Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays

By Miroslav Krstic, Andrey Smyshlyaev. IEEE Conference on Decision and Control, 2007

821 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/955a1a7b1af83924cff202b3dce6af9b3d1a32eb

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Citations in the corpus

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]).”
Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems (2010, methodology): “Proof: We first perform a stability analysis of the system using a standard Lyapunov functional as in [23], obtaining a stability estimate in terms of the norm”
Nonlinear control under wave actuator dynamics with time‐ and state‐dependent moving boundary (2015, methodology): “The approach for the boundary stabilization of the first-order hyperbolic PDEs and application to systems with delays is given in [23].”
Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input (2013, background): “, parabolic PDEs [34], wave equations [8], delay systems [24] or beams [33].”
Boundary Control of PDEs (2008, methodology): “Finally, the backstepping method is particularly suited for dealing with PDE–ODE or PDE–PDE cascades, for example, systems with actuator/sensor dynamics in the form of the pure delay [14].”
Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system (2011, methodology): “…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 adaptive…”
Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach (2017, methodology): “Since then, it has been applied to study the stability of parabolic equations in [32, 33], of hyperbolic systems in [21, 8, 9, 16, 17], of nonlinear parabolic equations in [35], of Korteweg-de Vries equations in [3] and of Kuramoto–Sivashinsky equations [27].”
Adaptive boundary stabilization for first‐order hyperbolic PDEs with unknown spatially varying parameter (2016, methodology): “Inspired by Krstić and Smyshlyaev [8], when g.x/ is known, the following controller can stabilize target system (7) in the sense of (8) and (9): U.t/ D Z 1 0 Nk.1; y/ w.y; t/ Z y 0 w.´; t/g.y ´/d´ dy; (12) where Nk.x; y/ is the kernel function satisfying the following equation: Nk.x; y/ D Z x y 0 N”
Observer design and output feedback stabilization for nonlinear multivariable systems with diffusion PDE-governed sensor dynamics (2013, methodology): “Even though it inevitably brings some conservativeness, the LMI-based design method proposed in this study provides an alternative as well as simple method, which is different from that used in [14–18], to solve the observer design problem for nonlinear multivariable systems with PDE-governed sensor”