Adaptive Synchronization for Generalized Lorenz Systems

Abstract

(15) can be stabilized by the proposed hybrid output feedback control scheme for a wide range of variations in the detecting time . IV. CONCLUDING REMARKSIn this note, a new hybrid output feedback control scheme was proposed to stabilize a class of continuous-time LTI systems with single output. The arguments were based on the multirate sampling technique and the Multiple-Lyapunov-Function theorem. While this note focused only on the single output case, the proposed design procedure could be extended to the case of multi-output (i.e., p > 1) without essential changes. In addition, the multirate sampling scheme can be extended via detecting the output y(t) more than once within a sampling period T s , e.g., over a sequence of detecting time 0 < 1 < 2 < 1 1 1 < k < Ts. Then, with more information on y(t), it becomes possible to further partition the state space and design more multiple-output feedback gains correspondingly, and hence improve the chance to stabilize the system. A natural question is how generic the method could be. We ask whether it is always possible to find a pair of sampling period T s and detecting time (or a sequence of detecting time 0 < 1 < 2 < 1 1 1 < k < Ts) such that the system (assumed to be reachable and observable) can be stabilized by the proposed multiple SOF controller scheme. Adaptive Synchronization for Generalized Lorenz SystemsXiyin Liang, Jiangfeng Zhang, and Xiaohua Xia Abstract-In literature it is conjectured that the states of the generalized Lorenz system with an unknown parameter can not be estimated by adaptive observers. In this paper we show that this unknown parameter and the states can actually be estimated simultaneously by some kind of adaptive observer. The proof is obtained by constructing some exponential observer to achieve chaotic synchronization for the generalized Lorenz system. The result implies that more work needs to be done to apply generalized Lorenz system in secure communication.

Design of hybrid controller for synchronization control of Chen chaotic system

“…Chaotic systems are nonlinear aperiodic systems with high sensitivity to initial conditions which leads to unpredictability of its long term dynamic behavior. Chen system, was found by Chen and Ueta in 1999 [2], which is similar but topological nonequivalent to Lorenz-like systems, such as Chua's circuit [3], Lü system [22], and the Lorenz system family [20].…”

Robust control with disturbance observer for UAV translational tracking

“…For MIMO linear systems , assuming detectability as well as the presence of a persistently exciting signal one may basically conclude that both, the state and the perturbation can asymptotically be estimated . [4] - [5].…”

A nonlinear adaptive observer with excitation-based switching

“…An alternative method used to design observers for system that cannot be recast in the canonical observer form by trivial state transformations consists in augmenting the dynamics of the observer with a filter, that takes as input the parameter-affine nonlinear function (see e.g. [6], [7] and [8]). We refer in particular to those systems in which the parameter-affine term does not only depend on measurable inputs and outputs but also on hidden (although observable) state variables (see e.g.…”

“…Under the same assumptions of Lelmna 3.1 and 3.2, consider the adaptive observer (2), (6), (7),(8) equipped with the excitation level-based switching strategy defined in (9) so as any excitation phase D.Te lasts longer than (31 1 In( Lo). Then, the discrete dynamics induced by sampling the adaptive observer in correspondence of the switching transitions has the asymptotic ISS property.DProof By the Gronwall-Bellman Lemma, the value of the Lyapunov function within the dis-excitation intervals can be bounded as follows:…”