Prostate Cancer Treatment Using Fixed-Time Synergetic Controller

Main Article Content

Arsit Boonyaprapasorn
Suwat Kuntanapreeda
Parinya Sa Ngiamsunthorn
Kaned Thung-Od


Treatment for prostate cancer can be determined based on nonlinear feedback control. In fixed-time feedback control, the bound of settling time can be pre-specified regardless of an initial condition. This control method has been successfully employed in various applications as seen in past literature. The synergetic control method is capable of controlling nonlinear systems under chattering free control inputs. Thus, studying the application of fixed-time synergetic control to synthesize the treatment for a prostate cancer patient was investigated in this study. The control prostate system was simulated to show the capability of the proposed treatment. Apparently, the state variables of the control system were driven to the required level within the pre-defined bound of the convergence time of the corresponding macro variables by the chattering-free control treatments. According to the proposed control treatment, the control prostate cancer system is fixed-time stable without chattering in the control treatment.


Download data is not yet available.

Article Details

How to Cite
Boonyaprapasorn, A., Kuntanapreeda, S. ., Sa Ngiamsunthorn, P., & Thung-Od, K. . (2022). Prostate Cancer Treatment Using Fixed-Time Synergetic Controller. SAU JOURNAL OF SCIENCE & TECHNOLOGY, 8(1), 40–50. Retrieved from
Research Article


World Health Organization. (2018, Sept. 1). “Cancer” [Online]. Available:

R. W. Ruddon, Cancer Biology, 4th ed., Oxford University Press, New York, USA, 2007.

American Cancer and Society. (2020, Aug. 1). “Cancer Facts & Figures 2020” [Online].Available: https://www.

P. Rawla, “Epidemiology of prostate cancer,” World Journal of Oncology, vol. 10, no. 2, pp. 63–89, 2019.

R. J. Rebello, C. Oing, K. E. Knudsen, S. Loeb, D. C. Johnson, R. E. Reiter, S. Gillessen, T. Van der Kwast, and R. G. Bristow, “Prostate cancer,” Nature Reviews Disease Primers, vol. 7, no. 9, pp. 1–27, 2021.

S. W. Leslie, T. L. Soon-Sutton, H. Sajjad, and L. E. Siref, Prostate Cancer, StatPearls Publishing, Treasure Island, Florida, USA, 2021.

M. Perera, M. J. Roberts, L. Klotz, C. S. Higano, N. Papa, S. Sengupta, D. Bolton, and N. Lawrentschuk, “Intermittent versus continuous androgen deprivation therapy for advanced prostate cancer,” Nature Reviews Urology, vol. 17, pp. 469–481, 2020.

M. Ideta, G. Tanaka, T. Takeuchi, and K. Aihara, “A mathematical model of intermittent androgen suppression for prostate cancer,” Journal of Nonlinear Science, vol. 18, no. 593, pp. 593–614, 2008.

T. L. Jackson, “A mathematical model of prostate tumor growth and androgen-independent relapse,” AIMS Mathematics, vol. 4, no. 1, pp. 187–201, 2004.

T. Phan, S. M. Crook, A. H. Bryce, C. C. Maley, E. J. Kostelich, and Y. Kuang, “Mathematical modeling of prostate cancer and clinical application (review),” Applied Sciences, vol. 10, no. 8, pp. 2721, 2020.

P. Dubey and S. Chakraborty, “Avoidance of the relapse condition of prostate cancer using super-twisting sliding mode control,” in Proc. 2019 International Conference on Intelligent Computing and Control Systems (ICCS), Madurai, India, 12-14 Jun. 2019, pp. 92–97.

G. Tanaka, Y. Hirata, S. L. Goldenberg, N. Bruchovsky, and K. Aihara, “Mathematical modelling of prostate cancer growth and its application to hormone therapy,” Philosophical Transactions of the Royal Society A, vol. 368, no. 1930, pp. 5029–5044, 2010.

V. Utkin, J. Guldner, and J. Shi, Sliding mode control in electro-mechanical systems, 2nd ed., CRC Press, Boca Raton, Florida, USA, 2009.

