Identifiability and identification of chaotic systems based on adaptive synchronization

Abstract

Abstract-This paper deals with the problem of synchronization of chaotic systems when the driven (slave, receiver) system has the same structure as the master (driving, emitter) system but its parameters are unknown. It is shown that the concept of synchronization provides an efficient way to find the unknown slave system parameters. Parameter mismatch between master and slave systems and high sensitivity of response to changes of these parameters were so far considered as crucial for security issues. This paper shows evidence that this claimed advantage becomes in fact a major drawback in chaos communication schemes since parameters can easily be found using adaptive synchronization and optimization tools. The general problem of identifiability of chaotic systems is defined and discussed in the context of possibilities for finding the unknown chaotic receiver parameters. Several typical systems used in experiments in chaos communication are tested for identifiability showing direct applications of the introduced concepts. In particular examples of the skew tent map, Hénon map, Markov maps and Chua's circuit are considered in detail illustrating the problems of global and local identifiability.

Circadian Phase Control Using Adaptive Synchronization

“…The typical chaos synchronization involving master-slave configuration was firstly introduced in Pecora and Carroll (1990). This concept was then applied for phase control problem in Pecora and Carroll (1993) and was developed for chaos synchronization with unknown parameters in Dedieu and Ogorzalek (1997); Fradkov and Pogromsky (1996); Chen and Jinhu (2002) . This paper investigates the phase control problem where the control law has more restriction.…”

Finite-time synchronization between two complex-variable chaotic systems with unknown parameters via nonsingular terminal sliding mode control

“…A fundamental scheme of chaos synchronization is the drive-response configuration, and the output of the response system should track the drive system asymptotically. Several control techniques have been investigated to realize chaos synchronization such as OGY method [1], feedback control method [2,3], active control method [4], backstepping method [5], adaptive control method [6][7][8][9][10][11][12][13], impulsive control method [14,15], coupling control method [16][17][18], sliding control method [19] and switching control method [20][21][22][23].…”

State and parameter estimation in nonlinear systems as an optimal tracking problem

“…The synchronization of the experimental data with the model system has been suggested as a way to incorporate experimental information into the model, see, e.g., [1][2][3][4][5][6][7][8][9][10]. Synchronization shows promise in enabling the desired estimation, but there are important issues associated with the selection of the coupling strength of the data into the model.…”