Gabriela Abadia-Doyle, William W. Hager, Anil V. Rao, Integral form of Legendre-Gauss-Lobatto collocation for optimal control, Journal of the Franklin Institute, 363 (2026) 108120, https://doi.org/10.1016/j.jfranklin.2025.108120
William W. Hager, Computational Methods in Optimal Control: Theory and Practice, Society for Industrial and Applied Mathematics, Phildelphia, PA, 2025, ISBN:978-1-61197-825-4
William W. Hager, Second-Order Sufficient Optimality Conditions in the
Calculus of Variations, Journal of Optimization Theory and Applications 205 (2025), 17:1-9, https://doi.org/10.1007/s10957-025-02639-y
William W. Hager, Extension of switch point algorithm to boundary-value problems, Computational Optimization and Applications 86 (2023), pp. 1229-1246, https://doi.org/10.1007/s10589-023-00530-y
Mahya Aghaee and William W. Hager, The Switch Point Algorithm, SIAM Journal on Control and Optimization, 59 (2021), pp. 2570-2593, https://doi.org/10.1137/21M1393315
Wanchun Chen, Wenhao Du, William W. Hager, and Liang Yang, Bounds for integration matrices that arise in Gauss and Radau collocation, Computational Optimization and Applications, 74 (2019), pp. 259-273, https://doi.org/10.1007/s10589-019-00099-5
Alexander T. Miller, William W. Hager, and Anil V. Rao, Mesh Refinement Method for Solving Optimal Control Problems with Nonsmooth Solutions Using Jump Function Approximations, Optimal Control Applications and Methods, 42 (2021), pp. 1119-1140 (DOI: 10.1002/oca.2719).
Alexander T. Miller, William W. Hager, and Anil V. Rao, A Preliminary Analysis of Mesh Refinement for Optimal Control Using Discontinuity Detection via Jump Function Approximations, AIAA SciTech Conference (2018), https://doi.org/10.2514/6.2018-0852.
William W. Hager, Hongyan Hou, and Anil V. Rao, Convergence Rate for a Radau Collocation Method Applied to Unconstrained Optimal Control, August 17, 2015, revised September 12, 2015. Cite as arXiv:1508.03783.
William W. Hager, Hongyan Hou, and Anil V. Rao, Convergence Rate for a Gauss Collocation Method Applied to Unconstrained Optimal Control, Journal of Optimization Theory and Application, 169 (2016), pp. 801-824 (doi: 10.1007/s10957-016-0929-7).
William W. Hager, Hongyan Hou, and Anil V. Rao, Lebesgue Constants Arising in a Class of Collocation Methods, IMA Journal of Numerical Analysis, 37 (2017), pp. 1884-1901 (doi: 10.1093/imanum/drw060)
Fengjin Liu, William W. Hager, and Anil V. Rao, Adaptive Mesh Refinement Method for Optimal Control Using Decay Rates of Legendre Polynomial Coefficients, IEEE Transactions on Control Systems Technology, 26 (2018), pp. 1475-1483. (doi:10.1109/TCST.2017.2702122).
Fengjin Liu, William W. Hager, and Anil V. Rao, Adaptive Mesh Refinement Method for Optimal Control Using Nonsmoothness Detection and Mesh Size Reduction, Journal of the Franklin Institute, 352 (2015), pp. 4081-4106 (doi:10.1016/j.jfranklin.2015.05.028).
Hongyan Hou, William W. Hager, and Anil V. Rao, Convergence of a Gauss Pseudospectral Method for Optimal Control, AIAA Conference on Guidance, Navigation, and Control, Minneapolis, Minnesota, 13-15 August 2012.
Christopher L. Darby, William W. Hager, and Anil V. Rao, Direct Trajectory Optimization Using a Variable Low-Order Adaptive Pseudospectral Method, Journal of Spacecraft and Rockets, 48 (2011), pp. 433-445 (doi: 10.2514/1.52136).
