Synthesis of Multimode Control Laws Under Disturbances Conditions Based on the Condition for Maximum of the Generalized Power Function in Automation Problems

The problem of optimal control of a nonlinear system under conditions of regular disturbances is considered. It is shown that changing the switching line makes it possible to increase the performance indicators in comparison with the solution obtained on the basis of the game approach. The possibility to improve performance indicators can be explained by the fact that the game solution is determined by the worst cases of disturbances that counteract the control. The paper presents a comparative analysis of the proposed solution with traditional control laws using the example of control of an unstable nonlinear system of the inverted pendulum type. The implementation of the proposed multi-mode control law in the control problems of complex technological processes makes it possible to increase their efficiency in terms of various indicators. Acknowledgments: The reported study was funded by RFBR, project number 19–31-90134.