Gain Scheduling-Inspired Boundary Control for Nonlinear Partial Differential Equations-Reference-Cited by-同舟云学术

Gain Scheduling-Inspired Boundary Control for Nonlinear Partial Differential Equations

Published:2011-08-01 Issue:5 Volume:133 Page:
ISSN:0022-0434
Container-title:Journal of Dynamic Systems, Measurement, and Control
language:en
Short-container-title:

Author:

Siranosian Antranik A.,Krstic Miroslav¹,Smyshlyaev Andrey¹,Bement Matt²

Affiliation:

1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093

2. Los Alamos National Laboratory, Los Alamos, NM 87545

Abstract

Abstract We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with an in-domain nonlinearity is considered first. For this system a nonlinear feedback law, based on gain scheduling, is derived explicitly, and a proof of local exponential stability, with an estimate of the region of attraction, is presented for the closed-loop system. Control designs (without proofs) are then presented for a string PDE and a shear beam PDE, both with Kelvin–Voigt (KV) damping and free-end nonlinearities of a potentially destabilizing kind. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization based design.

Publisher

ASME International

Subject

Computer Science Applications,Mechanical Engineering,Instrumentation,Information Systems,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/133/5/051007/6737274/051007_1.pdf

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