本篇論文提出了一種基於數位重新設計的混沌同步及其在圖像加密中的應用。首先，針對採樣非線性混沌系統，提出一種基於H2控制的數位重新設計滑模控制方法，以達到混沌系統同步控制的目的。接著，針對了具有不匹配擾動的採樣非線性系統，提出一種基於H-infinity控制的數位重新設計滑模控制方法，以達到混沌系統同步的目的。H-infinity控制方法和滑模控制的結合，不僅保證了系統的穩定性，而且消除了非線性和外部干擾的負面影響。與直接在離散系統中設計離散控制器相比，使用數位重新設計可以使設計離散滑模控制更加容易。除此之外，獲得了滑模軌跡的上限，而此上限是沒有被預先指出。隨後，提出了一種基於由混沌系統所建立的S-box圖像加密演算法。因此，基於混沌系統同步的解密方法可以成功地應用於通訊安全。

The digital-redesign sliding-mode control-based chaotic synchronization and its application to image encryption are newly proposed in this thesis. First, the chaotic synchronization control for the sampled-data nonlinear system based on the digital-redesign sliding-mode control integrated with the H2 control method is proposed. Next, the chaotic synchronization control for the sampled-data nonlinear system with mismatched disturbances based on the digital-redesign sliding-mode control integrated with H-infinity control method is proposed. The combination of H-infinity control method and the sliding-mode control not only guarantees the stability of the system but also eliminates the negative influence of the nonlinearity and the external disturbances. The utilization of the digital-redesign method makes the design of the discrete-time sliding-mode control more easily than directly designing the discrete-time controller in the discrete-time domain. Besides, the upper bound of sliding mode trajectories is obtained which is not indicated a prior. Subsequently, an image encryption algorithm based on an S-box establishing from the chaotic system has been proposed. Consequently, the chaotic-synchronization-based decryption approach can be successfully applied to secure communication.

[1] Abera, A.G/E, and Bandyopadhyay, B., “Digital Redesign of Sliding Mode Control with Application to Power System Stabilizer,” 34th Annual Conference of IEEE Industrial Electronics, Orlando, USA, 2008.
[2] Ahmad, F.F., Ghenai, C., Hamid, A.K., and Bettayeb, M, “Application of sliding mode control for maximum power point tracking of solar photovoltaic systems: A comprehensive review,” Annual Reviews in Control, vol. 49, pp. 173-196, 2020.
[3] Artiles, J. A.P., Chaves D. P.B., and Pimentel C., “Image encryption using block cipher and chaotic sequences,” Signal Processing: Image Communication, vol. 79, pp. 24-31, 2019.
[4] Asadollahi, M., Ghiasi, A.R., and Badamchizadeh, M.A, “Adaptive synchronization of chaotic systems with hysteresis quantizer input,” ISA Transactions, vol. 98, pp. 137-148, 2019.
[5] Bolting, J., Fergani, S., and Biannic, J.M., “Defay, F.; Stolle, M. Discrete Sliding Mode control of small UAS in tight formation flight under information constraints,” IFAC PapersOnline., vol. 49, pp. 332-337, 2016.
[6] Cheng, C.J., “Robust synchronization of uncertain unified chaotic systems subject to noise and its application to secure communication,” Applied Mathematics and Computation, vol. 219, pp. 2698-2712, 2012.
[7] Fang, J.S., Jason Tsai, S.H., Yan, J.J., Tzou, C.H., and Guo, S.M, “Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization,” Mathematics, vol. 7, 2019, https://doi.org/10.3390/math7121141.
[8] Feki, M., “An adaptive chaos synchronization scheme applied to secure communication,” Chaos, Solitons and Fractals, vol. 18, pp. 141-148, 2003.
[9] Feng, W., He, Y.G., Li, H.M., and Li, C.L., “Cryptanalysis of the integrated chaotic systems based image encryption algorithm,” Optik-international Journal for Light and Electron Optics, vol. 186, pp. 449-457, 2019.
[10] He, C., and Li, J., “Event-based aperiodically intermittent pinning synchronization control strategy for linearly coupled complex network,” Nonlinear Analysis: Hybrid Systems. vol. 36, Article ID 100836, 2020, https://doi.org/10.1016/j.nahs.2019.100836.
