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Optimal control on hybrid ODE Systems with application to a tick disease model
1.  Department of Mathematics, University of Tennessee, 1403 Circle Drive, Knoxville, TN 379961300, United States 
[1] 
Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control and Related Fields, 2018, 8 (3&4) : 809828. doi: 10.3934/mcrf.2018036 
[2] 
Lukáš Adam, Jiří Outrata. On optimal control of a sweeping process coupled with an ordinary differential equation. Discrete and Continuous Dynamical Systems  B, 2014, 19 (9) : 27092738. doi: 10.3934/dcdsb.2014.19.2709 
[3] 
Hongwei Lou, Weihan Wang. Optimal blowup/quenching time for controlled autonomous ordinary differential equations. Mathematical Control and Related Fields, 2015, 5 (3) : 517527. doi: 10.3934/mcrf.2015.5.517 
[4] 
Zhenyu Lu, Junhao Hu, Xuerong Mao. Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations. Discrete and Continuous Dynamical Systems  B, 2019, 24 (8) : 40994116. doi: 10.3934/dcdsb.2019052 
[5] 
Wei Mao, Yanan Jiang, Liangjian Hu, Xuerong Mao. Stabilization by intermittent control for hybrid stochastic differential delay equations. Discrete and Continuous Dynamical Systems  B, 2022, 27 (1) : 569581. doi: 10.3934/dcdsb.2021055 
[6] 
Sébastien Court, Karl Kunisch, Laurent Pfeiffer. Hybrid optimal control problems for a class of semilinear parabolic equations. Discrete and Continuous Dynamical Systems  S, 2018, 11 (6) : 10311060. doi: 10.3934/dcdss.2018060 
[7] 
JanHendrik Webert, Philip E. Gill, SvenJoachim Kimmerle, Matthias Gerdts. A study of structureexploiting SQP algorithms for an optimal control problem with coupled hyperbolic and ordinary differential equation constraints. Discrete and Continuous Dynamical Systems  S, 2018, 11 (6) : 12591282. doi: 10.3934/dcdss.2018071 
[8] 
Yuriy Golovaty, Anna MarciniakCzochra, Mariya Ptashnyk. Stability of nonconstant stationary solutions in a reactiondiffusion equation coupled to the system of ordinary differential equations. Communications on Pure and Applied Analysis, 2012, 11 (1) : 229241. doi: 10.3934/cpaa.2012.11.229 
[9] 
Nguyen Thi Hoai. Asymptotic approximation to a solution of a singularly perturbed linearquadratic optimal control problem with secondorder linear ordinary differential equation of state variable. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 495512. doi: 10.3934/naco.2020040 
[10] 
Bernard Dacorogna, Alessandro Ferriero. Regularity and selecting principles for implicit ordinary differential equations. Discrete and Continuous Dynamical Systems  B, 2009, 11 (1) : 87101. doi: 10.3934/dcdsb.2009.11.87 
[11] 
Zvi Artstein. Averaging of ordinary differential equations with slowly varying averages. Discrete and Continuous Dynamical Systems  B, 2010, 14 (2) : 353365. doi: 10.3934/dcdsb.2010.14.353 
[12] 
Yong Ren, Qi Zhang. Stabilization for hybrid stochastic differential equations driven by Lévy noise via periodically intermittent control. Discrete and Continuous Dynamical Systems  B, 2022, 27 (7) : 38113829. doi: 10.3934/dcdsb.2021207 
[13] 
Hai Huang, Xianlong Fu. Optimal control problems for a neutral integrodifferential system with infinite delay. Evolution Equations and Control Theory, 2022, 11 (1) : 177197. doi: 10.3934/eect.2020107 
[14] 
ȘtefanaLucia Aniţa. Optimal control for stochastic differential equations and related Kolmogorov equations. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022023 
[15] 
Tomasz Kapela, Piotr Zgliczyński. A Lohnertype algorithm for control systems and ordinary differential inclusions. Discrete and Continuous Dynamical Systems  B, 2009, 11 (2) : 365385. doi: 10.3934/dcdsb.2009.11.365 
[16] 
Holly Gaff. Preliminary analysis of an agentbased model for a tickborne disease. Mathematical Biosciences & Engineering, 2011, 8 (2) : 463473. doi: 10.3934/mbe.2011.8.463 
[17] 
Shangbing Ai. Global stability of equilibria in a tickborne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567572. doi: 10.3934/mbe.2007.4.567 
[18] 
Serge Nicaise. Stability and asymptotic properties of dissipative evolution equations coupled with ordinary differential equations. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021057 
[19] 
Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discretetime state observations. Discrete and Continuous Dynamical Systems  B, 2017, 22 (1) : 209226. doi: 10.3934/dcdsb.2017011 
[20] 
Djamila Moulay, M. A. AzizAlaoui, HeeDae Kwon. Optimal control of chikungunya disease: Larvae reduction, treatment and prevention. Mathematical Biosciences & Engineering, 2012, 9 (2) : 369392. doi: 10.3934/mbe.2012.9.369 
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