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Message Embedded Synchronization for the Generalized Lorenz System and Its Use for Chaotic Masking
Čelikovský, Sergej ; Lynnyk, Volodymyr
This paper implements and analyzes the well-known message embedded synchronization scheme for the case of the generalized Lorenz system. Such a synchronization may be used for chaotic masking scheme using a single channel only. This method was already discussed in the earlier literature for the particular classes of systems. In this paper, a more general class wheremessage embedded synchronization is possible is described. Then, it is shown that the generalized Lorenz system falls within that class. Furthermore, using the resulting synchronization, the novel secure encryption scheme is proposed. It requires very reasonable amount of data to encrypt and time to decrypt one bit. Basically, to encrypt one bit, only one iteration (i.e. only one real number of 6 valid digits) is needed. At the same time, 100 percent of the carrying chaotic signal can be used. The method is also demonstrated by numerical simulations of a digital data encryption and decryption.
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Microalgal Growth Problem for the Photosynthetitc Factory and its Optimization: An Overview and Further Analysis
Čelikovský, Sergej
The overview of the micro-algal growth problem for the photosynthetic factory and its optimal control solution is presented here. First, the model description and its properties like Haldan steady state dynamics, light integration property and the forward invariance of the set of biologically well-de ned states are described. This shows that the model meets basic experimentally based requirements. Further, its optimal control problem is formulated and solved analytically for the one dimensional singular perturbation based reduction. Properties of the optimal control for the reduced model are discussed and compared with some experimental observations. Among them, the general biotechnological paradigm that on large time intervals the optimal solution is, in certain sense, almost constant, is substantiated. As a new original result of this paper, the explicit solvable di erentiable equation for the unsaturated part of the optimal control is derived.
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Comparison of Nonlinear Observers for Underactuated Mechanical Systems
Anderle, Milan ; Čelikovský, Sergej
This paper provides the comparison of nonlinear observers for underactuated mechanical systems with aplication to Acrobot walking. Namely, it aims to compare a reduced observer for the Acrobot angular velocities based on the respective angles measurements with a observer for the Acrobot angular velocity and angle based on the other angular velocity and angle measurement and then to combine this observers with the earlier developed full state feedback controllers. For the Acrobot it is not possible to measure the angle between its stance leg and the surface directly because this angle is underactuated. One possibility of measuring this angle is using laser beam sensor and then computation the stance angle from that distance. Main disadvantage of this approach is the high price of the laser beam sensor. The other observer is based on angular velocity of stance leg measurement using the digital gyroscope.
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Porovnání analytických a numerických metod v oblasti řízení Acrobota
Anderle, M. ; Čelikovský, Sergej
This paper aims to compare the performance of various techniques for the stabilization of the error dynamics of the Acrobot’s walking like reference trajectory. Both the walking reference planning and the tracking feedback design are based on the Acrobot’s model partial exact feedback linearization of order 3. Namely, such an exact system transformation leads to an almost linear system where error dynamics along trajectory to be tracked is a 4 dimensional linear time varying system having 3 time varying entries only, the remaining entries are either zero or equal to one.
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