2021/04/27 by Rami Katz, Emilia Fridman, Katz, Rami +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2104.13294
openalex publication_date 2021/04/27 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We study constant input delay compensation by using finite-dimensional\nobserver-based controllers in the case of the 1D heat equation. We consider\nNeumann actuation with nonlocal measurement and employ modal decomposition with\nN+1 modes in the observer. We introduce a chain of M sub-predictors that\nleads to a closed-loop ODE system coupled with infinite-dimensional tail. Given\nan input delay r, we present LMI stability conditions for finding M and N\nand the resulting exponential decay rate and prove that the LMIs are always\nfeasible for any r. We also consider a classical observer-based predictor and\nshow that the corresponding LMI stability conditions are feasible for any r\nprovided N is large enough. A numerical example demonstrates that the\nclassical predictor leads to a lower-dimensional observer. However, it is known\nto be hard for implementation due to the distributed input signal.\n