A Nussbaum gain adaptive synchronization of a new hyperchaotic system with input uncertainties and unknown parameters

The sign of unknown input coefficients is assumed to be known in most papers about the input uncertainties. In this paper, a Nussbaum gain method is adopted to cope with the situation that both the sign and the value of input are unknown. And the unknown parameters can be estimated under the situation of unknown sign of control. The synchronization is achieved for a class of hyperchaotic systems with unknown parameters and input uncertainties by adopting of the Nussbaum gain method and the global terminal adaptive method. And the conclusions are made as follows: First, the proposed method is effective in the situation that the sign of input is unknown. Second, the estimation of unknown parameters can be achieved only when the number of unknown parameters satisfied some condition and no uncertainty exist in the input of systems. Third, the unknown parameters cannot be estimated correctly with common adaptive method when there are input uncertainties in the system. But the Nussbaum gain method can get good result in the estimation of unknown parameters. At last, numerical simulations are done to show the effectiveness of the proposed method.