生物啟發控制媒介的使用在農業,醫學,工業和環境系統裡是非常普遍的.生物啟發控制系統的動態主要依賴於受控目標與類捕食者或類獵物的控制媒介間的類食性作用.這些生物啟發控制媒介,譬如:農藥,肥料或藥物,的數量,在整個控制過程裡是很難被任意決定的,而且可能會因為被受控目標,如:害蟲,作物或病原,吸收而減少,或是隨時間衰變.因此,為了管理的目的或是模型參照追蹤,一個合適的時程管理方針藉由脈衝引入生物啟發控制媒介,如:週期性灌溉作物/餵食牲畜或時程性投藥/治療,是必須的.此時程管理方針必須能確保強健性的參照追蹤性能,即便是處於來自隨機的內部波動和不確定的環境擾動的干擾之下.在此研究裡,我們提出一個對非線性隨機生物啟發控制系統的時程管理方針藉由強健性脈衝追蹤控制的策略,來削弱隨機內部波動和不確定性環境擾動對預期的參照追蹤和脈衝控制輸入的影響.此強健性脈衝追蹤控制策略可協助管理者決定使用何種生物啟發控制媒介以及脈衝引入控制媒介的數量.為了簡化設計流程避開對複雜Hamilton Jacobi integration inequality (HJII) 的求解,我們結合全域線性化方法與數值近似來處理HJII中的非線性和積分,如此一個等效的LMIs便可被用來有效地求解此強健性脈衝追蹤控制問題.我們也用模擬結果來驗證此脈衝追蹤控制設計應用在非線性隨機生物啟發控制系統的效率.

The dynamics of bio-inspired control systems mainly rely on the trophic-like interactions among the controlled objects and their predator-like or prey-like control agents. The amounts of the bio-inspired control agents like pesticide, fertilizer or drugs are difficult to be arbitrarily specified during the whole control process, and may be fewer and fewer because they are absorbed by controlled objects like pest, crop or pathogen, or decay with time. Therefore, for some managing purpose or model reference tracking, a proper scheduled managing policy by impulsively introducing bio-inspired control agents, such as periodic irrigation/feeding for crop/livestock or scheduled dosing/treatment for patients, will be necessary. The scheduled managing policy should ensure a robust reference tracking performance even under the interference from random intrinsic fluctuation and uncertain environmental disturbance. In this study, we propose a scheduled managing policy for nonlinear stochastic bio-inspired control systems via a robust impulsive tracking control strategy to attenuate the effects of random intrinsic fluctuations and uncertain environmental noises on desired reference tracking and impulsive control input. To simplify the design procedure without solving a complex Hamilton Jacobi integration inequality (HJII), we combine the global linearization approach with numerical approximation to deal with nonlinearity and integration in HJII so that an equivalent LMIs is proposed for solving this robust impulsive tracking control problem efficiently. Simulation results are also given to verify the efficiency of the impulsive tracking control design of nonlinear stochastic bio-inspired control systems.

[1] M. Helms, S. S. Vattam, and A. K. Goel, "Biologically inspired design: process and products," Design Studies, vol. 30, pp. 606-622, 2009.
[2] A. Brabazon and M. O'Neill, Biologically inspired algorithms for financial modelling: Springer, 2006.
[3] G. M. Nicoletti, M. Syrjakow, D. P. Berdux, H. Szczerbicka, F. Klflgl, Y. Bissiri, W. S. Dunbar, and A. Hall, "Biologically-Inspired Systems," Intelligent Applications in a Material World Select Papers from IPMM-2001, p. 239, 2002.
[4] E. Dujardin and S. Mann, "Bio-inspired materials chemistry," Advanced Materials, vol. 14, p. 775, 2002.
[5] M. H. Dickinson, "Bionics: Biological insight into mechanical design," Proceedings of the National Academy of Sciences, vol. 96, pp. 14208-14209, 1999.
[6] J. O. Kephart, "A biologically inspired immune system for computers," in Artificial Life IV: proceedings of the fourth international workshop on the synthesis and simulation of living systems, 1994, pp. 130-139.
