Flatness based feedback design for hyperbolic distributed parameter systems with spatially varying coefficients

Abstract State feedback design for a hybrid system consisting of a spatially one-dimensional second order hyperbolic distributed parameter system with spatially dependent coefficients and a finite dimensional linear system is considered. The approach relies on the flatness based parametrization of the solutions which is obtained by integration along the characteristics. Based on this parametrization the design of flatness based feedback controllers is proposed in order to achieve an arbitrary desired closed loop dynamics. Approximation strategies of the obtained infinite dimensional control laws are proposed.

[1]  Joachim Rudolph,et al.  Controller Canonical Forms and Flatness Based State Feedback for 1D Hyperbolic Systems , 2012 .

[2]  S. Mitter,et al.  Representation and Control of Infinite Dimensional Systems , 1992 .

[3]  David L. Russell,et al.  Canonical forms and spectral determination for a class of hyperbolic distributed parameter control systems , 1978 .

[4]  Frank Woittennek,et al.  On flatness and controllability of simple hyperbolic distributed parameter systems , 2011 .

[5]  Marianna A. Shubov.  Spectrum rearrangement via feedback control for nonhomogeneous damped string , 2012, IMA J. Math. Control. Inf..

[6]  Frank Woittennek,et al.  Controllability of Networks of Spatially One-Dimensional Second Order PDEs---An Algebraic Approach , 2010, SIAM J. Control. Optim..

[7]  F. John.  Partial differential equations , 1967 .

[8]  Miroslav Krstic,et al.  Boundary Stabilization of a 1-D Wave Equation with In-Domain Antidamping , 2010, SIAM J. Control. Optim..

[9]  D. W. Krumme,et al.  Differential-difference equations and nonlinear initial-boundary value problems for linear hyperbolic partial differential equations , 1968 .

[10]  Pierre Rouchon,et al.  Flatness of Heavy Chain Systems , 2001, SIAM J. Control. Optim..

[11]  David L. Russell,et al.  Neutral FDE canonical representations of hyperbolic systems , 1991 .

[12]  Constantin Corduneanu,et al.  Functional Equations with Causal Operators , 2002 .

[13]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .