Nonsingular Continuous Finite-Time Convergent Guidance Law with Impact Angle Constraints

Luyao Zang,Defu Lin,Yi Ji

doi:10.1155/2019/6024240

Luyao Zang, Defu Lin + Show 1 more

Open Access

https://doi.org/10.1155/2019/6024240

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Abstract

This paper documents a novel nonsingular continuous guidance which can drive the line-of-sight (LOS) angular rate to converge to zero in finite time in the presence of impact angle constraints. More specifically, based on the second-order sliding mode control (SMC) theory, a second-order observer (2-OB) is presented to estimate the unknown target maneuvers, while a super twisting algorithm- (STA-) based guidance law is presented to restrict the LOS angle and angular rate. Compared with other terminal sliding mode guidance laws, the proposed guidance law absorbs the merits of the conventional linear sliding mode (LSM) and terminal sliding mode (TSM) and uses switching technique to avoid singularity. In order to verify the stability of the proposed guidance law, a finite-time bounded (FTB) function is invited to prove the boundedness of the proposed observer-controller system and a Lyapunov approach is presented to prove the finite-time convergence (FTC) of the proposed sliding system. Rigorous theoretical analysis and numerical simulations demonstrate the mentioned properties.

Highlights

Facing the modern battleground, zero miss distance is not the only operational effect index of accurately guided weapon guidance [1]
Ease of implementation, and successful history of application, the well-known proportional navigation guidance (PNG) law [2,3,4,5] and its variants have been widely used in engineering practice in the last few decades
Because of the terrible disturbance resulting from target maneuvers, environment noise, and measurement error, PNG cannot provide the qualified performance in some extreme cases

Summary

Introduction

Zero miss distance is not the only operational effect index of accurately guided weapon guidance [1]. By using the SMC technique, Zhou et al [15] proposed a novel FTC guidance law to guide the LOS angular rate to converge to zero or within a small neighborhood of zero in finite time. Moon et al [16] provided an adaptive sliding mode guidance approach based on the reaching law, in which the key point is that the convergent rate should increase in proportion to the decrease in the distance between the missile and the target. Some perturbations such as measurement error and environmental noise may result in performance degradation Considering these problems, this paper discusses a new nonsingular continuous impact-angle-constraint SMC guidance law that forces the system state to converge to a sliding manifold in finite time as well as drives the sliding manifold to converge to zero in finite time. The rest of this paper is organized as follows: the planar and spherical mathematical model of the engagement phase is provided, and the guidance strategy is discussed in Section 2; the 2-OB and the finite-time convergent guidance approach is proposed in Section 3; some simulation results are given and discussed in Section 4; a brief conclusion of this paper is given in Section 5; some proofs of the proposed propositions are given in Appendices A, B, and III

Problem Formulation

Guidance Law Design and Stability Analysis

Case Study

Conclusion