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Optimal control methodology for the counter-terrorism strategies: the relaxation based approach. (English) Zbl 1496.91042

Summary: This paper deals with a novel application of the advanced optimal control techniques to a counter-terrorism optimal decision-making problem. The recently developed model of the counter-terrorism security policies (see [L. Armijo, Pac. J. Math. 16, 1–3 (1966; Zbl 0202.46105)]) naturally incorporates a competing interest group dynamics. The optimal dynamics can be found in this case by considering a specific optimal control problem. in our work we propose an essential formal improvement of the above applied optimal control problem and its numerical treatment. We formulate a suitable phase-constrained optimal control problem for the initial counter-terrorism model and study a specific relaxation of this model. The proposed \(\beta\)-relaxation approach makes it possible to eliminate some model inconsistencies and to design an optimal counter-terrorism strategy. We develop a new numeric algorithm for the improved dynamic optimization problem. We next study some analytic properties of this algorithm. The resulting computational technique involves a gradient based method in combination with the proposed relaxation scheme (see [V. Azhmyakov and W. Schmidt, J. Optim. Theory Appl. 130, No. 1, 61–77 (2006; Zbl 1135.49020)]). The obtained numerical approach is finally applied to an illustrative example.

MSC:

91B06 Decision theory
49N90 Applications of optimal control and differential games
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