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New Results in Stabilization of Uncertain Nonholonomic Systems: An Event-Triggered Control Approach

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Abstract

This paper reports latest developments in event-triggered and self-triggered control of uncertain nonholonomic systems in the perturbed chained form. In order to tackle the effects of drift uncertain nonlinearities, nonholonomic constraints and nonsmooth aperiodic sampling in event-based control, a novel systematic design scheme is proposed by integrating set-valued maps with state-separation and state-scaling techniques. The stability analysis of the closed-loop event-triggered control system is based on the cyclic-small-gain techniques that overcome the limitation of Lyapunov theory in the construction of Lyapunov functions for nonsmooth dynamical systems and enjoy inherent robustness properties due to the use of gain-based characterization of robust stability. More specifically, the closed-loop event-triggered control system is transformed into an interconnection of multiple input-to-state stable systems, to which the cyclic-small-gain theorem is applied for robust stability analysis. New self-triggered mechanisms are also developed as natural extensions of the event-triggered control result. The proposed event-based control design approach is new and original even when the system model is reduced to the ideal unperturbed chained form. Interestingly, the proposed methodology is also applicable to a broader class of nonholonomic systems subject to state and input-dependent uncertainties. The efficacy of the obtained event-triggered controllers is validated by a benchmark example of mobile robots subject to parametric uncertainties and a measurement noise such as bias in the orientation.

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Authors and Affiliations

  1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110004, China

    Tengfei Liu, Pengpeng Zhang & Mengxi Wang

  2. Department of Electrical and Computer Engineering, New York University, 370 Jay Street, Brooklyn, NY, 11201, USA

    Zhong-Ping Jiang

Authors
  1. Tengfei Liu
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  2. Pengpeng Zhang
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  3. Mengxi Wang
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  4. Zhong-Ping Jiang
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Corresponding author

Correspondence to Zhong-Ping Jiang.

Additional information

This work was supported in part by the National Natural Science Foundation of China Grant Nos. 61633007 and U1911401, and in part by the National Natural Science Foundation of China under Grant No. EPCN-1903781.

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Liu, T., Zhang, P., Wang, M. et al. New Results in Stabilization of Uncertain Nonholonomic Systems: An Event-Triggered Control Approach. J Syst Sci Complex 34, 1953–1972 (2021). https://doi.org/10.1007/s11424-021-1235-5

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  • DOI: https://doi.org/10.1007/s11424-021-1235-5

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