Adaptive observers for non-square positive real infinite dimensional systems - Demetriou, Michael A. (Proceedings of the American Control Conference, 2016)
This paper considers the adaptive estimation of parabolic partial differential equations with boundary control and observation. Structured perturbations enter at the boundary and are collocated either with the control or the measurement. Various combinations of boundary control, observation and structured perturbations are considered and viewed as evolution equations in a Hilbert space via the use of Dirichlet maps. When certain conditions are met, the systems can utilize results on the adaptive estimation of positive real infinite dimensional systems. Extensive simulation studies of 1D parabolic partial differential equation with the structured perturbation collocated either with the input or the output operator are presented to demonstrate the utilization of results on adaptive estimation of positive real infinite dimensional systems for diffusion PDEs.