Fast Mesh Refinement in Pseudospectral Optimal Control

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy: simply increase the order N of the Lagrange interpolating polynomial, and the mathematics of convergence automates the...

[1]  Qi Gong,et al.  High-Accuracy Trajectory Optimization for a Trans-Earth Lunar Mission , 2011 .

[2]  I. M. Ross,et al.  A Nonsmooth Calculus for Solving Some Graph-Theoretic Control Problems , 2016 .

[3]  I. Michael Ross,et al.  A Spectral Patching Method for Direct Trajectory Optimization , 2000 .

[4]  Sagar Bhatt,et al.  Optimal Propellant Maneuver Flight Demonstrations on ISS , 2013 .

[5]  Qi Gong,et al.  Low-Thrust, High-Accuracy Trajectory Optimization , 2007, Journal of Guidance, Control, and Dynamics.

[6]  Elsayed M. E. Elbarbary,et al.  Integration Preconditioning Matrix for Ultraspherical Pseudospectral Operators , 2006, SIAM J. Sci. Comput..

[7]  I. Michael Ross,et al.  Pseudospectral Knotting Methods for Solving Optimal Control Problems , 2004 .

[8]  I. Michael Ross,et al.  Discrete verification of necessary conditions for switched nonlinear optimal control systems , 2001, Proceedings of the 2004 American Control Conference.

[9]  N. Bedrossian,et al.  Overclock My Satellite , 2012, IEEE Spectrum.

[10]  I. Michael Ross,et al.  Costate computation by a Chebyshev pseudospectral method , 2010 .

[11]  I. Michael Ross,et al.  Advances in Pseudospectral Methods for Optimal Control , 2008 .

[12]  Sagar Bhatt,et al.  Overclock my satellite, sophisticated algorithms boost performance on the cheap , 2012 .

[13]  Qi Gong,et al.  The Bellman Pseudospectral Method , 2008 .

[14]  W. Finden,et al.  An error term and uniqueness for Hermite-Birkhoff interpolation involving only function values and/or first derivative values , 2008 .

[15]  I. Michael Ross,et al.  Pseudospectral Methods for Infinite-Horizon Nonlinear Optimal Control Problems , 2005 .

[16]  Sagar Bhatt,et al.  ZERO PROPELLANT MANEUVER TM FLIGHT RESULTS FOR 180 ° ISS ROTATION , 2007 .

[17]  Wei Kang,et al.  Pseudospectral Optimal Control and Its Convergence Theorems , 2008 .

[18]  Qi Gong,et al.  PSEUDOSPECTRAL OPTIMAL CONTROL ON ARBITRARY GRIDS , 2009 .

[19]  I. Michael Ross,et al.  Spectral Algorithm for Pseudospectral Methods in Optimal Control , 2008, Journal of Guidance, Control, and Dynamics.

[20]  I. Michael Ross,et al.  On the convergence of nonlinear optimal control using pseudospectral methods for feedback linearizable systems , 2007 .

[21]  B. Conway.  The problem of spacecraft trajectory optimization , 2010 .

[22]  Qi Gong,et al.  A pseudospectral method for the optimal control of constrained feedback linearizable systems , 2006, IEEE Transactions on Automatic Control.

[23]  Sheehan Olver,et al.  A Fast and Well-Conditioned Spectral Method , 2012, SIAM Rev..

[24]  Qi Gong,et al.  Pseudospectral Optimal Control for Military and Industrial Applications , 2007, 2007 46th IEEE Conference on Decision and Control.

[25]  Jan S. Hesthaven,et al.  Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators , 1998 .

[26]  W. Hager.  Runge-Kutta Discretizations of Optimal Control Problems , 2000 .

[27]  James M. Longuski,et al.  Optimal Control with Aerospace Applications , 2013 .

[28]  Wei Kang,et al.  Zero-propellant maneuver guidance , 2009, IEEE Control Systems.

[29]  F. Clarke.  Functional Analysis, Calculus of Variations and Optimal Control , 2013 .

[30]  Kui Du,et al.  On Well-Conditioned Spectral Collocation and Spectral Methods by the Integral Reformulation , 2015, SIAM J. Sci. Comput..

[31]  Li-Lian Wang,et al.  A Well-Conditioned Collocation Method Using a Pseudospectral Integration Matrix , 2013, SIAM J. Sci. Comput..

[32]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[33]  Qi Gong,et al.  Spectral and Pseudospectral Optimal Control Over Arbitrary Grids , 2016, J. Optim. Theory Appl..

[34]  A. L. Herman,et al.  Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules , 1996 .

[35]  William W. Hager,et al.  Pseudospectral methods for solving infinite-horizon optimal control problems , 2011, Autom..

[36]  Dan Kosloff,et al.  A modified Chebyshev pseudospectral method with an O(N –1 ) time step restriction , 1993 .

[37]  Jie Shen,et al.  Spectral Methods: Algorithms, Analysis and Applications , 2011 .

[38]  Bruce A. Conway,et al.  A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems , 2011, Journal of Optimization Theory and Applications.

[39]  I. Michael Ross,et al.  Scaling and Balancing for High-Performance Computation of Optimal Controls , 2018, Journal of Guidance, Control, and Dynamics.

[40]  William E. Wiesel,et al.  Large Time Scale Optimal Control of an Electrodynamic Tether Satellite , 2008 .

[41]  I. Michael Ross,et al.  Direct trajectory optimization by a Chebyshev pseudospectral method , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[42]  I. Michael Ross,et al.  Flight Implementation of Shortest-Time Maneuvers for Imaging Satellites , 2014 .

[43]  W. Kang.  Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems , 2010 .

[44]  I. Michael Ross,et al.  A review of pseudospectral optimal control: From theory to flight , 2012, Annu. Rev. Control..

[45]  I. J. Schoenberg.  On Hermite-Birkhoff interpolation☆ , 1966 .