Performance Analysis of Guidance Laws Based on Timescale Gap

An analytical treatment of performance analysis of guidance laws is possible only in simplistic scenarios. As the complexity of the guidance system increases, a search for analytical solutions becomes quite impractical. In this paper, a new performance measure, based upon the notion of a timescale gap that can be computed through numerical simulations, is developed for performance analysis of guidance laws. Finite time Lyapunov exponents are used to define the timescale gap. It is shown that the timescale gap can be used for quantification of the rate of convergence of trajectories to the collision course. Comparison between several guidance laws, based on the timescale gap, is presented. Realistic simulations to study the effect of aerodynamics and atmospheric variations on the timescale gap of these guidance laws are also presented.

[1]  S. Bharadwaj,et al.  Timescale Analysis for Nonlinear Dynamical Systems , 2003 .

[2]  Moshe Idan,et al.  Integrated sliding mode autopilot-guidance for dual-control missiles , 2005 .

[3]  Antonios Tsourdos,et al.  Earliest Intercept Line Guidance Using a Game Theory Approach , 2006 .

[4]  Mauricio Guelman,et al.  A qualitative study of proportional navigation , 1971, IEEE Transactions on Aerospace and Electronic Systems.

[5]  Didik Soetanto,et al.  Geometric analysis of flight control command for tactical missile guidance , 2001, IEEE Trans. Control. Syst. Technol..

[6]  M. Guelman.  The closed-form solution of true proportional navigation , 1976, IEEE Transactions on Aerospace and Electronic Systems.

[7]  Debasish Ghose,et al.  Capturability of a Geometric Guidance Law in Relative Velocity Space , 2009, IEEE Transactions on Control Systems Technology.

[8]  Paul Zarchan,et al.  Tactical and strategic missile guidance , 1990 .

[9]  Jason L. Speyer,et al.  Game-Theoretic Homing Missile Guidance with Autopilot Lag , 2007 .

[10]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[11]  Unified approach to missile guidance laws: a 3D extension , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[12]  S. Bharadwaj,et al.  Identifying Time-Scale Structure for Simplified Guidance Law Development , 1997 .

[13]  V. H. L. Cheng,et al.  Advanced midcourse guidance for air-to-air missiles , 1986 .

[14]  Antonios Tsourdos,et al.  Direct Intercept Guidance using Differential Geometry Concepts , 2005 .

[15]  A. M. Lyapunov.  The general problem of the stability of motion , 1992 .

[16]  Anna Trevisan,et al.  Periodic Orbits, Lyapunov Vectors, and Singular Vectors in the Lorenz System , 1998 .

[17]  B. Sridhar,et al.  Missile guidance laws based on singular-perturbation methodology , 1979 .

[18]  M.S. Bhat,et al.  Capturability Analysis of a Geometric Guidance Law in Relative Velocity Space , 2007, 2007 American Control Conference.

[19]  G. Anderson.  Comparison of Optimal Control and Differential Game Intercept Missile Guidance Laws , 1981 .

[20]  Ufuk Topcu,et al.  Lyapunov Exponents and Vectors for Determining the Geometric Structure of Nonlinear Dynamical Systems , 2005 .

[21]  Neil Fenichel.  Geometric singular perturbation theory for ordinary differential equations , 1979 .

[22]  Li Dong,et al.  Near optimal midcourse guidance law for flight vehicle , 1998 .

[23]  Wiesel.  Modal feedback control on chaotic trajectories. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Ufuk Topcu,et al.  Two-Timescale Nonlinear Dynamics and Slow Manifold Determination , 2005 .