[11] Hermassi, H., Rhouma, R., and Belghith, S., “Improvement of an image encryption algorithm based on hyper chaos,” Telecommunication Systems, vol.52, pp. 539-549, 2013.
[12] Herrera, M., Camacho, O., Leiva, H., and Smith, C, “An approach of dynamic sliding mode control for chemical processes,” Journal of Process Control., vol. 85, pp. 112-120, 2020.
[13] Hussain, I., Anees, A., Alkhakdi, A.H., Algarni, A., and Aslam, M., “Construction of chaotic quantum magnets and matrix Lorenz systems S-boxes and their applications,” Chinese Journal of Physics, vol. 56, pp. 1609-1621, 2018.
[14] Jahanshahi, H., Yousefpour, A., Munoz-Pacheco, J.M., Moroz, I., Wei, Z., and Castillo, O, “A new multi-stable fractional-order four-dimensional system with self-excited and hidden chaotic attractors: Dynamic analysis and adaptive synchronization using a novel fuzzy adaptive sliding mode control method.” Applied Soft Computing Journal, vol. 87, Article ID 105943, 2020, https://doi.org/10.1016/j.asoc.2019.105943.
[15] Jing, C.H., Xu, H.G., and Niu, X.J, “Adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators,” ISA Transaction, vol. 91, pp. 41-51, 2019.
[16] Kchaou, A., Naamane, A., Koubaa, Y., and M’sirdi, N, “Second-order sliding mode-based MPPT control for photovoltaic applications,” Solar Energy, vol. 155, pp. 758-769, 2017.
[17] Li, S., Du, X., “Discrete-Time Terminal Sliding Mode Control Systems Based on Euler’s Discretization,” IEEE Transaction on Industrial Electronics, vol. 59, pp. 1161-1170, 2012.
[18] Li, Z., Park, J.B., Joo Y.H., Zhang, B., and Chen G., “Bifurcations and Chaos in a Permanent-Magnet Synchronous Motor,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, pp. 383-387, 2002.
[19] Liu, H., Kadir, A., and Gong, P., “A fast color encryption scheme using one-time S-Boxes based on complex chaotic system and random noise,” Optics Communication, vol. 338, pp. 340-347, 2015.
[20] Lu, J., Wu, X., and Lu, J., “Synchronization of a unified chaotic system and the application in secure communication,” Physics Letters A, vol.305, pp.365-370, 2002.
[21] Merabet, A., Labib, L., Ghias, A.M.Y.M., Aldurra, A., and Debbouza, M, “Dual-mode operation based second-order sliding mode control for grid-connected solar photovoltaic energy system,” Electrical Power and Energy Systems, vol. 111, pp. 459-474, 2019.
[22] Morais, C.F., Braga, M.F., Tongnetti, E.S., Oliveira, R.C.L.F., and Peres, P.L.D, “ and digital redesign of analog controllers for continuous-time polytopic systems,” IFAC PapersOnLine, vol. 50, pp. 6691-6696, 2017.
[23] Norouzi, A., Ebrahimi, K., and Kock, C.R, “Integral Discrete-time Sliding Mode Control of Homogeneous Charge Compression Ignition (HCCI) Engine Load and Combustion Timing,” IFAC PapersOnline., vol. 52, pp. 153-158, 2019.
[24] Ousaasid, M., Cherkaoui, M., Nejmi, A., and Maaroufi, M., “Nonlinear Torque Control for PMSM: A Lyapunov Technique Approach,” World Academy of Science, Engineering and Technology, vol. 6, 2005.
[25] Özkaynak, F., “On the effect of chaotic system in performance characteristic of chaos based s-box designs,” vol. 550, 2020, https://doi.org/10.1016/j.physa.2019.124072.
[26] Patre, B.M., Londhe, P.S., Waghmare, L.M., and Mohan, S., “Disturbance estimator based non-singular fast fuzzy terminal sliding mode control of an autonomous underwater vehicle,” Ocean Engineering, vol. 159, pp. 372-387, 2018.
