Construction of Optimal Control Laws for a Model of Information Diffusion in a Social Group
Tóm tắt
The article investigates a modified model of information propagation (diffusion). The model differs from the original model [2] by the choice of the optimized functional. The one-dimensional nonlinear optimal control problem is posed and solved by the Pontryagin maximum principle. It is shown that the optimal control is a relay function of time with at most one switching point. For some particular cases, the optimal-control switching point allows an explicit analytical description in terms of the problem parameters. In the general case, the optimal solution can be constructed by solving numerically the maximum-principle boundary-value problem. A one-dimensional convex minimization problem on a finite time interval (the planning horizon) is suggested for finding the optimal-control switching point. Easily verified condition on the problem parameters are given, guaranteeing the existence of the optimalcontrol switching point.
Tài liệu tham khảo
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