[7] J. O. Kephart, G. B. Sorkin, W. C. Arnold, D. M. Chess, G. J. Tesauro, S. R. White, and T. Watson, "Biologically inspired defenses against computer viruses," in IJCAI (1), 1995, pp. 985-996.
[8] A. Tero, S. Takagi, T. Saigusa, K. Ito, D. P. Bebber, M. D. Fricker, K. Yumiki, R. Kobayashi, and T. Nakagaki, "Rules for biologically inspired adaptive network design," Science, vol. 327, pp. 439-442, 2010.
[9] S. George, D. Evans, and L. Davidson, "A biologically inspired programming model for self-healing systems," in Proceedings of the first workshop on Self-healing systems, 2002, pp. 102-104.
[10] D. W. Green, "Tissue bionics: examples in biomimetic tissue engineering," Biomedical Materials, vol. 3, p. 034010, 2008.
[11] M. Yunhai, Y. Jiulin, T. Jin, L. Meng, and S. Jian, "Structural Characteristics in Natural Biomaterials and Developing Trend of Bionic Material [J]," Journal of Agricultural Mechanization Research, vol. 8, p. 001, 2009.
[12] W. Gurney and R. M. Nisbet, Ecological dynamics: Oxford University Press, Oxford, 1998.
[13] S. L. Pimm, Food webs: Springer, 1982.
[14] G. C. Goodwin, S. F. Graebe, and M. E. Salgado, Control system design vol. 240: Prentice Hall New Jersey, 2001.
[15] B. Friedland, Control system design: an introduction to state-space methods: Courier Dover Publications, 2012.
[16] J. Ernel and R. Peet, "3 Resource management and natural hazards," New Models In Geog, vol. 1, 2013.
[17] F. R. Førsund and S. Strøm, Environmental economics and management: pollution and natural resources: Routledge, 2013.
[18] B. Mitchell, Resource & Environmental Management: Routledge, 2013.
[19] D. D. Chiras and J. P. Reganold, Natural resource conservation: Management for a sustainable future: Benjamin Cummings, 2010.
[20] S. C. Hackett, Environmental and natural resources economics: theory, policy, and the sustainable society: ME Sharpe, 2011.
[21] A.-A. M. Ussif and U. R. Sumaila, "Modeling the dynamics of regulated resource systems: a fishery example," Ecological Economics, vol. 52, pp. 469-479, 2005.
[22] B. K. Williams, "Optimal stochastic control in natural resource management: framework and examples," Ecological Modelling, vol. 16, pp. 275-297, 1982.
[23] B. K. Williams, "Adaptive optimization and the harvest of biological populations," Mathematical biosciences, vol. 136, pp. 1-20, 1996.
[24] C. W. Clark, "Economically optimal policies for the utilization of biologically renewable resources," Mathematical biosciences, vol. 12, pp. 245-260, 1971.
[25] E. Chauvet, J. E. Paullet, J. P. Previte, and Z. Walls, "A Lotka-Volterra three-species food chain," Mathematics Magazine, pp. 243-255, 2002.
[26] P. J. Morin and S. P. Lawler, "Food web architecture and population dynamics: theory and empirical evidence," Annual Review of Ecology and Systematics, vol. 26, pp. 505-529, 1995.
[27] Y. Tan and L. Chen, "Modelling approach for biological control of insect pest by releasing infected pest," Chaos, Solitons & Fractals, vol. 39, pp. 304-315, 2009.
[28] P. DeBach and D. Rosen, Biological control by natural enemies: CUP Archive, 1991.
[29] B. Alloway and D. C. Ayres, Chemical principles of environmental pollution: CRC Press, 1997.
[30] FAO. (2003, Agriculture,food and water. Available: http://www.fao.org/docrep/006/y4683e/y4683e00.HTM
[31] M. Fung-Kee-Fung, T. Oliver, L. Elit, A. Oza, H. Hirte, and P. Bryson, "Optimal chemotherapy treatment for women with recurrent ovarian cancer," Current Oncology, vol. 14, p. 195, 2007.
[32] H. R. Joshi, "Optimal control of an HIV immunology model," Optimal control applications and methods, vol. 23, pp. 199-213, 2002.
[33] A. S. Matveev and A. V. Savkin, "Application of optimal control theory to analysis of cancer chemotherapy regimens," Systems & control letters, vol. 46, pp. 311-321, 2002.
[34] F. G. Ball and O. D. Lyne, "Optimal vaccination policies for stochastic epidemics among a population of households," Mathematical biosciences, vol. 177, pp. 333-354, 2002.
[35] J. Lou, Y. Lou, and J. Wu, "Threshold virus dynamics with impulsive antiretroviral drug effects," Journal of Mathematical Biology, vol. 65, pp. 623-652, 2012.
[36] T. Gao, W. Wang, and X. Liu, "Mathematical analysis of an HIV model with impulsive antiretroviral drug doses," Mathematics and Computers in Simulation, vol. 82, pp. 653-665, 2011.
[37] G. Z. Zeng, L. S. Chen, and L. H. Sun, "Complexity of an SIR epidemic dynamics model with impulsive vaccination control," Chaos, Solitons & Fractals, vol. 26, pp. 495-505, 2005.
[38] J. Hui and L.-S. Chen, "Impulsive vaccination of SIR epidemic models with nonlinear incidence rates," Discrete and Continuous Dynamical Systems Series B, vol. 4, pp. 595-606, 2004.
[39] S. Bunimovich-Mendrazitsky, H. Byrne, and L. Stone, "Mathematical model of pulsed immunotherapy for superficial bladder cancer," Bulletin of mathematical biology, vol. 70, pp. 2055-2076, 2008.
[40] A. Lakmeche and O. Arino, "Nonlinear mathematical model of pulsed-therapy of heterogeneous tumors," Nonlinear Analysis: Real World Applications, vol. 2, pp. 455-465, 2001.
[41] D. D. S. P. S. Bainov, Systems with impulse effect : stability, theory and applications. Chichester: Ellis Horwood Limited, 1989.
[42] X. Liu, Y. Liu, and K. L. Teo, "Stability analysis of impulsive control systems," Mathematical and computer modelling, vol. 37, pp. 1357-1370, 2003.
[43] T. Yang, "Impulsive control," IEEE Transactions on Automatic Control, vol. 44, pp. 1081-1083, 1999.
[44] T. Yang, Impulsive control theory vol. 272: Springer, 2001.
[45] G. Jiang and Q. Lu, "Impulsive state feedback control of a predator–prey model," Journal of Computational and Applied Mathematics, vol. 200, pp. 193-207, 2007.
[46] Z. Liu and R. Tan, "Impulsive harvesting and stocking in a Monod–Haldane functional response predator–prey system," Chaos, Solitons & Fractals, vol. 34, pp. 454-464, 2007.
[47] C. Li, X. Liao, and X. Zhang, "Impulsive synchronization of chaotic systems," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 15, p. 023104, 2005.
[48] X. Zhang, Z. Shuai, and K. Wang, "Optimal impulsive harvesting policy for single population," Nonlinear Analysis: Real World Applications, vol. 4, pp. 639-651, 2003.
[49] C. Li, L. Chen, and K. Aihara, "Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 18, p. 023132, 2008.
[50] X. Lu and W.-H. Chen, "A Lyapunov functional approach to impulsive control of Takagi-Sugeno fuzzy delay systems," in Control and Decision Conference (CCDC), 2012 24th Chinese, 2012, pp. 3808-3813.
[51] J. Ackermann, A. Bartlett, D. Kaesbauer, W. Sienel, and R. Steinhauser, Robust control: Springer, 1993.
[52] B.-S. Chen, C.-S. Tseng, and H.-J. Uang, "Mixed H 2/H∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach," Fuzzy Systems, IEEE Transactions on, vol. 8, pp. 249-265, 2000.
[53] B.-S. Chen, W.-H. Chen, and H.-L. Wu, "Robust global linearization filter design for nonlinear stochastic systems," Circuits and Systems I: Regular Papers, IEEE Transactions on, vol. 56, pp. 1441-1454, 2009.
