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Synchronization of inferior olive neurons via \({\mathcal {L}}_1\) adaptive feedback

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Abstract

This paper considers the synchronization of inferior olive neurons based on the \({\mathcal {L}}_1\) adaptive control theory. The ION model treated here is the cascade connection of two nonlinear subsystems, termed ZW and UV subsystems. It is assumed that the structure of the nonlinear functions and certain parameters of the IONs are not known, and disturbance inputs are present in the system. First, an \({\mathcal {L}}_1\) adaptive control system is designed to achieve global synchrony of the ZW subsystems using a single control input. This controller can accomplish local synchrony of the UV subsystems if the linearized UV subsystem is exponentially stable. For global synchrony of the UV subsystems, an \({\mathcal {L}}_1\) adaptive control law is designed. Each of these controllers includes a state predictor, an update law, and a control law. In the closed-loop system, global synchrony of the complete models of the IONs (the interconnected ZW and UV subsystems) is accomplished using these two adaptive controllers. Simulations results show that in the closed-loop system, the IONs are synchronized, despite unmodeled nonlinearities, disturbance inputs, and parameter uncertainties in the system.

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Authors and Affiliations

  1. University of Nevada Las Vegas, Las Vegas, NV , 89154-4026, USA

    Srujan K. Chalike

  2. Division of Electronic Information and Communication, University of Kwandong, Gangneung-si, Gangwon, 210-701, Republic of Korea

    Keum W. Lee

  3. Department of Electrical and Computer Engineering, University of Nevada Las Vegas, 89154-4026, Las Vegas, NV, USA

    Sahjendra N. Singh

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  1. Srujan K. Chalike
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  2. Keum W. Lee
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  3. Sahjendra N. Singh
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Correspondence to Sahjendra N. Singh.

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Chalike, S.K., Lee, K.W. & Singh, S.N. Synchronization of inferior olive neurons via \({\mathcal {L}}_1\) adaptive feedback. Nonlinear Dyn 78, 467–483 (2014). https://doi.org/10.1007/s11071-014-1454-6

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  • DOI: https://doi.org/10.1007/s11071-014-1454-6

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