Abstract
The paper is devoted to investigation of game problems on bringing a trajectory of dynamic system to a cylindrical terminal set. We proceed with representation of a trajectory of dynamic system in the form, in which the block of initial data is separated from the control block. This makes it feasible to consider a wide spectrum of functional-differential systems. The method of resolving functions, based on use of the inverse Minkovski functionals, serves as ideological tool for study. Attention is focused on the case when Pontryagin’s condition does not hold. In this case the upper and lower resolving functions of two types are introduced. With their help sufficient conditions of approach a terminal set in a finite time are deduced. Various method schemes are provided and comparison with Pontryagin’s first direct method is given. Efficiency of suggested mathematical scheme is illustrated with a model example.
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Chikrii, A.A., Petryshyn, R., Cherevko, I., Bigun, Y. (2019). Method of Resolving Functions in the Theory of Conflict—Controlled Processes. In: Kondratenko, Y., Chikrii, A., Gubarev, V., Kacprzyk, J. (eds) Advanced Control Techniques in Complex Engineering Systems: Theory and Applications. Studies in Systems, Decision and Control, vol 203. Springer, Cham. https://doi.org/10.1007/978-3-030-21927-7_1
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