Funnel control for boundary control systems

We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop system is proved by using nonlinear operator theory. We apply our results to both hyperbolic and parabolic equations.

[1]  Tosio Kato Perturbation theory for linear operators , 1966 .

[2]  Tosio Kato,et al.  Nonlinear semigroups and evolution equations , 1967 .

[3]  J. Diestel,et al.  On vector measures , 1974 .

[4]  P. Raviart,et al.  Finite Element Approximation of the Navier-Stokes Equations , 1979 .

[5]  Jeffrey Rauch,et al.  Symmetric positive systems with boundary characteristic of constant multiplicity , 1985 .

[6]  P. Grisvard Elliptic Problems in Nonsmooth Domains , 1985 .

[7]  R. Showalter Monotone operators in Banach space and nonlinear partial differential equations , 1996 .

[8]  R. Nagel,et al.  One-parameter semigroups for linear evolution equations , 1999 .

[9]  Chris Sangwin,et al.  Tracking with prescribed transient behaviour , 2002 .

[10]  Kirsten Morris,et al.  Well-posedness of boundary control systems , 2003, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[11]  A. Boukricha Nonlinear Semigroups , 2004 .

[12]  O. Staffans Well-Posed Linear Systems , 2005 .

[13]  Eugene P. Ryan,et al.  Tracking with Prescribed Transient Behavior for Nonlinear Systems of Known Relative Degree , 2007, SIAM J. Control. Optim..

[14]  J. A. Villegas,et al.  A Port-Hamiltonian Approach to Distributed Parameter Systems , 2007 .

[15]  G. Weiss,et al.  Observation and Control for Operator Semigroups , 2009 .

[16]  W. Arendt,et al.  From Forms to Semigroups , 2011, 1104.1013.

[17]  Hans Zwart,et al.  Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces , 2012 .

[18]  Bjorn Augner,et al.  Stability and Stabilization of Infinite-dimensional Linear Port-Hamiltonian Systems , 2013, 1312.4307.

[19]  G. Burton Sobolev Spaces , 2013 .

[20]  Timo Reis,et al.  Funnel Control for the Boundary Controlled Heat Equation , 2015, SIAM J. Control. Optim..

[21]  Carsten Trunk,et al.  The Byrnes-Isidori Form for Infinite-Dimensional Systems , 2016, SIAM J. Control. Optim..

[22]  H. Alt,et al.  Linear Functional Analysis , 2016 .

[23]  G. Bastin,et al.  Stability and Boundary Stabilization of 1-D Hyperbolic Systems , 2016 .

[24]  Timo Reis,et al.  Funnel control for nonlinear systems with known strict relative degree , 2018, Autom..

[25]  Bjorn Augner Stabilisation of Infinite-Dimensional Port-Hamiltonian Systems via Dissipative Boundary Feedback , 2018 .

[26]  Bjorn Augner,et al.  Well-Posedness and Stability of Infinite-Dimensional Linear Port-Hamiltonian Systems with Nonlinear Boundary Feedback , 2015, SIAM J. Control. Optim..

[27]  Felix L. Schwenninger,et al.  Funnel control in the presence of infinite-dimensional internal dynamics , 2019, Syst. Control. Lett..

[28]  Felix Schwenninger,et al.  Funnel control for a moving water tank , 2019, Autom..