Adaptive Boundary Control for Unstable Parabolic PDEs—Part I: Lyapunov Design Export

@article{KrsticSmyshlyaev_TAC08, abstract = {We develop adaptive controllers for parabolic partial differential equations (PDEs) controlled from a boundary and containing unknown destabilizing parameters affecting the interior of the domain. These are the first adaptive controllers for unstable PDEs without relative degree limitations, open-loop stability assumptions, or domain-wide actuation. It is the first necessary step towards developing adaptive controllers for physical systems such as fluid, thermal, and chemical dynamics, where actuation can be only applied non-intrusively, the dynamics are unstable, and the parameters, such as the Reynolds, Rayleigh, Prandtl, or Peclet numbers are unknown because they vary with operating conditions. Our method builds upon our explicitly parametrized control formulae to avoid solving Riccati or Bezout equations at each time step. Most of the designs we present are state feedback but we present two benchmark designs with output feedback which have infinite relative degree.}, author = {Krstic, M. and Smyshlyaev, A.}, booktitle = {Automatic Control, IEEE Transactions on}, citeulike-article-id = {3444566}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TAC.2008.927798}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4623267}, doi = {10.1109/TAC.2008.927798}, journal = {Automatic Control, IEEE Transactions on}, keywords = {adaptation\_adaptive\_control, boundry\_control\_pdes, lyapunov\_method}, number = {7}, pages = {1575--1591}, posted-at = {2008-10-23 23:19:13}, priority = {2}, title = {Adaptive Boundary Control for Unstable Parabolic PDEs\&\#x2014;Part I: Lyapunov Design}, url = {http://dx.doi.org/10.1109/TAC.2008.927798}, volume = {53}, year = {2008} }

TY - JOUR ID - KrsticSmyshlyaev_TAC08 L3 - citeulike-article-id:3444566 N2 - We develop adaptive controllers for parabolic partial differential equations (PDEs) controlled from a boundary and containing unknown destabilizing parameters affecting the interior of the domain. These are the first adaptive controllers for unstable PDEs without relative degree limitations, open-loop stability assumptions, or domain-wide actuation. It is the first necessary step towards developing adaptive controllers for physical systems such as fluid, thermal, and chemical dynamics, where actuation can be only applied non-intrusively, the dynamics are unstable, and the parameters, such as the Reynolds, Rayleigh, Prandtl, or Peclet numbers are unknown because they vary with operating conditions. Our method builds upon our explicitly parametrized control formulae to avoid solving Riccati or Bezout equations at each time step. Most of the designs we present are state feedback but we present two benchmark designs with output feedback which have infinite relative degree. IS - 7 JF - Automatic Control, IEEE Transactions on EP - 1591 TI - Adaptive Boundary Control for Unstable Parabolic PDEs—Part I: Lyapunov Design VL - 53 T2 - Automatic Control, IEEE Transactions on SP - 1575 KW - adaptation_adaptive_control KW - boundry_control_pdes KW - lyapunov_method AU - Krstic, M AU - Smyshlyaev, A PY - 2008/// UR - http://dx.doi.org/10.1109/TAC.2008.927798 ER -