Optimal boundary control of Kuramoto-Sivashinsky equation

This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE) in an appropriate functional space setting. Low dimensional representation of the KSE is used in the synthesis of a finite dimensional linear quadratic regulator (LQR) in the full-state feedback control realization and in a compensator design with a Luenberger-type observer. The proposed control problem formulation and the performance and robustness of the closed-loop system in the full state-feedback, output-feedback and in the output-feedback with the presence of noise controller realization have been evaluated through simulations.

[1]  Roger Temam,et al.  Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attr , 1985 .

[2]  Thomas I. Seidman,et al.  Boundary feedback stabilization of a parabolic equation , 1984 .

[3]  Liang-Heng Chen,et al.  Nonlinear waves on liquid film surfaces—II. Bifurcation analyses of the long-wave equation , 1986 .

[4]  C. H. Lee,et al.  Reduced-order-based feedback control of the Kuramoto-Sivashinsky equation , 2005 .

[5]  M. Krstić,et al.  Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation , 2001 .

[6]  Hsueh-Chia Chang,et al.  Nonlinear waves on liquid film surfaces—I. Flooding in a vertical tube , 1986 .

[7]  G. Hagen,et al.  Absolute stability via boundary control of a semilinear parabolic PDE , 2006, IEEE Transactions on Automatic Control.

[8]  Ruth F. Curtain,et al.  On Stabilizability of Linear Spectral Systems via State Boundary Feedback , 1985 .

[9]  Miroslav Krstic,et al.  Boundary control of an unstable heat equation via measurement of domain-averaged temperature , 2001, IEEE Trans. Autom. Control..

[10]  Stuart Townley,et al.  From PDEs with Boundary Control to the Abstract State Equation with an Unbounded Input Operator: A Tutorial , 2000, Eur. J. Control.

[11]  Panagiotis D. Christofides,et al.  Feedback control of the Kuramoto-Sivashinsky equation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[12]  Christopher I. Byrnes,et al.  Static and dynamic controllers for boundary controlled distributed parameter systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[13]  Panagiotis D. Christofides,et al.  Predictive control of parabolic PDEs with boundary control actuation , 2006 .

[14]  Roger Temam,et al.  Inertial Manifolds for the Kuramoto-Sivashinsky Equation and an Estimate of their Lowest Dimension , 1986 .

[15]  Explicit Formulae for Boundary Control of Parabolic PDEs , 2004 .

[16]  J. Schwartz.  Perturbations of spectral operators, and applications. I. Bounded perturbations. , 1954 .

[17]  J. Seinfeld,et al.  Distributed Parameter Systems: Theory and Applications , 1989 .

[18]  W. Harmon Ray,et al.  Boundary identification and control of distributed parameter systems using singular functions , 1999 .

[19]  Toshio Tsuzmn,et al.  On the Formation of Dissipative Structures in Reaction-Diffusion Systems , 1975 .

[20]  W. H. Ray,et al.  Boundary identification and control of distributed parameter systems using singular functions , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[21]  Roberto Triggiani,et al.  Boundary feedback stabilizability of parabolic equations , 1980 .

[22]  Yoshiki Kuramoto,et al.  On the Formation of Dissipative Structures in Reaction-Diffusion Systems Reductive Perturbation Approach , 1975 .

[23]  P. Christofides,et al.  Global stabilization of the Kuramoto–Sivashinsky equation via distributed output feedback control , 2000 .