This paper reports a new 3-dimensional autonomous chaotic system with four nonlinearities. The system is studied with respect to its numerical solutions in phase space, including sensitive dependence on initial conditions, equilibrium points, bifurcation, and maximal Lyapunov exponent. It is shown that the system is dissipative and has a fractional Lyapunov dimension. Besides, a basin of attraction is determined by the Newton-Raphson's method. To show its practicality, the new system is implemented by means of an analog electronic circuit. Aperiodicity of the experimental signal is verified by means of an improved power spectral density estimator, viz., the Welch's method. Also, the correlation dimension is estimated from the experimental time series with the result confirming that the responses are deterministic chaos. Finally, an electronic design of a secure communication application is carried out, wherein a nontrivial square wave is modulated by a master chaotic signal. The modulated signal is subsequently recovered by a slave system, and the fast convergence to zero of the information recovery error substantiates the effectiveness of the design.

No abstract

This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.

In this study, a neuro-controller with adaptive deadzone compensation for a class of unknown SISO non-linear systems in a Brunovsky form with uncertain deadzone input is presented. Based on a proper smooth parameterisation of the deadzone, the unknown dynamics is identified by using a continuous time recurrent neural network whose weights are adjusted on-line by stable differential learning laws. On the basis of this neural model so obtained, a feedback linearisation controller is developed in order to follow a bounded reference trajectory specified. By means of Lyapunov analysis, the boundedness of all the closed-loop signals as well as the weights and deadzone parameter estimations is rigorously proven. Besides, the exponential convergence of the actual tracking error to a bounded zone is guaranteed. The effectiveness of this scheme is illustrated by a numerical simulation.