In this paper the method of solving a terminal continuous linear quadratic optimal control problem using the penalty functions method is transferred to a weakly nonlinear continuous formulation using the SDRE approach technique. The applicability of this approach to a terminal discrete linear quadratic optimal control problem is also demonstrated. In addition, it is shown that it is possible to improve the accuracy of phase constraints satisfaction using the Richardson extrapolation procedure.
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Yulia Danik, Mikhail Dmitriev, Dmitry Makarov. A penalty functions method for feadback control design in terminal weakly nonlinear optimal control problems // Proceedings of the 8th International School-Seminar on Nonlinear Analysis and Extremal Problems (NLA-2024). Irkutsk, Russia, June 24–28, 2024. Irkutsk : ISDCT SB RAS, 2024, pp. 56–58.