[54] S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory vol. 15: SIAM, 1994.
[55] A. J. Jordan and J. P. Nowacki, "Global linearization of non-linear state equations," International Journal of Applied Electromagnetics and Mechanics, vol. 19, pp. 637-642, 2004.
[56] S. Hassani, "Dirac delta function," in Mathematical Methods, ed: Springer, 2009, pp. 139-170.
[57] N. Yu-Jun and M. Ge, "Impulsive control of stochastic system under the sense of stochastic asymptotical stability," Chinese Physics B, vol. 19, p. 110511, 2010.
[58] B. S. Chen, W. H. Chen, and H. L. Wu, "Robust H2/H∞ Global Linearization Filter Design for Nonlinear Stochastic Systems," IEEE Trans. Circuits and Systems I, vol. 56, pp. 1441-1454, 2009.
[59] K. Tanaka and H. O. Wang, Fuzzy control systems design and analysis: a linear matrix inequality approach: Wiley. com, 2004.
[60] R. Courant, Differential and integral calculus vol. 2: John Wiley & Sons, 2011.
[61] M. Kocvara and M. Stingl, "PENNON: A code for convex nonlinear and semidefinite programming," Optimization Methods and Software, vol. 18, pp. 317-334, 2003.
[62] C. S. Tseng, B. S. Chen, and H. J. Uang, "Fuzzy tracking control design for nonlinear dynamic systems via TS fuzzy model," IEEE Trans. fuzzy systems, vol. 9, pp. 381-392, 2001.
[63] J. Murray, "Mathematical Biology," 2008.
[64] W. L. Hall and B. E. Rehberg, "Fertilizer/pesticide composition and method of treating plants," ed: Google Patents, 1992.
[65] D. Tilman, K. G. Cassman, P. A. Matson, R. Naylor, and S. Polasky, "Agricultural sustainability and intensive production practices," Nature, vol. 418, pp. 671-677, 2002.
[66] J. P. Reganold, R. I. Papendick, and J. F. Parr, "Sustainable agriculture," Scientific American, vol. 262, pp. 112-120, 1990.
[67] J. G. Hillier and A. N. E. Birch, "Bi-trophic Mathematical Model for Pest Adaptation to a Resistant Crop," Journal of theoretical biology, vol. 215, pp. 305-319, 2002.
[68] F. Biafore and C. D'Attellis, "Exact Linearisation and Control of a HIV-1 Predator-Prey Model," in Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the, 2006, pp. 2367-2370.
[69] C. V. Forst, "Host–pathogen systems biology," in Infectious Disease Informatics, ed: Springer, 2010, pp. 123-147.
[70] R. Gatenby, "Application of competition theory to tumour growth: implications for tumour biology and treatment," European Journal of Cancer, vol. 32, pp. 722-726, 1996.
[71] R. A. Gatenby, "Models of tumor-host interaction as competing populations: implications for tumor biology and treatment," Journal of theoretical biology, vol. 176, pp. 447-455, 1995.
[72] J. I. Boullata and L. M. Hudson, "Drug–nutrient interactions: A broad view with implications for practice," Journal of the Academy of Nutrition and Dietetics, vol. 112, pp. 506-517, 2012.
[73] D. Genser, "Food and drug interaction: consequences for the nutrition/health status," Annals of Nutrition and Metabolism, vol. 52, pp. 29-32, 2008.
[74] M. A. Nowak, S. Bonhoeffer, G. M. Shaw, and R. M. May, "Anti-viral drug treatment: dynamics of resistance in free virus and infected cell populations," Journal of theoretical biology, vol. 184, pp. 203-217, 1997.
[75] H. W. Hethcote, "The mathematics of infectious diseases," SIAM review, vol. 42, pp. 599-653, 2000.
[76] P. Vineis and M. Berwick, "The population dynamics of cancer: a Darwinian perspective," International journal of epidemiology, vol. 35, pp. 1151-1159, 2006.
[77] B. Øksendal, Stochastic differential equations: Springer, 2003.