A gradient-based stochastic search approach for optimal harvesting strategy in shrimp culture
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- 英文论文题名：A gradient-based stochastic search approach for optimal harvesting strategy in shrimp culture
- 论文作者：Wu Xiang ; Liu Qiaodan ; Lei Bangjun ; Zhang Kanjian
- 英文论文作者：Wu Xiang ; Liu Qiaodan ; Lei Bangjun ; Zhang Kanjian ; School of Mathematical Sciences ; Guizhou Normal University ; School of Electrical Engineering ; Southeast University ; School of Electrical and Information Engineering ; Guizhou Institute of Technology ; School of Automation ; Southeast University
- 年：2017
- 作者机构：School of Mathematical Sciences,Guizhou Normal University;School of Electrical Engineering,Southeast University;School of Electrical and Information Engineering,Guizhou Institute of Technology;School of Automation,Southeast University;
- 英文论文关键词：Optimal control ; Nonlinear impulsive system ; Binary novel variable ; Penalty function ; Shrimp culture
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：S968.22
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：213k
- 原文格式：D
- 会议级别：全国
摘要
This paper considers an optimal harvesting strategy problem arising in shrimp culture. The problem is formulated as an optimal control problem of nonlinear impulsive system. Since the impulsive switching constraints is very complex, the impulsive switching instants are unknown, and the objective function is not continuously differentiable, it is difficult to solve this problem by standard optimization methods. To overcome the difficulty, by introducing a novel binary variable for each sale price of shrimp, relaxing the binary variable, and imposing a penalty function on the relaxation term, the nonlinear impulsive system optimal control problem is transformed into a parameter optimization problem, which can be solved efficiently using any gradient-based optimization technique. Then, a gradient-based stochastic search approach is proposed for solving this problem.Finally, a harvesting strategy problem is presented to illustrate the efficiency of the approach proposed.
This paper considers an optimal harvesting strategy problem arising in shrimp culture. The problem is formulated as an optimal control problem of nonlinear impulsive system. Since the impulsive switching constraints is very complex, the impulsive switching instants are unknown, and the objective function is not continuously differentiable, it is difficult to solve this problem by standard optimization methods. To overcome the difficulty, by introducing a novel binary variable for each sale price of shrimp, relaxing the binary variable, and imposing a penalty function on the relaxation term, the nonlinear impulsive system optimal control problem is transformed into a parameter optimization problem, which can be solved efficiently using any gradient-based optimization technique. Then, a gradient-based stochastic search approach is proposed for solving this problem.Finally, a harvesting strategy problem is presented to illustrate the efficiency of the approach proposed.
This paper considers an optimal harvesting strategy problem arising in shrimp culture. The problem is formulated as an optimal control problem of nonlinear impulsive system. Since the impulsive switching constraints is very complex, the impulsive switching instants are unknown, and the objective function is not continuously differentiable, it is difficult to solve this problem by standard optimization methods. To overcome the difficulty, by introducing a novel binary variable for each sale price of shrimp, relaxing the binary variable, and imposing a penalty function on the relaxation term, the nonlinear impulsive system optimal control problem is transformed into a parameter optimization problem, which can be solved efficiently using any gradient-based optimization technique. Then, a gradient-based stochastic search approach is proposed for solving this problem.Finally, a harvesting strategy problem is presented to illustrate the efficiency of the approach proposed.
引文
[1]R.E.Brummett,Comparison of African tilapia partial harvesting systems,Aquaculture 214(1):103–114,2002.
[2]D.R.Teichert-Coddington,D.Martinez,E.Ramirez,Partial nutrient budgets for semi-intensive shrimp farms in Honduras,Aquaculture 190(1):139–154,2000.
[3]H.Lemonnier,S.Faninoz,Effect of water exchange on effluent and sediment characteristics and on partial nitrogen budget in semi-intensive shrimp ponds in New Caledonia,Aquaculture Res.37(9):938–948,2006.
[4]B.Hari,B.M.Kurup,J.T.Varghese,J.W.Schrama,M.C.J.Verdegem,The effect of carbohydrate addition on water quality and the nitrogen budget in extensive shrimp culture systems,Aquaculture 252(2):248–263,2006.
[5]J.P.Debenay,C.Marchand,N.Molnar,A.Aschenbroich,T.Meziane,Foraminiferal assemblages as bioindicators to assess potential pollution in mangroves used as a natural biofilter for shrimp farm effluents(New Caledonia).Mar.Pollut.Bull.93(1):103–120,2015.
