Abstract
Previous works by these authors offer the numerical method of successive approximations for developing the solutions of the problem of stabilization of nonlinear systems with standard functional. This paper considers applying this method for studying the problem with singular control. It is achieved by introducing an auxiliary problem. The solution for the auxiliary problem provides a smooth approximation to the solution of the initial problem. The paper presents the algorithms for constructing an approximate solution for the initial problem. It is demonstrated that unlike direct algorithms of optimal control, these algorithms allow registering the saturation point, thus enabling one to register and study singular regimes.
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This research was supported by the Russian Science Foundation, grant no. 16-11-10352.
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Afanas’ev, A.P., Dzyuba, S.M., Emelyanova, I.I., Putilina, E.V. (2019). Numerical Implementation of the Contact of Optimal Trajectory with Singular Regime in the Optimal Control Problem with Quadratic Criteria and Scalar Control. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_17
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