Generalized projective synchronization for a class of chaotic systems with parameter mismatching, unknown external excitation, and uncertain input nonlinearity

In this paper, the concept of the generalized projective synchronization in practical type (GPSPT) is introduced and the GPSPT of uncertain horizontal platform systems with parameter mismatching, unknown external excitation, and uncertain input nonlinearity is investigated. Based on the differential inequality methodology, a tracking control is proposed to realize the GPSPT for the uncertain horizontal platform systems with parameter mismatching, unknown external excitation, and uncertain input nonlinearity. Not only the desired scaling factor, the guaranteed exponential convergence rate, and convergence radius can be pre-specified, but also the parameter mismatching and unknown external excitation can be simultaneously conquered by the proposed control. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result.