[6]L.R.Martinez-Cordova,M.Emerenciano,A.Miranda-Baeza,M.Martinez-Porchas,Microbial-based systems for aquaculture of fish and shrimp:an updated review.Rev.Aquaculture7(2):131–148,2015.
[7]M.A.de Lorenzo,E.W.S.Candia,D.D.Schleder,P.C.Rezende,W.Q.Seiffert,F.do Nascimento Vieira,Intensive hatchery performance of Pacific white shrimp in the biofloc system under three different fertilization levels,Aquacultural Eng.72:40–44,2016).
[8]Q.Wang,D.Lu,Y.Fang,Stability analysis of impulsive fractional differential systems with delay.Appl.Math.Lett.40:1–6,2015.
[9]L.Lee,Y.Liu,J.Liang,X.Cai,Finite time stability of nonlinear impulsive systems and its applications in sampled-data systems.ISA Trans.57:172–178,2015.
[10]A.Ashyralyev,Y.A.Sharifov,Optimal control problems for impulsive systems with integral boundary conditions.Electronic J.Differ.Eq.80:1–11,2013.
[11]F.Taringoo,P.E.Caines,On the optimal control of impulsive hybrid systems on riemannian manifolds.SIAM J.Control Optim.51(4):3127–3153,2013.
[12]M.Claeys,D.Arzelier,D.Henrion,J.B.Lasserre,Measures and LMIs for impulsive nonlinear optimal control.IEEE Trans.Automat.Control,59(5):1374–1379,2014.
[13]X.Wu,K.Zhang,M.Cheng,Computational method for optimal machine scheduling problem with maintenance and production.Int.J.Prod.Res.2016,DOI:10.1080/00207543.2016.1245451.
[14]Y.Xiao,D.Cheng,H.Qin,Optimal impulsive control in periodic ecosystem.Syst.Control Lett.55(7):558–565,2006.
[15]C.Y.F.Ho,B.W.K.Ling,Y.Q.Liu,P.K.S.Tam,K.L.Teo,Optimal PWM control of switched-capacitor DC-DC power converters via model transformation and enhancing control techniques.IEEE Trans.Circuits Syst.55(5):1382-1391,2008.
[16]N.U.Ahmed,Existence of optimal controls for a general class of impulsive systems on Banach spaces.SIAM J.Control Optim.42(2):669–685,2003.
[17]A.Bressan Jr,F.Rampazzo,Impulsive control systems with commutative vector fields.J.Optim.Theory Appl.71(1):67–83,1991.
[18]V.Azhmyakov,V.G.Boltyanski,A.Poznyak,Optimal control of impulsive hybrid systems.Nonlinear Anal.Hybrid Syst.2(4):1089–1097,2008.
[19]G.N.Silva,R.B.Vinter,Necessary conditions for optimal impulsive control problems.SIAM J.Control Optim.35(6):1829–1846,1997.
[20]A.Arutyunov,D.Karamzin,F.Pereira,A nondegenerate maximum principle for the impulse control problem with state constraints.SIAM J.Control Optim.43(5):1812–1843,2005.
[21]A.V.Arutyunov,D.Y.Karamzin,F.Pereira,Pontryagins maximum principle for constrained impulsive control problems.Nonlinear Anal.Theory Methods Appl.75(3):1045–1057,2012.
[22]V.Dykhta,O.Samsonyuk,Some applications of Hamilton CJacobi inequalities for classical and impulsive optimal control problems.Eur.J.Control 17(1):55–69,2011.
[23]K.H.Wong,W.M.Tang,Optimal control of switched impulsive systems with time delay,ANZIAM J.53(04):292–307,2012.
[24]X.Wu,K.Zhang,C.Sun,Parameter tuning of multiproportional-integral-derivative controllers based on optimal switching algorithms.J.Optim.Theory Appl.159(2):454–472,2013.
[2]D.R.Teichert-Coddington,D.Martinez,E.Ramirez,Partial nutrient budgets for semi-intensive shrimp farms in Honduras,Aquaculture 190(1):139–154,2000.
[3]H.Lemonnier,S.Faninoz,Effect of water exchange on effluent and sediment characteristics and on partial nitrogen budget in semi-intensive shrimp ponds in New Caledonia,Aquaculture Res.37(9):938–948,2006.
