Research on Bounded Nussbaum Gain Adaptive Method

For common Nussbaum gain method, there exists a disadvantage that the nonlinear gain of the controller is unbounded essentially, which will cause many weaknesses because of the high gain of the controller. A new concept, which is called bounded Nussbaum gain function, is firstly proposed in this paper. What is different from the common Nussbaum gain function is that it can reduce the gain of the whole controller. And even better than that, it can ensure the gain of the controller is bounded. So the gain of the whole system can be controlled as small as possible, which is meaningful for the realization of many controllers in many actual nonlinear physical systems. Also, the new Nussbaum gain function is applied in a one order control system to give a example. Finally, The stability of the control system with the new Nussbaum function is proved and the simulation is done to testify the rightness and effectiveness of the new method.