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

An adaptive observer for hyperbolic systems with application to UnderBalanced Drilling

“…Over the past decade there has been a steady increase of interest in adaptive boundary control. Recently, outputfeedback adaptive designs for parabolic PDEs have been developed in Krstic and Smyshlyaev [2008], Smyshlyaev and Krstic [2007a,b], Bekiaris-Liberis et al [2013], BreschPietri et al [2012]. Similarly, in this paper, we extend the backstepping observer of Di Meglio et al [2013a].…”

A comparative study for the boundary control of a reaction-diffusion process: MPC vs backstepping

“…The proof, detailed in Appendix, is based on the one developed in Krstić and Smyshlyaev [2008a], but we here exploit the Dirichlet boundary conditions and gain g to obtain a wider range for the choice of the update gain γ.…”

“…Backstepping control of PDE systems with non-constant parameters were treated in Smyshlyaev and Krstić [2005]. The adaptive backstepping control of parabolic PDE systems with unknown parameters was addressed using either Lyapunov design Krstić and Smyshlyaev [2008a], passive estimator Smyshlyaev and Krstić [2007a], or swapping identifiers Smyshlyaev and Krstić [2007b].…”

“…The robustness of the MPC-IMC approach is addressed and an adaptive backstepping is developed in the usual case. In that case, we also provide a more reactive update law than in Krstić and Smyshlyaev [2008a] in the case of Dirichlet boundary conditions. In the usual case, the MPC strategy proves to be performant in simulations despite a computational cost lower than the backstepping's ones.…”

Robust adaptive constrained boundary control for a suspension cable system of a helicopter

“…[21][22][23][24][25][26][27] The control problem of a string system modeled by a PDE was considered in the work of Qu,24 in which a robust adaptive boundary controller was designed. A new idea of the sliding mode control design was raised for the boundary control problem of a distributed parameter system governed by a parabolic PDE in the work of Cheng et al 25 In order to restrain the vibration, a boundary controller was proposed by utilizing the Lyapunov direct method for a riser system in the work of He et al 26 In the work of He and Zhang, 27 by applying boundary control schemes, the boundary control problem of flexible wings was studied for a robotic aircraft system, which was represented by a set of distributed parameter systems.…”