Time-Domain Finite Element Method for Inverse Problem of Aircraft Maneuvers

A method for solving nonlinear inverse problems is proposed. The inverse problem is formulated as a general optimization problem with equality constraints that are functions of state variables. The optimality conditions are derived by a variational approach. A time-domain e niteelement method is used to discretize the derived governing equations.Theproposedmethodcanutilizethecontrolredundancyinaredundantcasethroughtheproperselection of the performanceindex and constraints. Timedifferentiation oftrajectory constraintsand partial differentiation of output variables with respect to the control inputs are not required, and there is no numerical integration in the developed algorithm. Examples of inverse solutions for an aileron roll maneuver and a bank-to-bank maneuver of aircraft are presented.

[1]  Robert R. Bless.  Time-domain finite elements in optimal control with application to launch-vehicle guidance , 1991 .

[2]  Dewey H. Hodges,et al.  Weak Hamiltonian finite element method for optimal control problems , 1991 .

[3]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[4]  Alexander Leonessa,et al.  Solution of aircraft inverse problems by local optimization , 1995 .

[5]  R. Mittra,et al.  Time-domain (FE/FDTD) technique for solving complex electromagnetic problems , 1998 .

[6]  Dewey H. Hodges,et al.  FINITE ELEMENT SOLUTION OF OPTIMAL CONTROL PROBLEMS WITH STATE-CONTROL INEQUALITY CONSTRAINTS , 1992 .

[7]  Thomas F. Coleman,et al.  Optimization Toolbox User's Guide , 1998 .

[8]  Ping Lu.  An inverse dynamics approach to trajectory optimization for an aerospace plane , 1992 .

[9]  Arthur E. Bryson,et al.  Inverse and Optimal Control for Desired Outputs , 1992 .

[10]  Ronald A. Hess,et al.  Inverse simulation of large-amplitude aircraft maneuvers , 1993 .

[11]  Ping Lu,et al.  Optimal aircraft terrain-following analysis and trajectory generation , 1995 .

[12]  Dewey H. Hodges,et al.  State-constrained booster trajectory solutions via finite elements and shooting , 1993 .

[13]  A. Bryson,et al.  Optimal programming problems with a bounded state space. , 1968 .

[14]  K. Komisarek,et al.  An investigation of new FETD/ABC methods of computation of scattering from three-dimensional material objects , 1999 .

[15]  Anthony J. Calise,et al.  A Weak Hamiltonian Finite Element Method for Optimal Guidance of an Advanced Launch Vehicle , 1989, 1989 American Control Conference.

[16]  Jianming Jin,et al.  Efficient time-domain and frequency-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method , 1998 .

[17]  Dewey H. Hodges,et al.  Finite element method for the solution of state-constrained optimal control problems , 1995 .

[18]  Eric M. Queen,et al.  Variational Trajectory Optimization Tool Set: Technical description and user's manual , 1993 .

[19]  Arthur E. Bryson,et al.  OPTIMAL PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS , 1963 .

[20]  O. Kato,et al.  An interpretation of airplane general motion and contol as inverse problem , 1986 .

[21]  Duane T. McRuer,et al.  Aircraft Dynamics and Automatic Control , 1973 .