Nonlinear feedback control and systems of partial differential equations

1989 ◽  
Vol 17 (1) ◽  
pp. 41-94 ◽  
Author(s):  
Robert Hermann
Keyword(s):  
Partial Differential Equations ◽  
Feedback Control ◽  
Differential Equations ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Partial Differential

Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations

2009 ◽  
Author(s):  
Antranik A. Siranosian ◽  
Miroslav Krstic ◽  
Andrey Smyshlyaev ◽  
Matt Bement
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Design Method ◽  
Nonlinear Partial Differential Equations ◽  
Gain Scheduling ◽  
System Control ◽  
Nonlinear Feedback ◽  
Partial Differential ◽  
System A ◽  
Shear Beam

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 a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.

PDE Control of a Flexible Two-Link Manipulator

2001 ◽  
Author(s):  
X. Zhang ◽  
W. Xu ◽  
S. S. Nair ◽  
V. Chellaboina
Keyword(s):  
Partial Differential Equations ◽  
Feedback Control ◽  
Differential Equations ◽  
Control Design ◽  
Partial Differential ◽  
Pde Control

Abstract A stable strain feedback control design is proposed for a flexible two-link manipulator using a model with partial differential equations directly. Stability is established using a Lyapunov-based design.

Gain Scheduling-Inspired Boundary Control for Nonlinear Partial Differential Equations

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Antranik A. Siranosian ◽  
Miroslav Krstic ◽  
Andrey Smyshlyaev ◽  
Matt Bement
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Design Method ◽  
Nonlinear Partial Differential Equations ◽  
Gain Scheduling ◽  
System Control ◽  
Nonlinear Feedback ◽  
Partial Differential ◽  
System A ◽  
Shear Beam

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.

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