[27] Rigatos, G., Siano P., Wira P., and Hamida A., “An H-infinity approach to optimal control of doubly-fed reluctance machines,” IFAC-PaperOnLine, vol. 49, pp. 116-122, 2016.
[28] Singla, M., Shieh, L.S., Song, G.B., Xie L.B., and Zhang, Y.P, “A new optimal sliding mode controller design using scalar sign function,” ISA Transactions, vol. 53, pp. 267-279, 2014.
[29] Sumantri, B., Uchiyama, N., and Sano, S, “Least square based sliding mode control for a quad-rotor helicopter and energy saving by chattering reduction,” Mechanical Systems and Signal Processing, vol. 66-67, pp. 769-784, 2016.
[30] Tasi, Jason S.H., Fang, J. S., Yan, J.J., Dai, M.C., Guo, S.M., and Shieh, L.S., “Hybrid robust discrete sliding mode control for generalized continuous chaotic systems subject to external disturbances,” Nonlinear Analysis: Hybrid Systems, vol. 29, pp. 74-84, 2018.
[31] Tsai, Jason S.H., Cheng, H., Moussighi, M.M., and Shieh, L.S, “Digital redesign of observer-based weighting switch controller for cascaded analog systems with state saturation and external loads,” ISA Transaction, vol. 44, pp. 93-115, 2005.
[32] Wu, Y., Huangfu, Y., Ma, R., Ravey, A., and Chrenko, D, “A strong robust DC-DC converter of all-digital high-order sliding mode control for fuel cell power applications,” Journal of Power Sources, vol. 413, pp. 222-23, 2019.
[33] Xie, L.B., Shieh, L.S., Tsai, J. S.H., Guo, S.M., and Dunn, A.C, “Digital redesign of analog smith predictor for systems with long input time delays,” Journal of the Franklin Institute, vol. 354, pp. 5797-5812, 2017.
[34] Xiong, L.Y., Li, P.H., and Wang, J, “High-order sliding mode control of DFIG under unbalanced grid voltage conditions,” Electrical Power and Energy Systems, vol. 117, Article ID 105608, 2020, https://doi.org/10.1016/j.ijepes.2019.105608.
[35] Xu, Q.S., and Li, Y.M., “Micro-/Nanopositioning Using Model Predictive Output Integral Discrete Sliding Mode Control,” IEEE Transaction on Industrial Electronics, vol.59, vol. 1161-1170, 2012.
[36] Yang, F, Mou, J., Ma, C., and Cao, Y., “Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application,” Optics and Lasers in Engineering, vol. 129, Article ID 106031, 2020, https://doi.org/10.1016/j.optlaseng.2020.106031.
[37] Yao, S.H., Gao, G.Q., Gao, Z.Q., and Li, S, “Active disturbance rejection synchronization control for parallel electro-coating conveyor,” ISA Transactions. 2020, https://doi.org/10.1016/j.isatra.2020.01.035.
[38] Zeinali, M., and Notash, L., “Adaptive sliding mode control with uncertainty estimator for robot manipulators,” Mechanism and Machine Theory, vol. 45, pp. 80-90, 2010.
[39] Zhang, W., Teng, Y., Wei, S., Xiong, H., and Ren, H, “The robust H-infinity control of UUV with Riccati equation solution interpolation,” Ocean Engineering, vol. 156, pp. 252-262, 2018.
[40] Zhang, Y.Y., Li, R.F., Xue, T., Liu, Z.M., and Yao, Z.X, “An analysis of the stability and chattering reduction of high-order sliding mode tracking control for a hypersonic vehicle,” Information Sciences, vol. 348, pp. 25-48, 2016.
[41] Zheng, K.M., Hu, Y.M., and Wu, B, “Intelligent fuzzy sliding mode control for complex robot system with disturbances,” European Journal of Control, vol. 51, pp. 95-109, 2020.
[42] Zhou, Y., Ahn, S.Y., Wang, M., and Hoogendoorn, S, “Stabilizing mixed vehicular platoons with connected automated vehicles An H-infinity approach,” Transportation Research Part B: Methodological, vol. 132, pp. 152-170, 2020.