[4]B.Hari,B.M.Kurup,J.T.Varghese,J.W.Schrama,M.C.J.Verdegem,The effect of carbohydrate addition on water quality and the nitrogen budget in extensive shrimp culture systems,Aquaculture 252(2):248–263,2006.
[5]J.P.Debenay,C.Marchand,N.Molnar,A.Aschenbroich,T.Meziane,Foraminiferal assemblages as bioindicators to assess potential pollution in mangroves used as a natural biofilter for shrimp farm effluents(New Caledonia).Mar.Pollut.Bull.93(1):103–120,2015.
[6]L.R.Martinez-Cordova,M.Emerenciano,A.Miranda-Baeza,M.Martinez-Porchas,Microbial-based systems for aquaculture of fish and shrimp:an updated review.Rev.Aquaculture7(2):131–148,2015.
[7]M.A.de Lorenzo,E.W.S.Candia,D.D.Schleder,P.C.Rezende,W.Q.Seiffert,F.do Nascimento Vieira,Intensive hatchery performance of Pacific white shrimp in the biofloc system under three different fertilization levels,Aquacultural Eng.72:40–44,2016).
[8]Q.Wang,D.Lu,Y.Fang,Stability analysis of impulsive fractional differential systems with delay.Appl.Math.Lett.40:1–6,2015.
[9]L.Lee,Y.Liu,J.Liang,X.Cai,Finite time stability of nonlinear impulsive systems and its applications in sampled-data systems.ISA Trans.57:172–178,2015.
[10]A.Ashyralyev,Y.A.Sharifov,Optimal control problems for impulsive systems with integral boundary conditions.Electronic J.Differ.Eq.80:1–11,2013.
[11]F.Taringoo,P.E.Caines,On the optimal control of impulsive hybrid systems on riemannian manifolds.SIAM J.Control Optim.51(4):3127–3153,2013.
[12]M.Claeys,D.Arzelier,D.Henrion,J.B.Lasserre,Measures and LMIs for impulsive nonlinear optimal control.IEEE Trans.Automat.Control,59(5):1374–1379,2014.
[13]X.Wu,K.Zhang,M.Cheng,Computational method for optimal machine scheduling problem with maintenance and production.Int.J.Prod.Res.2016,DOI:10.1080/00207543.2016.1245451.
[14]Y.Xiao,D.Cheng,H.Qin,Optimal impulsive control in periodic ecosystem.Syst.Control Lett.55(7):558–565,2006.
[15]C.Y.F.Ho,B.W.K.Ling,Y.Q.Liu,P.K.S.Tam,K.L.Teo,Optimal PWM control of switched-capacitor DC-DC power converters via model transformation and enhancing control techniques.IEEE Trans.Circuits Syst.55(5):1382-1391,2008.
[16]N.U.Ahmed,Existence of optimal controls for a general class of impulsive systems on Banach spaces.SIAM J.Control Optim.42(2):669–685,2003.
[17]A.Bressan Jr,F.Rampazzo,Impulsive control systems with commutative vector fields.J.Optim.Theory Appl.71(1):67–83,1991.
[18]V.Azhmyakov,V.G.Boltyanski,A.Poznyak,Optimal control of impulsive hybrid systems.Nonlinear Anal.Hybrid Syst.2(4):1089–1097,2008.
[19]G.N.Silva,R.B.Vinter,Necessary conditions for optimal impulsive control problems.SIAM J.Control Optim.35(6):1829–1846,1997.
[20]A.Arutyunov,D.Karamzin,F.Pereira,A nondegenerate maximum principle for the impulse control problem with state constraints.SIAM J.Control Optim.43(5):1812–1843,2005.
[21]A.V.Arutyunov,D.Y.Karamzin,F.Pereira,Pontryagins maximum principle for constrained impulsive control problems.Nonlinear Anal.Theory Methods Appl.75(3):1045–1057,2012.
[22]V.Dykhta,O.Samsonyuk,Some applications of Hamilton CJacobi inequalities for classical and impulsive optimal control problems.Eur.J.Control 17(1):55–69,2011.
[23]K.H.Wong,W.M.Tang,Optimal control of switched impulsive systems with time delay,ANZIAM J.53(04):292–307,2012.
[24]X.Wu,K.Zhang,C.Sun,Parameter tuning of multiproportional-integral-derivative controllers based on optimal switching algorithms.J.Optim.Theory Appl.159(2):454–472,2013.
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