Reference governors and maximal output admissible sets for linear periodic systems

References

• Arimoto, S., Kawamura, S., & Miyazaki, F. (1984). Bettering operation of robots by learning. Journal of Robotic Systems, 1(2), 123–140. doi: 10.1002/rob.4620010203
   Web of Science ®Google Scholar
• Bittanti, S., & Bolzern, P. (1985). Stabilizability and detectability of linear periodic systems. Systems and Control Letters, 6(2), 141–145. doi:10.1016/0167-6911(85)90083-0.
   Web of Science ®Google Scholar
• Bittanti, S., & Colaneri, P. (2000). Invariant representations of discrete-time periodic systems. Automatica, 36(12), 1777–1793. doi:10.1016/S0005-1098(00)00087-X.
   Web of Science ®Google Scholar
• Bittanti, S., & Colaneri, P. (2001). Stabilization of periodic systems: Overview and advances. IFAC Proceedings Volumes, 34(12), 153–160. doi: 10.1016/S1474-6670(17)34077-6
   Google Scholar
• Bittanti, S., & Colaneri, P. (2009). Periodic systems: Filtering and control. London: Springer-Verlag.
   Google Scholar
• Blanchini, F., & Ukovich, W. (1993). Linear programming approach to the control of discrete-time periodic systems with uncertain inputs. Journal of Optimization Theory and Applications, 78(3), 523–539. doi: 10.1007/BF00939880
   Web of Science ®Google Scholar
• Böhm, C., Yu, S., & Allgöwer, F. (2009). Predictive control for constrained discrete-time periodic systems using a time-varying terminal region. In Proceedings of the 14th international conference on methods and models in automation and robotics (pp. 537–542). doi:10.3182/20090819-3-PL-3002.00093.
   Google Scholar
• Brunovsky, P. (1969). Controllability and linear closed-loop controls in linear periodic systems. Journal of Differential Equations, 6, 296–313. doi:10.1016/0022-0396(69)90019-9.
   Web of Science ®Google Scholar
• Chen, C. T. (2012). Linear system theory and design (4th ed.). New York: Oxford University Press.
   Google Scholar
• Chen, Y., & Wen, C. (1999). Iterative learning control: Convergence, robustness and applications. London: Springer-Verlag.
   Google Scholar
• Ching, S., Eun, Y., Gross, E., Hamby, E. S., Kabamba, P. T., Meerkov, S. M., & A. A. Menezes (2010). Modeling and control of cyclic systems in xerography. In Proceedings of the American control conference (pp. 4283–4288).
   Google Scholar
• Colaneri, P., De Souza, C., & Kucera, V. (1998). Output stabilizability of periodic systems: Necessary and sufficient conditions. Proceedings of the American Control Conference, 5, 2795–2796. doi:10.1109/ACC.1998.688363.
   Google Scholar
• de Lima, T. P. (2001). Studying a basic price equation as a periodic system. IFAC Proceedings Volumes, 34(12), 55–60. doi: 10.1016/S1474-6670(17)34061-2
   Google Scholar
• De Souza, C. E., & Trofino, A. (2000). An LMI approach to stabilization of linear discrete-time periodic systems. International Journal of Control, 73(8), 696–703. doi:10.1080/002071700403466.
   Web of Science ®Google Scholar
• Dugundji, J., & Wendell, J. H. (1983). Some analysis methods for rotating systems with periodic coefficients. AIAA Journal, 21(6), 890–897. doi:10.2514/3.8167.
   Web of Science ®Google Scholar
• Eun, Y., Gross, E. M., Kabamba, P. T., Meerkov, S. M., Menezes, A. A., & Ossareh, H. R. (2013). Cyclic control: Reference tracking and disturbance rejection. IEEE Transactions on Control Systems Technology, 21(3), 753–764. doi:10.1109/TCST.2012.2193400.
   Web of Science ®Google Scholar
• Faraday, M. (1831). On peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philosophical Transactions of the Royal Society of London, 121, 299–340. doi:10.1098/rstl.1831.0018.
   Google Scholar
• Floquet, G. (1883). Sur les équations différentielles linéaires à coefficients périodiques. Annales scientifiques de l'École Normale Supérieure, 12, 47–88. doi: 10.24033/asens.220
   Google Scholar
• Freuer, A., Reble, M., Böhm, C., & Allgöwer, F. (2010). Efficient model predictive control for linear periodic systems. Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems-MTNS, 5(9), 1403–1409.
   Google Scholar
• Garone, E., Cairano, S. D., & Kolmanovsky, I. (2017). Reference and command governors for systems with constraints: A survey on theory and applications. Automatica, 75, 306–328. doi: 10.1016/j.automatica.2016.08.013
   Web of Science ®Google Scholar
• Garone, E., & Nicotra, M. M. (2015). Explicit reference governor for constrained nonlinear systems. IEEE Transactions on Automatic Control, 61(5), 1379–1384. doi: 10.1109/TAC.2015.2476195
   Web of Science ®Google Scholar
• Garone, E., & Nicotra, M. M. (2016, May). Explicit reference governor for constrained nonlinear systems. IEEE Transactions on Automatic Control, 61(5), 1379–1384. doi:10.1109/TAC.2015.2476195.