A. Kolesnikov, “Introduction of synergetic control,” in Proc. 2014 American Control Conference (ACC), Portland, Oregon, USA, 4–6 Jun. 2014, pp. 3013–3016.

A. A. Kolesnikov, Synergetics control theory, Energoatomizdat, Moscow, Russia, 1994.

A. A. Kolesnikov and G. E. Veselov, Modern Applied Control Theory: Synergetic Approach in Control Theory, TSURE Press, Moscow-Taganrog, Russia, 2000, pp. 4477–4479.

E. Santi, A. Monti, D. Li, K. Proddutur, and R. A. Dougal, “Synergetic control for power electronics applications: A comparison with the sliding mode approach,” Journal of Circuits, Systems and Computers, vol. 1, no. 4, pp. 737–760, 2004.

S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, 2000.

H. M. Becerra, C. R. Vázquez, G. Arechavaleta, and J. Delfin, “Predefined-time convergence control for high-order integrator systems using time base generators,” IEEE Transactions on Control Systems Technology, vol. 26, no. 5, pp. 1866–1873, 2018.

C. -H. Liu and M. -Y. Hsiao, “A finite time synergetic control scheme for robot manipulators,” Computers & Mathematics with Applications, vol. 64, no. 5, pp. 1163–1169, 2012.

D. Zehar, A. Chérif, K. Benmahammed, and K. Behih, “Fast terminal synergetic control of underactuated system,” in Proc. 2018 15th International Multi-Conference on Systems, Signals & Devices (SSD), Yasmine Hammamet, Tunisia, 19–22 Mar. 2018, pp. 1184–1189.

A. Kanchanaharuthai and E. Mujjalinvimut, “Adaptive finite-time synergetic control design for power systems with static var compensator,” International Journal of Innovative Computing, Information and Control, vol. 16, no. 3, pp. 1007–1020, 2020.

A. Hachana and M. N. Harmas, “Terminal synergetic control for blood glucose regulation in diabetes patients,” Journal of Dynamic Systems, Measurement, and Control, vol. 140, no. 10, pp. 100801, 2018.

A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, 2012.

J. Wang, L. Liu, C. Liu, and J. Liu, “Fixed-time synergetic control for a seven-dimensional chaotic power system model,” International Journal of Bifurcation and Chaos, vol. 29, no. 10, pp. 1–14, 2019.

S. Huang, L. Xiong, J. Wang, P. Li, Z. Wang, and M. Ma, “Fixed-time synergetic controller for stabilization of hydraulic turbine regulating system,” Renewable Energy, vol. 157, pp. 1233–1242, 2020.

A. Al-Hussein, F. R. Tahir and V. Pham, “Fixed-time synergetic control for chaos suppression in endocrine glucose-insulin regulatory system,” Control Engineering Practice, vol. 108, no. 104723, pp. 1–10, 2021.

A. Boonyaprapasorn, T. Choopojcharoen, P. Sa-Ngiamsunthorn, S. Kuntanapreeda, E. Pengwang, S. Natsupakpong, W. Wechsatol, and T. Maneewarn, “Fixed-time synergetic approach for biological

pest control based on Lotka-Volterra.model,” IEEE Access, vol. 9, pp. 47303–47319, 2021.

B. Yang and W. Lin, “Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback,” IEEE Transactions on Automatic Control, vol. 49, pp. 1069–1080, 2004.

C. Hu, J. Yu, Z. Chen, H. Jiang, and T. Huang, “Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks,” Neural Networks, vol. 89, pp. 74–83, 2017.

Z. Zuo and L. Tie, “Distributed robust finite-time nonlinear consensus protocols for multi-agent systems,” International Journal of Systems Science, vol. 47, no. 6, pp. 1366–1375, 2016.

Z. Zuo, “Non-singular fixed-time terminal sliding mode control of non-linear systems,” IET Control Theory & Applications, vol. 9, pp. 545–552, 2015.

Most read articles by the same author(s)