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Ushakov, Vladimir N.; Ershov, Aleksandr A.; Ushakov, Andrey V.; Kuvshinov, Oleg A.

Control system depending on a parameter. (English) Zbl 1471.93135

Ural Math. J. 7, No. 1, 120-159 (2021).
Summary: A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.

Cited in 3 Documents

MSC:

93C10 Nonlinear systems in control theory
93B03 Attainable sets, reachability
93C15 Control/observation systems governed by ordinary differential equations

Keywords:

control system; differential inclusion; reachable set; integral funnel; parameter dependence; approximation
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\textit{V. N. Ushakov} et al., Ural Math. J. 7, No. 1, 120--159 (2021; Zbl 1471.93135)
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