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Ponencia
Explicit boundary control of a reaction-diffusion equation on a disk
(Elsevier, 2014)
This paper introduces an explicit full-state boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on a disk. The backstepping method is used to design the control law. ...
Ponencia
Backstepping-Based Exponential Stabilization of Timoshenko Beam with Prescribed Decay Rate
(Elsevier, 2022)
In this paper, we present a rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE backstepping. We introduce a transformation to map the Timoshenko ...
Ponencia
Boundary control of a singular reaction-diffusion equation on a disk
(Elsevier, 2016)
Recently, the problem of boundary stabilization for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However, ...
Ponencia
Local exponential H2 stabilization of a 2x2 quasilinear hyperbolic system using backstepping
(Institute of Electrical and Electronics Engineers (IEEE), 2011)
We consider the problem of boundary stabilization for a quasilinear 2×2 system of first-order hyperbolic PDEs. We design a full-state feedback control law, with actuation on only one end of the domain, and prove local H 2 ...
Ponencia
Folding Backstepping Approach to Parabolic PDE Bilateral Boundary Control
(Elsevier, 2019)
We consider the stabilization problem for an unstable 1-D diffusion-reaction partial differential equation using a so-called folding transformation. The diffusion-reaction equation is transformed into a 2 ×2 system of ...
Ponencia
Backstepping stabilization of an underactuated 3 X 3 linear hyperbolic system of fluid flow transport equations
(Institute of Electrical and Electronics Engineers (IEEE), 2012)
We investigate the boundary stabilization of a particular subset of 3×3 linear hyperbolic systems with varying coefficients on a bounded domain. The system is underactuated since only one of the three hyperbolic PDEs is ...
Ponencia
Backstepping control of a hyperbolic PDE system with zero characteristic speed
(Elsevier, 2022)
In this paper, we study the single-input boundary feedback stabilization of 3 × 3 linear hyperbolic partial differential equations (PDEs) with two counterconvecting PDEs and the third one with zero characteristic speed. ...
Ponencia
Bilateral boundary control of one-dimensional first- and second-order PDEs using infinite-dimensional backstepping
(Institute of Electrical and Electronics Engineers (IEEE), 2016)
This paper develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with an ...
Ponencia
Output feedback control of radially-dependent reaction-diffusion PDEs on balls of arbitrary dimensions
(Elsevier, 2020)
Recently, the problem of boundary stabilization and estimation for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping ...
Ponencia
Volterra boundary control laws for a class of nonlinear parabolic partial differential equations
(Elsevier, 2004)
The efforts on boundary control of general classes of nonlinear parabolic PDEs with nonlinearities of superlinear growth have so far only resulted in counterexamples-results that show that finite time blow up occurs for ...