Robust Adaptive Modified Projective Synchronization of Chaotic Complex Systems with Disturbances

The modified projective synchronization (MPS), is also called the full state hybrid projective synchronization (FSHPS), which was proposed in [98]. The Lyapunov’s direct method has been used to realize MPS of two identical chaotic [98] and hyperchaotic [99] real systems. Notably, in many practical situations, the system parameters or even system models may be perturbed and cannot be known exactly in priority. Therefore, the adaptive control scheme [100–107], which has been widely used for chaos synchronization, is an effective method to synchronize two uncertain chaotic systems in sense of MPS. For example, the adaptive control method has been used to achieve MPS of chaotic (hyperchaotic) real systems with unknown parameters [102] and synchronized two different uncertain chaotic (hyperchaotic) real systems with the same and different order in sense of MPS [103], separately. This section is divided into two subsections, covering the definition of MPS for chaotic complex systems and the realization of robust adaptive MPS.