A robust fuzzy trajectory estimation design of high speed reentry vehicles

An H_∞ fuzzy trajectory estimation is proposed for robust tracking guidance and early warning in antitactical ballistic missile systems with model uncertainties and external disturbances. In order to avoid solving the nonlinear Hamilton-Jacobi-Isaac (H-J-I) partial differential equation for H trajectory estimation of the nonlinear reentry vehicle (RV) dynamic equation, the Takagi and Sugeno fuzzy linear model is employed to interpolate piecewise to approximate the RV nonlinear dynamic equation. Then, from the fuzzy linear model, a fuzzy H_∞ state estimator is developed for robust trajectory estimation of RV with optimal attenuation of the worst-case effect of system uncertainties such as approximation error, external disturbance, maneuver and unpredictable external forces in flight and other sources. The proposed method parameterizes the H_∞ trajectory estimation problem in terms of an eigenvalue problem (EVP), so that the worst-case effect of system uncertainties on the trajectory estimation error is minimized in the robust trajectory estimation design subject to certain linear matrix inequality (LMI) constraints. Convex optimization techniques are employed to solve the EVP of the H_∞ fuzzy trajectory estimation in antitactical ballistic missile systems. Simulation results indicate that the proposed method possesses a satisfactory performance.