kim

Jung

Han

et al. 2015

IEEE Trans. Aerosp. Electron. Syst.

134

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Nonlinear guidance laws that consider impact time constraints are proposed. Two-dimensional and three-dimensional impact time control guidance laws are derived using Lyapunov stability theory. Under the consideration of the nonlinear kinematics, it is shown that the missile states converge to the desired equilibrium point by the Lyapunov stability theory. The singularity issue of the proposed guidance laws is also analyzed. Numerical simulations are performed to verify the performance of the proposed guidance laws.

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“…Then, Lyapunov's stability theorem is employed to obtain the guidance commands. This approach has been successfully used for one-and two-dimensional problems (No, Chong, & Rho, 2001a;No, Cochran, & Kim, 2001b). Results obtained from the fully six-degree-of-freedom (6-DOF) nonlinear simulation of representative flight scenarios are presented to demonstrate the applicability of the proposed method.…”

Section: Introductionmentioning

confidence: 94%