Abstract
In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicability of the approach is illustrated by considering two different chaotic systems: Liu chaotic system and Genesio–Tesi chaotic system. The numerical results have shown the effectiveness of obtained theoretical results. Finally, the theoretical results are implemented on an FPGA, confirming the feasibility of the synchronization scheme and showing that it is hardware realizable.
Highlights
Neural networks can be considered as nonlinear mathematical functions whose parameters are adjusted to describe the behavior of a static or dynamic system [1]
It is worth noting that the Lyapunov–Krasovskii approach has been demonstrated to be an efficient method to deal with the global asymptotic stability of a recurrent neural network with time delay [19, 20]
Neural networks are forced to follow reference signals generated by a chaotic system, achieving the synchronization state. e control law that guarantees trajectory tracking was obtained by considering the Lyapunov–Krasovskii and Lur’e theory. e applicability of the approach was illustrated by considering two different chaotic systems: Liu’s chaotic system and Genesio–Tesi chaotic system
Summary
Neural networks can be considered as nonlinear mathematical functions whose parameters are adjusted to describe the behavior of a static or dynamic system [1]. It is worth noting that the Lyapunov–Krasovskii approach has been demonstrated to be an efficient method to deal with the global asymptotic stability of a recurrent neural network with time delay [19, 20]. New Lyapunov–Krasovskii functionals are proposed to achieve the synchronization behavior of delay neural networks with two time scales for the fixed and adaptive coupling schemes [22]. Inspired by all the above works, this paper focuses on the problem of tracking a given reference trajectory It proposes a trajectory tracking scheme in which a time-delay neural network is forced to follow a chaotic system’s reference signal, achieving a drive-response synchronization state between the neural network and the chaotic system.
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