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Research Papers

# $L1$ Adaptive Controller for a Class of Nonlinear Systems

[+] Author and Article Information
Jie Luo

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: jie.luo@engr.uconn.edu

Chengyu Cao

Assistant Professor
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: ccao@engr.uconn.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 21, 2011; final manuscript received November 30, 2013; published online March 10, 2014. Assoc. Editor: Rama K. Yedavalli.

J. Dyn. Sys., Meas., Control 136(3), 031023 (Mar 10, 2014) (8 pages) Paper No: DS-11-1121; doi: 10.1115/1.4026302 History: Received April 21, 2011; Revised November 30, 2013

## Abstract

This paper presents an extension of the $L1$ adaptive controller to a class of nonlinear systems where the control effectiveness is time-varying and unknown, but with a known sign. Moreover, this class of nonlinear systems contains time-varying and unknown state-dependent nonlinearities. The proposed $L1$ adaptive controller consists of three components, a state predictor used to estimate real states, an adaptive law used to update the adaptive parameters in the state predictor, and a low-pass filtered control law. First, the stable closed-loop reference system is constructed. Then, the estimation errors between estimated states and real states are proved to be arbitrarily small by increasing the adaptation rate. After that, we further prove that the adaptive controller ensures uniformly bounded transient and asymptotical tracking of the reference system. The performance bounds can be systematically improved by increasing the adaptation rate. Simulation results on a single-link nonlinear robot arm verify the theoretical findings.

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## References

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## Figures

Fig. 1

Performance of L1 adaptive controller for Scenario 1

Fig. 2

Performance of L1 adaptive controller for Scenario 2

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