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A purely adaptive controller to synchronize and control chaotic systems
No full textFollowing the work presented by the author in a previous paper, a model reference adaptive controller, which requires minimal knowledge of the system structures, is synthesized to control or synchronize chaotic systems. This is achieved by exploiting the boundedness of chaotic evolutions. Moreover, when the linear term of the error equation is characterized by a Hurwitz matrix, the control law is reduced to a pure discontinuous action, whose amplitude is adaptively estimated. The method is applied to the control of a Lorenz system and the synchronization of two dentical Chua circuit
Normal forms of border collision in high dimensional non-smooth maps
No full textThis paper is concerned with the derivation of normal form maps associated to border-collision events in n-dimensional piecewise smooth discrete systems. It is shown that these maps can be put in a standard form by means of appropriate coordinate transformations which reduces, in the two-dimensional case, to the border-collision normal form map studied by Yorke et al. (1994). This represents a key step towards the derivation of a general classification of border-collisions in high-dimensional systems
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