### A general synchronization method of chaotic communication systems via Kalman filtering

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With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity....

This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained...

Let $L:{\mathbb{R}}^{N}\times {\mathbb{R}}^{N}\to \mathbb{R}$ be a borelian function and consider the following problems$$inf\left\{F\left(y\right)={\int}_{a}^{b}L(y\left(t\right),{y}^{\text{'}}\left(t\right))\phantom{\rule{0.166667em}{0ex}}\mathrm{d}t:\phantom{\rule{0.166667em}{0ex}}y\in AC([a,b],{\mathbb{R}}^{N}),y\left(a\right)=A,\phantom{\rule{0.166667em}{0ex}}y\left(b\right)=B\right\}\phantom{\rule{2.0em}{0ex}}\phantom{\rule{1.0em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\left(P\right)$$$$\phantom{\rule{-17.07182pt}{0ex}}inf\left\{{F}^{...}\right\}$$

Let $L:{\mathbb{R}}^{N}\times {\mathbb{R}}^{N}\to \mathbb{R}$ be a Borelian function and consider the following problems $$inf\left\{F\left(y\right)={\int}_{a}^{b}L(y\left(t\right),{y}^{\text{'}}\left(t\right))\phantom{\rule{0.166667em}{0ex}}\mathrm{d}t:\phantom{\rule{0.166667em}{0ex}}y\in AC([a,b],{\mathbb{R}}^{N}),y\left(a\right)=A,\phantom{\rule{0.166667em}{0ex}}y\left(b\right)=B\right\}\phantom{\rule{2.0em}{0ex}}\phantom{\rule{1.0em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\left(P\right)$$ $$inf\left\{{F}^{**}\left(y\right)={\int}_{a}^{b}{L}^{**}(y\left(t\right),{y}^{\text{'}}\left(t\right))\phantom{\rule{0.166667em}{0ex}}\mathrm{d}t:\phantom{\rule{0.166667em}{0ex}}y\in AC([a,b],{\mathbb{R}}^{N}),y\left(a\right)=A,\phantom{\rule{0.166667em}{0ex}}y\left(b\right)=B\right\}\xb7\phantom{\rule{1.0em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\left({P}^{**}\right)$$ We give a sufficient condition, weaker then superlinearity, under which $infF=inf{F}^{**}$ if L is just continuous in x. We then extend a result of Cellina on the Lipschitz regularity of the minima of (P) when L is not superlinear.

In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control...

We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the...

Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...

Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states....

Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for...