An Analytical Approach to Min-Time Control of Discrete-Time Linear Systems with Constrained Input

[1] F. L. Lewis, D. Vrabie, and V. L. Syrmos, Optimal control. John Wiley & Sons, 2012.

[2] R. Kosut, "Suboptimal control of linear time-invariant systems subject to control structure constraints," IEEE Transactions on Automatic Control, vol. 15, no. 5, pp. 557-563, 1970.

[3] W. L. Garrard, "Suboptimal feedback control for nonlinear systems," Automatica, vol. 8, no. 2, pp. 219-221, 1972.

[4] S. Nasini and R. Nessah, "An almost exact solution to the min completion time variance in a single machine," European Journal of Operational Research, vol. 294, no. 2, pp. 427-441, 2021.

[5] A. Polyakov and J.-P. Richard, "Suboptimal LMI-based solution of minimum time control problem," IFAC Proceedings Volumes, vol. 47, no. 3, pp. 2475-2480, 2014.

[6] T. Abualrub, I. Sadek, and F. El Nachar, "Wavelet based approximations in the optimal control of parabolic problems," Journal of Control Theory and Applications, vol. 11, pp. 103-107, 2013.

[7] G. Colombo and T. T. Le, "Higher order discrete controllability and the approximation of the minimum time function," Discrete and Continuous Dynamical Systems, vol. 35, no. 9, pp. 4293-4322, 2015.

[8] M. Akbarian, N. Eghbal, and N. Pariz, "A Novel method for optimal control of piecewise affine systems using semi-definite programming," International Journal of Industrial Electronics Control and Optimization, vol. 3, no. 1, pp. 59-68, 2020.

[9] M. R. Jardin and A. E. Bryson Jr, "Methods for computing minimum-time paths in strong winds," Journal of Guidance, Control, and Dynamics, vol. 35, no. 1, pp. 165-171, 2012.

[10] C.-H. Lee, M.-J. Tahk, and J.-I. Lee, "Generalized formulation of weighted optimal guidance laws with impact angle constraint," IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 2, pp. 1317-1322, 2013.

[11] S. Gutman, "On optimal guidance for homing missiles," Journal of Guidance and Control, vol. 2, no. 4, pp. 296-300, 1979.

[12] J. Zhang, Q. Xiao, and L. Li, "Solution space exploration of low-thrust minimum-time trajectory optimization by combining two homotopies," Automatica, vol. 148, p. 110798, 2023.

[13] Z. Shabani and H. Tajadodi, "A numerical scheme for constrained optimal control problems," International Journal of Industrial Electronics Control and Optimization, vol. 2, no. 3, pp. 233-238, 2019.

[14] A. Luo, "Minimun time optimal control of stepping motor," Journal of Central South University of Technology, vol. 2, pp. 54-58, 1995.

[15] G. Pin and T. Parisini, "Robust minimum-time constrained control of nonlinear discrete-time systems: New results," in IEEE Conference on Decision and Control and European Control Conference, 2011, pp. 1710-1715.

[16] D. Chen, L. Bako, and S. Lecoeuche, "The minimum-time problem for discrete-time linear systems: a non-smooth optimization approach," in IEEE International Conference on Control Applications, 2012, pp. 196-201.

[17] G. Lini, A. Piazzi, and L. Consolini, "Algebraic solution to minimum-time velocity planning," International Journal of Control, Automation and Systems, vol. 11, pp. 805-814, 2013.

[18] S. Bichiou, M. K. Bouafoura, and N. benhadj Braiek, "Minimum time control synthesis for high order LTI systems," in International Conference on Electrical Sciences and Technologies in Maghreb, 2014, pp. 1-6.

[19] M. Cerf, "Fast solution of minimum-time low-thrust transfer with eclipses," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 233, no. 7, pp. 2699-2714, 2019.

[20] L. Consolini, M. Laurini, M. Locatelli, and A. Minari, "A solution of the minimum-time speed planning problem based on lattice theory," Journal of the Franklin Institute, vol. 357, no. 12, pp. 7617-7637, 2020.

[21] G. Ciaramella and G. Fabrini, "Multilevel techniques for the solution of HJB minimum-time control problems," Journal of Systems Science and Complexity, vol. 34, no. 6, pp. 2069-2091, 2021.

[22] V. Ghaffari, "Control Law Design with Dead-beat Property in Continuous-Time Dynamical Systems," International Journal of Industrial Electronics Control and Optimization, vol. 2, no. 3, pp. 189-196, 2019.

[23] S. Gao, J.-e. Feng, Z. Li, and C. Xiang, "Minimum-Time Control of Boolean Control Networks: A Fast Graphical Approach," IEEE Transactions on Circuits and Systems II: Express Briefs, 2023.

[24] J. Yan, C. Wu, X. Yang, C. Chen, and X. Guan, "Minimum Time Formation Control of AUVs with Smooth Transition in Communication Topology," IEEE Robotics and Automation Letters, 2024.

[25] M. Pagone, M. Boggio, C. Novara, A. Proskurnikov, and G. C. Calafiore, "Continuous-time nonlinear model predictive control based on Pontryagin Minimum Principle and penalty functions," International Journal of Control, pp. 1-17, 2024.

[26] V. Ghaffari, "The Exact Solution of Min-Time Optimal Control Problem in Constrained LTI Systems: A State Transition Matrix Approach," AUT Journal of Modeling and Simulation, vol. 51, no. 2, pp. 103-110, 2019.

[27] R. E. Kopp, "Pontryagin maximum principle," in Mathematics in Science and Engineering, vol. 5: Elsevier, 1962, pp. 255-279.