Adaptive Control of Parabolic PDEs

By Andrey Smyshlyaev, Miroslav Krstic. 2010

389 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/8fc6c5aee2cb87725e68cf2ec67b2874f3835a0c

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In Control and Systems Engineering

Citations in the corpus

Real-time physics-model-based simulation of the current density profile in tokamak plasmas (2011, background): “State observers for partial differential equations are extensively treated in [29] which may be used as a starting point for further work in this direction.”
Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input (2013, background): “To convert hyperbolic PDEs into integral equations, one must define characteristic curves in the —plane along which the equations are integrated.”
Boundary exponential stabilization of 1-D inhomogeneous quasilinear hyperbolic systems (2015, methodology): “The third one is the “Backstepping method”, which is now a popular mathematical tool to stabilize the finite dimensional and infinite dimensional dynamic systems (see [13, 14, 19, 20, 21]).”
Modeling and Vibration Control for a Nonlinear Moving String With Output Constraint (2015, background): “In recent years, increasing attentions have been given on control design of various distributed parameter systems [17]–[24].”
Vibration Control of a Flexible Beam With Output Constraint (2015, positive): “Recently, by using the backstepping method, a novel boundary controller/observer is designed to stabilize the string and beam model and to track the target system [21], [22].”
Adaptive Partial Differential Equation Observer for Battery State-of-Charge/State-of-Health Estimation Via an Electrochemical Model (2014, background): “measurements is a significant fundamental challenge [26], for the following reason.”
Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system (2011, methodology): “The basis of our designs is the backstepping method [10]; initially developed for parabolic equations, it has been applied to first-order hyperbolic equations [12], delay systems [11], second-order hyperbolic equations [18], fluid flows [20], nonlinear PDE equations [21] and even used for PDE adapti”