Optimal control of phytoplankton–fish model with the impulsive feedback control

Translation, solving scheme, and implementation of a periodic and optimal impulsive state control problem

“…From Theorems 3.1 and 4.3 in [11], it is obtained that for fixed (p 0 , z 0 ) system (4.1) has an OOPS A→B from A((1e 1 )p 1 , (1e 2 )H) to B(e 1 , H). Then Zhao et al [11] formulated an OCP and strived to seek the appropriate harvesting rates e * 1 and e * 2 to maximize the cost function J(e 1 , e 2 ) = C 1 e 1 p 1 + C 2 e 2 H in an impulsive period. C 1 and C 2 describe the prices per unit biomass of the phytoplankton and fish, respectively.…”

“…In our paper, based on the periodic solution theory in [11], we know that the resources are exploited in a period mode. Then, what strategies are implemented to optimize the cost function at the minimal cost?…”

“…The topic about impulsive state feedback controls (abbreviated as ISFC) has been investigated extensively in the last decades due to its potential applications in culturing microorganisms [1][2][3], pest integrated management [4][5][6], disease control [7,8], fish harvesting [9][10][11], and wildlife management [12,13]. For example, [1] proposed a bioprocess model with ISFC to acquire an equivalent stable output by the precise feeding.…”

“…Ref. [11] proposed a phytoplankton-fish model with ISFC and then formulated an optimal control problem (OCP, for short) and strived to find the appropriate harvesting rates to maximize the cost function in an impulsive period. Here, the solvability of the system in one period provides convenience for solving the OCP by Lagrange multiplier.…”

Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control

“…In mathematics, impulsive differential equations (IDES) is such a powerful tool to describe these phenomena that rapid changes in biological populations are caused by the variety of the pests control by artificial intervention [12][13][14][15][16][17][18][19][20][21][22]. In recent years, the theoretical studies on IDES have produced a lot of good research results [23][24][25][26][27][28][29][30][31][32][33][34]. Based on the theoretical research, some scholars have introduced impulsive differential equations in Lotka-Volterra system such as the regular release of predators [35][36][37]; the periodic release of infected pests [38][39][40]; the periodic release of predators together with regular spray of pesticides [41][42][43]; the periodic release of predators and infected pests together with regular spray of pesticides [39,44].…”