JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (7): 15-20.doi: 10.6040/j.issn.1671-9352.0.2017.578

Previous Articles     Next Articles

Optimal control of forest evolution system in polluted environment

CAO Xue-jing, LUO Zhi-xue   

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2017-11-14 Online:2018-07-20 Published:2018-07-03

Abstract: The optimal control problem of a forest evolution system in polluted environment was discussed. Firstly, the model was proposed and the existence and uniqueness of the solution were proved by Banach fixed point theorem. Then, the unique solution of the optimal control is obtained according to the properties of convex functional and Mazur lemma.

Key words: forest evolution system, optimal control, Banach fixed point theorem, environmental pollution, Mazur lemma

CLC Number: 

  • O175.1
[1] HALLAM T G, CLARK C E, LASSITER R R. Effects of toxicants on populations: a qualitative approach I. equilibrium environmental exposure[J]. Ecological Modelling, 1983, 18(4): 291-304.
[2] HALLAM T G, CLARK C E, JORDAN G S. Effects of toxicants on populations: a qualitative approach II. first order kinetics[J]. Journal of Mathematical Biology, 1983, 18(1): 25-37.
[3] HALLAM T G, DE LUNA J T. Effects of toxicants on populations: a qualitative approach III. environmental and food chain pathways[J]. Journal of Theoretical Biology, 1984, 109(3): 411-429.
[4] LUO Zhixue, HE Zerong. Optimal control for age-dependent population hybrid system in a polluted environment[J]. Applied Mathematics and Computation, 2014, 228(1): 68-76.
[5] LUO Zhixue, FAN Xueliang. Optimal control for an age-dependent competitive species model in a polluted environment[J]. Applied Mathematics and Computation, 2014, 228(1): 91-101.
[6] WANG Dingjiang, ZHANG Yufeng. The property of solution of a nonstationary forest evolution system[J]. Systems Science and Systems Engineering, 1993, 2(3): 281-288.
[7] 高德智,许香敏.森林发展系统中的最优控制问题[J].系统工程理论与实践, 1999(4): 90-93. GAO Dezhi, XU Xiangmin. Optimal control problems in forest evolution system[J]. Systems Engineering-Theory and Practice, 1999(4): 90-93.
[8] 马知恩.种群生态学的数学建模与研究[M].合肥:安徽教育出版社, 1996: 168-175. MA Zhien. Mathematical modeling and research on population ecology[M]. Hefei: Anhui Education Press, 1996: 168-175.
[9] HE Zerong, LIU Yan. An optimal birth control problem for a dynamical population model with size-structure[J]. Nonlinear Analysis: Real World Applications, 2012, 13(3): 1369-1378.
[10] LIU Yan, CHENG Xiaoliang, HE Zerong. On the optimal harvesting of size-structured population dynamics[J]. Applied Mathematics-A Journal of Chinese Universities, 2013, 28(2): 173-186.
[11] ANITA S. Analysis and control of age-dependent population dynamics[M]. Boston: Kluwer Academic, 2000: 67-70.
[1] ZHANG Tai-nian, LI Zhao-xing. Convergence analysis for inverse problems in a degenerate parabolic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 35-42.
[2] LIU Jiang-bi, LUO Zhi-xue. Optimal control for a nonlinear diffusion system with age-dependent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 136-142.
[3] NIE Tian-yang, SHI Jing-tao. The connection between DPP and MP for the fully coupled forward-backward stochastic control systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 121-129.
[4] CAI Chao. An inverse problem of identifying the coefficient in a Kolmogorov type equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 127-134.
[5] YU Yong-sheng, GONG Zhao-hua, LIU Chong-yang. Optimal control problem in the microbial fed-batch fermentation process [J]. J4, 2011, 46(11): 117-121.
[6] ZHANG Huan-shui1, SONG Xin-min1, XIE Li-hua2. Stage-by-Stage optimization approach to optimal control for general timedelay systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2011, 46(10): 45-56.
[7] CHEN Li. Properties on Z for anticipated BSDE and application  in stochastic  control with delay [J]. J4, 2010, 45(4): 16-20.
[8] GUO Lei . The optimal control problem of deterministic jumping transition systems [J]. J4, 2007, 42(7): 82-86 .
[9] LI Zhi-tao,WANG Gang-chen and MU Chao . The local necessary condition for a type of stochastic optimal control problem and its application to a portfolio choice problem [J]. J4, 2007, 42(6): 7-11 .
[10] CHEN Li, . Singular LQ suboptimal control problem with disturbance rejection [J]. J4, 2006, 41(2): 74-77 .
[11] GUO Lei,YU Rui-lin and TIAN Fa-zhong . Optimal control of one kind general jump transition systems [J]. J4, 2006, 41(1): 35-40 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!