Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method
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Elnagar, G., Kazemi, M., Razzaghi, M.: The pseudospectral Legendre method for discretizing optimal control problems. IEEE Trans. Autom. Control 40(10), 1793–1796 (1995)
Elnagar, G., Kazemi, M.: Pseudospectral Chebyshev optimal control of constrained nonlinear dynamical systems. Comput. Optim. Appl. 11(2), 195–217 (1998)
Fahroo, F., Ross, I.M.: A spectral patching method for direct trajectory optimization. J. Astronaut. Sci. 48(2–3), 269–286 (2000)
Fahroo, F., Ross, I.M.: Costate estimation by a Legendre pseudospectral method. J. Guid. Control Dyn. 24(2), 270–277 (2001)
Ross, I.M., Fahroo, F.: Legendre Pseudospectral Approximations of Optimal Control Problems. Lecture Notes in Control and Information Sciences. Springer, Berlin (2003)
Rao, A.V.: Extension of a pseudospectral Legendre method for solving non-sequential multiple-phase optimal control problems. In: AIAA Guidance, Navigation, and Control Conference, Austin, Texas, August 11–14, 2003. AIAA Paper 2003-5634
Williams, P.: Jacobi pseudospectral method for solving optimal control problems. J. Guid. Control Dyn. 27(2), 293–297 (2004)
Williams, P.: Application of pseudospectral methods for receding horizon control. J. Guid. Control Dyn. 27(2), 310–314 (2004)
Williams, P.: Hermite-Legendre-Gauss-Lobatto direct transcription methods in trajectory optimization. In: American Astronautical Society, Spaceflight Mechanics Meeting, August 2005
Ross, I.M., Fahroo, F.: Pseudospectral knotting methods for solving optimal control problems. J. Guid. Control Dyn. 27(3), 397–405 (2004)
Fahroo, F., Ross, I.M.: On discrete-time optimality conditions for pseudospectral methods. In: AIAA Guidance, Navigation, and Control Conference, Keystone, Colorado, August 2006. AIAA Paper 2006-6304
Fahroo, F., Ross, I.M.: Pseudospectral methods for infinite-horizon nonlinear optimal control problems. J. Guid. Control Dyn. 31(4), 927–936 (2008)
Benson, D.A.: A Gauss pseudospectral transcription for optimal control. Ph.D. thesis, MIT (2004)
Benson, D.A., Huntington, G.T., Thorvaldsen, T.P., Rao, A.V.: Direct trajectory optimization and costate estimation via an orthogonal collocation method. J. Guid. Control Dyn. 29(6), 1435–1440 (2006)
Huntington, G.T.: Advancement and analysis of a Gauss pseudospectral transcription for optimal control. Ph.D. thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology (2007)
Kameswaran, S., Biegler, L.T.: Convergence rates for direct transcription of optimal control problems using collocation at Radau points. Comput. Optim. Appl. 41(1), 81–126 (2008)
Reddien, G.W.: Collocation at Gauss points as a discretization in optimal control. SIAM J. Control Optim. 17(2) (1979)
Cuthrell, J.E., Biegler, L.T.: On the optimization of differential-algebraic processes. AIChe J. 33(8), 1257–1270 (1987)
Cuthrell, J.E., Biegler, L.T.: Simultaneous optimization and solution methods for batch reactor control profiles. Comput. Chem. Eng. 13(1/2), 49–62 (1989)
Ross, I.M., Fahroo, F.: Advances in pseudospectral methods for optimal control. In: AIAA Guidance, Navigation, and Control Conference, Honolulu, Hawaii, August 2008. AIAA Paper 2008-7309
Ross, I.M., Fahroo, F.: Convergence of the costates do not imply convergence of the controls. J. Guid. Control Dyn. 31(4), 1492–1497 (2008)
Huntington, G.T., Benson, D.A., Rao, A.V.: Optimal configuration of tetrahedral spacecraft formations. J. Astronaut. Sci. 55(2), 141–169 (2007)
Huntington, G.T., Rao, A.V.: Optimal reconfiguration of spacecraft formations using the Gauss pseudospectral method. J. Guid. Control Dyn. 31(3), 689–698 (2008)
Hager, W.W.: Numerical analysis in optimal control. In: Hoffmann, K.-H., Lasiecka, I., Leugering, G., Sprekels, J., Troeltzsch, F. (eds.) International Series of Numerical Mathematics, vol. 139, pp. 83–93. Birkhäuser, Basel (2001)
Hager, W.W., Dontchev, A., Poore, A., Yang, B.: Optimality, stability, and convergence in nonlinear control. Appl. Math. Optim. 31, 297–326 (1995)
Hager, W.W.: Runge-Kutta methods in optimal control and the transformed adjoint system. Numer. Math. 87, 247–282 (2000)
Patterson, M.A.: OptimalPrime: A MATLAB software for solving non-sequential multiple-phase optimal control problems using pseudospectral methods. Dept. of Mechanical and Aerospace Engineering, University of Florida (August 2008)
Gill, P.E., Murray, W., Saunders, M.A.: User’s Guide for SNOPT Version 7: Software for Large Scale Nonlinear Programming (February 2006)