Divya Garg, William W. Hager, and Anil V. Rao, Pseudospectral methods for solving infinite-horizon optimal control problems, Automatica, 47 (2011), pp. 829-837. (DOI:10.1016/j.automatica.2011.01.085)
C. L. Darby, W. W. Hager, and A. V. Rao, An hp-Adaptive Pseudospectral Method for Solving Optimal Control Problems, Optimal Control, Applications and Methods, 32 (2011), pp. 476-502 (DOI: 10.1002/oca.957).
Overview of the SIAM Conference on Control and Its Applications, July 11-14, 2001
W. W. Hager, Numerical analysis in optimal control, presented at the Conference on Optimal Control of Complex Structures, June 4–10, 2000, Oberwolfach, Germany, organized by K.-H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels and F. Troeltzsch (in International Series of Numerical Mathematics, Vol. 139, Birkhauser Verlag, Basel/Switzerland, 2001, pp. 83-93)
A. L. Dontchev, W. W. Hager, and K. Malanowski, Error bounds for the Euler approximation of a state and control constrained optimal control problem, Numerical Functional Analysis and Optimization, 21 (2000), pp. 653-682.
W. W. Hager, Runge-Kutta discretizations of optimal control problems in System Theory, Modeling, Analysis, and Control, T. E. Djaferis and I. C. Schick, eds., Kluwer, Norwell, MA, 2000, pp. 233-244
W. W. Hager, Runge-Kutta methods in optimal control and the transformed adjoint system, Numerische Mathematik, 87 (2000), pp. 247-282.
A. L. Dontchev, W. W. Hager, and V. M. Veliov, Uniform convergence and mesh independence of Newton’s method for discretized variational problems, SIAM Journal on Control and Optimization, 39 (2000), pp. 961-980.
A. L. Dontchev and W. W. Hager, The Euler approximation in state constrained optimal control, Mathematics of Computation, 70 (2001), pp. 173-203.
A. L. Dontchev and W. W. Hager, A new approach to Lipschitz continuity in state constrained optimal control, Systems and Control Letters, 35 (1998), pp. 137-143.
A. L. Dontchev and W. W. Hager, Lipschitzian stability for state constrained nonlinear optimal control SIAM Journal on Control and Optimization, 36 (1998), pp. 698-718.
A. L. Dontchev and W. W. Hager, Lipschitzian stability in nonlinear control and optimization, SIAM Journal on Control and Optimization, 31 (1993), pp. 569-603.
W. W. Hager, Multiplier methods for nonlinear optimal control, SIAM Journal on Numerical Analysis, 27 (1990), pp. 1061-1080.
W. W. Hager and G. D. Ianculescu, Dual approximations in optimal control, SIAM Journal on Control and Optimization, 22 (1984), pp. 423-465.
W. W. Hager,Convex control and dual approximations, Part I, Control and Cybernetics, 8 (1979), pp. 5-22.
W. W. Hager,Convex control and dual approximations, Part II, Control and Cybernetics, 8 (1979), pp. 73-86.
W. W. Hager and J. Rogers, Minimum drag surfaces, Applied Mathematics and Optimization, 4 (1978), pp. 197-207.
W. W. Hager and S. K. Mitter, Lagrange duality theory for convex control problems, SIAM Journal on Control and Optimization, 14 (1976), pp. 843-856.
W. W. Hager and L. L. Horowitz,Convergence and stability properties of the discrete Riccati operator equation and the associated optimal control and filtering problems, SIAM Journal on Control and Optimization, 14 (1976), pp. 295-312.
W. W. Hager,Rates of Convergence for Discrete Approximations to Unconstrained Control Problems, SIAM Journal on Numerical Analysis, 13 (1976), pp. 449-472.
Optcon1.0, C Code for solving unconstrained control problems using explict Runge-Kutta discretizations and the conjugate gradient code CG_DESCENT (Master’s Thesis of Shuo Li, 2006)
