Backstepping observers for a class of parabolic PDEs

Stability of partial difference equations governing control gains in infinite-dimensional backstepping

We examine the stability properties of a class of LTV di"erence equations on an in&nite-dimensional state space that arise in backstepping designs for parabolic PDEs. The nominal system matrix of the di"erence equation has a special structure: all of its powers have entries that are −1, 0, or 1, and all of the eigenvalues of the matrix are on the unit circle. The di"erence equation is driven by...

Infinite dimensional backstepping for nonlinear parabolic PDEs

Backstepping observer design for parabolic PDEs with measurement of weighted spatial averages

This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the stat...

A Convex Optimization Approach for Backstepping PDE Design: Volterra and Fredholm Operators

Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are o...

Adaptive boundary control for unstable parabolic PDEs - Part II: Estimation-based designs

Abstract— The certainty equivalence approach to adaptive control is commonly used with two types of identifiers: passivitybased identifiers and swapping identifiers. The ‘passive’ (also known as ‘observer-based’) approach is the prevalent identification technique in existing results on adaptive control for PDEs but has so far not been used in boundary control problems. The swapping approach, pr...