Control of a non-holonomic mobile robot system with parametric uncertainty

In this paper, the control of a mobile robot system via a feedback linearization controller and anti-control of chaos with parametric uncertainty is researched. Anti-control is also applied to convert non-chaotic systems to chaotic ones and to create chaos dynamic. The synchronization of system errors with a chaotic gyroscope system is researched for energy reduction and performance improvement. In the other words, control effort is based on synchronizing the error system with chaos for decreasing control cost. The combination of these techniques yields high efficiency and global convergence of trajectories, even in the presence of parametric uncertainty, which has been shown by simulation. Finally, the energy of control signals is calculated and compared for showing the energy reduction

Adaptive sliding mode observers in uncertain chaotic cryptosystems with a relaxed matching condition

We study the performance of adaptive sliding mode observers in chaotic synchronization and communication in the presence of uncertainties. The proposed robust adaptive observer-based synchronization is used for cryptography based on chaotic masking modulation (CM). Uncertainties are intentionally injected into the chaotic dynamical system to achieve higher security and we use robust sliding mode observer design methods for the uncertain nonlinear dynamics. In addition, a relaxed matching condition is introduced to realize the robust observer design. Finally, a Lorenz system is employed as an illustrative example to demonstrate the effectiveness and feasibility of the proposed cryptosyste

Synchronization universality classes and stability of smooth, coupled map lattices

We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic behavior implies that the synchronization transition belongs to the multiplicative noise universality class, while stable chaos implies that the synchronization transition belongs to the directed percolation universality class.Comment: 6 pages, 7 figure

Synchronization Limits of Chaotic Circuits

Through system modeling with electronic circuits, two circuits were constructed that exhibit chaos over a wide ranges of initial conditions. The two circuits were one that modeled an algebraically simple “jerk” function and a resistor-inductor-diode (RLD) circuit where the diode was reverse-biased on the positive voltage cycle of the alternating current source. Using simulation data from other experiments, the waveforms, bifurcation plots, and phase space plots of the concrete circuit were verified. Identical circuits were then built containing variable components and coupled to their original, matching circuits. The variable components were used to observe a wide range of conditions to establish the desynchronization parameters and the range of synchronization

Robust synchronization for 2-D discrete-time coupled dynamical networks

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany