Applications of adjoint theory to problems in aerospace and defence science

Abstract

The adjoint simulation method is an efficient, computerised method for the performance analysis of linear time varying systems excited by deterministic and/or stochastic inputs. It is based on the impulse response function (or weighting function) of the so-called adjoint system---an associated linear system derived from the original system by clever utilisation of the mathematical principle of duality. We demonstrate the power of adjoint simulation in the context of guided missile homing loop studies and present a Matlab tool for its speedy implementation and execution. As an example, the tool analyses the miss distance performance of a generic guided missile against an evading target in two dimensional space. References Statistical performance analysis of nonlinear stochastic systems by the Monte Carlo method volume 23-1 of Mathematics and Computers in Simulation J. , pages 21--23, 1981. doi:10.1016/0378-4754(81)90004-5 Zarchan, P. Tactical and Strategic Missile Guidance , 5th Edition, AIAA Progress in Astronautics and Aeronautics, 2007. Weiss, M. Adjoint Method for Missile Performance Analysis on State-Space Models, volume 28-2 of Guidance, Control and Dynamics J. , pages 236--248, AIAA ,2005. Laning, J. H. and Battin, R. H. Random Processes in Automatic Control , McGraw-Hill Book Company, New York, NY, 1956. D. Bucco and M. Weiss. Development of a Matlab/Simulink Tool to Facilitate System Analysis and Simulation via the Adjoint and Covariance Methods, AIAA MST Conference , Aug 2007. http://www.aiaa.org/agenda.cfm?lumeetingid=1501&formatview=1&dateget=22-Aug-07 DeRusso, P. M., Roy, R. J., Close, C. M., and Desrochers, A. A. State Variables for Engineers, 2nd Edition , John Wiley and Sons, Inc., New York, NY, 1998. Moretti, G. Best Practices for Adopting Model-Based Design in Electronic System Development, White-paper, Gabe on EDA , 2007. http//www.mathworks.com/products/simulink/technicalliterature.html