Equilibrium Strategy and Application of Pareto Cooperative Game With Linear Quadratic Positive System

In this study, we study the equilibrium strategy of a Pareto cooperative differential game with a continuous-time linear positive system in the infinite time domain and a quadratic performance index. In view of the deterministic linear feedback strategy of the gamer strategy and the situation of only two players and multiple players, the equilibrium problem of the Pareto cooperative game in the corresponding situation is studied. The main results are as follows: First, the stability conditions of the corresponding deterministic feedback system under the deterministic feedback strategy of two players and multiple players are studied, and the existence conditions of the equilibrium deterministic closed-loop feedback strategy of Pareto cooperative differential game and the optimal performance index values of the corresponding deterministic feedback control system are obtained, respectively. Second, the conditions for the existence of non-negative solutions of the Pareto equilibrium solutions of positive systems are updated. In addition, a numerical simulation of the deterministic feedback strategy is carried out using a four-dimensional numerical example, which shows the effectiveness of the conclusions. Finally, the application of the Pareto equilibrium strategy in water pollution control cases is confirmed by studying the application of Pareto equilibrium strategy with certainty feedback.