   Web of Science ®Google Scholar
• Garone, E., Nicotra, M. M., & Ntogramatzidis, L. (2018). Explicit reference governor for linear systems. International Journal of Control, 91(6), 1415–1430. doi: 10.1080/00207179.2017.1317832
   Web of Science ®Google Scholar
• Gilbert, E. G., & Kolmanovsky, I. (1999). Fast reference governors for systems with state and control constraints and disturbance inputs. International Journal of Robust and Nonlinear Control, 9, 1117–1141. doi:https://doi.org/10.1002/(SICI)1099-1239(19991230)9:15¡1117::AID-RNC447¿3.0.CO;2-I.
   Web of Science ®Google Scholar
• Gilbert, E. G., Kolmanovsky, I., & Tan, K. T. (1995). Discrete-time reference governors and the nonlinear control of systems with state and control constraints. International Journal of Robust and Nonlinear Control, 5(5), 487–504. doi: 10.1002/rnc.4590050508
   Web of Science ®Google Scholar
• Gilbert, E. G., & Tan, K. T. (1991). Linear systems with state and control constraints: the theory and applications of maximal output admissible sets. IEEE Transactions on Automatic Control, 36(9), 1008–1020. doi: 10.1109/9.83532
   Web of Science ®Google Scholar
• Gondhalekar, R., & Jones, C. N (2009). A unified framework for multirate and multiplexed model predictive control via periodic systems. Proceedings of the IEEE Conference on Decision Control. doi:10.1109/CDC.2009.5400284.
   Google Scholar
• Herceg, M., Kvasnica, M., Jones, C., & Morari, M. (2013). Multi-parametric toolbox 3.0. In Proceedings of the European control conference.
   Google Scholar
• Hosseinzadeh, M., & Garone, E. (2019). An explicit reference governor for the intersection of concave constraints. In IEEE transactions on automatic control.
   Google Scholar
• Johnson, W. (1994). Helicopter theory. New York: Dover Publications.
   Google Scholar
• Kabamba, P. (1986). Monodromy eigenvalue assignment in linear periodic systems. IEEE Transactions on Automatic Control, 31(10), 950–952. doi: 10.1109/TAC.1986.1104132
   Web of Science ®Google Scholar
• Kalabić, U. (2015). Reference governors: Theoretical extensions and practical applications (PhD Dissertation). University of Michigan.
   Google Scholar
• Kerrigan, E. C. (2000). Robust constraint satisfaction: Invariant sets and predictive control (Unpublished doctoral dissertation). University of Cambridge.
   Google Scholar
• Kolmanovsky, I., Garone, E., & Di Cairano, S. (2014). Reference and command governors: A tutorial on their theory and automotive applications. In Proceedings of the American control conference (pp. 226–241). doi:10.1109/ACC.2014.6859176.
   Google Scholar
• Kolmanovsky, I., & Gilbert, E. G. (1998). Theory and computation of disturbance invariant sets for discrete-time linear systems. Mathematical Problems in Engineering, 4(4), 317–367. doi: 10.1155/S1024123X98000866
   Web of Science ®Google Scholar
• Li, N. I., Kolmanovsky, I., & Girard, A. (2016). A reference governor for nonlinear systems based on quadratic programming. In ASME 2016 dynamic systems and control conference (pp. V001T02A005–V001T02A005).
   Google Scholar
• Nguyen, H., & Bourdais, R. (2014). Constrained control of discrete-time linear periodic system. American Control Conference (ACC), 2014, 2960–2965.
   Google Scholar
• Nguyen, H. N., Bourdais, R., & Gutman, P. O. (2014). Improved MPC design for constrained linear periodic systems. 2014 European Control Conference, ECC, 2014, 1462–1467. doi:10.1109/ECC.2014.6862367.
   Google Scholar
• Nicotra, M. M., Garone, E., & Kolmanovsky, I. V. (2016). Fast reference governor for linear systems. Journal of Guidance, Control, and Dynamics, 40(2), 461–465. doi: 10.2514/1.G000337
   Web of Science ®Google Scholar
• Psiaki, M. L. (2001). Magnetic torquer attitude control via asymptotic periodic linear quadratic regulation. Journal of Guidance, Control, and Dynamics, 24(2), 386–394. doi:10.2514/2.4723.
   Web of Science ®Google Scholar
• Vaidyanathan, P. (1993). Multirate systems and filter banks. Upper Saddle River, NJ: Prentice-Hall, Inc.
   Google Scholar
• Wang, Y., Gao, F., & Doyle, III, F. J. (2009). Survey on iterative learning control, repetitive control, and run-to-run control. Journal of Process Control, 19(10), 1589–1600. doi: 10.1016/j.jprocont.2009.09.006
   Web of Science ®Google Scholar
• Wiśniewski, R., & Blanke, M. (1999). Fully magnetic attitude control for spacecraft subject to gravity gradient. Automatica, 35(7), 1201–1214. doi:10.1016/S0005-1098(99)00021-7.
   Web of Science ®Google Scholar