Delayed finite-dimensional observer-based control of 1-D parabolic PDEs

Sampled-Data Boundary Feedback Control of 1-D Parabolic PDEs

The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D linear parabolic systems on bounded domains. It is shown that the continuous-time boundary feedback applied in a sample-and-hold fashion guarantees closed-loop exponential stability, provided that the sampling period is sufficiently small. Two different continuous-time feedback designs ...

A comparison of adaptive software for 1-D parabolic PDEs

In this paper we describe BACOL, a high-order, spatially and temporally adaptive software package for solving systems of one-dimensional parabolic partial differential equations and then compare it with several related software packages. BACOL employs collocation at Gaussian points with a B-spline basis for the spatial discretization. A modification of DASSL is used for the time integration of ...

Decay Estimates for 1-D Parabolic PDEs with Boundary Disturbances

In this work decay estimates are derived for the solutions of 1-D linear parabolic PDEs with disturbances at both boundaries and distributed disturbances. The decay estimates are given in the 2 L and 1 H norms of the solution and discontinuous disturbances are allowed. Although an eigenfunction expansion for the solution is exploited for the proof of the decay estimates, the estimates do not re...

Control of 1-D parabolic PDEs with Volterra nonlinearities, Part I: Design

Boundary control of nonlinear parabolic PDEs is an open problem with applications that include fluids, thermal, chemically-reacting, and plasma systems. In this paper we present stabilizing control designs for a broad class of nonlinear parabolic PDEs in 1-D. Our approach is a direct infinite dimensional extension of the finite-dimensional feedback linearization/backstepping approaches and empl...

Infinite dimensional backstepping for nonlinear parabolic PDEs