## Optimal control of averaged state of a population dynamics model.(English)Zbl 1481.49006

N’Guérékata, Gaston M. (ed.) et al., Studies in evolution equations and related topics. Cham: Springer. STEAM-H, Sci. Technol. Eng. Agric. Math. Health, 113-127 (2021).
Summary: In this chapter, we study the average control of a population dynamic model with age dependence and spatial structure in a bounded domain $$\Omega \subset \mathbb{R}^3$$. We assume that we can act on the system via a control in a sub-domain $$\omega$$ of $$\Omega$$. We prove that we can bring the average of the state of our model at time $$t = T$$ to a desired state. By means of Euler-Lagrange first-order optimality condition, we expressed the optimal control in terms of average of an appropriate adjoint state that we characterize by an optimality system.
For the entire collection see [Zbl 1476.34004].

### MSC:

 49J20 Existence theories for optimal control problems involving partial differential equations 92D25 Population dynamics (general) 35Q93 PDEs in connection with control and optimization 93C05 Linear systems in control theory
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### References:

 [1] B. Ainseba; S. Anita and M. Langlais,On the optimal control for nonlinear age-structured population dynamic model, Electronic J. Diff. Eq., 28(2002), 1-9. · Zbl 1016.92026 [2] A. Hafdallah, A. Ayadi , Optimal control of electromagnetic wave displacement with an unknown velocity of propagation, International Journal of Control, 92(2018), 2693-2700. · Zbl 1425.93130 [3] C. Kenne, G. Leugering, and G. Mophou, Optimal control of a population dynamics model with missing birth rate, SIAM J. Control Optim., 58 (2020), 1289-1313. · Zbl 1453.49004 [4] M. Langlais, Solutions fortes pour une classe de problèmes aux limites dégénérés, Comm. in Partial Differential Equations 4 (8)(1979), 869-897. · Zbl 0438.35032 [5] M. Lazar, E. Zuazua , Averaged control and observation of parameter-depending wave equations, Comptes Rendus Mathématique, 352(2014), 497-502. · Zbl 1302.35043 [6] J. Lohéac, & E. Zuazua, Averaged controllability of parameter dependent conservative semigroups, Journal of Differential equations, 262(2017), pp. 1540-1574. · Zbl 1352.93025 [7] Q. Lu, & E. Zuazua, Averaged controllability for random evolution partial differential equations, Journal de Mathématiques Pures et Appliquées, 105(2016), 367-414. · Zbl 1332.93058 [8] G. Mophou, R. G. F. Tiomela & A. Seibou, Optimal control of averaged state of a parabolic equation with missing boundary condition, International Journal of Control, (2018), https://doi.org/10.1080/00207179.2018.1556810. · Zbl 1453.49005 [9] A. Ouedraogo and O. Traoré, Optimal control for a nonlinear population dynamics problem, Portugaliae Mathematica, 62(2005), 217-229. · Zbl 1082.92038 [10] E. Zuazua, Averaged control, Automatica, 50(2014), 3070-3087 · Zbl 1309.93029
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