Rafael Vazquez

Local exponential H2 stabilization of 2x2 quasilinear hyperbolic systems using backstepping

In this work, we consider the problem of boundary stabilization for a quasilinear

Local exponential H 2 stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping

2\times2

Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system

system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves

Boundary Observer for Output-Feedback Stabilization of Thermal-Fluid Convection Loop

H^2

Backstepping stabilization of an underactuated 3 × 3 linear hyperbolic system of fluid flow equations

exponential stability of the closed-loop system. Our proof uses a backstepping transformation to find new variables for which a strict Lyapunov function can be constructed. The kernels of the transformation are found to verify a Goursat-type

Collocated output-feedback stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping

4\times4

A Closed-Form Full-State Feedback Controller for Stabilization of 3D Magnetohydrodynamic Channel Flow

system of first-order hyperbolic PDEs, whose well-posedness is shown using the method of characteristics and successive approximations. Once the kernels are computed, the stabilizing feedback law can be explicitly constructed from them.

Marcum Q-functions and explicit feedback laws for stabilization of constant coefficient 2 × 2 linear hyperbolic systems

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 H2 exponential stability of the closed-loop system. The proof of stability is based on the construction of a strict Lyapunov function. The feedback law is found using the recently developed backstepping method for 2 × 2 system of first-order hyperbolic linear PDEs, developed by the authors in a previous work, which is briefly reviewed.

Swath-acquisition planning in multiple-satellite missions: an exact and heuristic approach

We consider the problem of boundary stabilization and state estimation for a 2×2 system of first-order hyperbolic linear PDEs with spatially varying coefficients. First, we design a full-state feedback law with actuation on only one end of the domain and prove exponential stability of the closed-loop system. Then, we construct a collocated boundary observer which only needs measurements on the controlled end and prove convergence of observer estimates. Both results are combined to obtain a collocated output feedback law. The backstepping method is used to obtain both control and observer kernels. The kernels are the solution of a 4 × 4 system of first-order hyperbolic linear PDEs with spatially varying coefficients of Goursat type, whose well-posedness is shown.

Backstepping control of the Stefan problem with flowing liquid

In this paper, we consider a 2-D model of thermal fluid convection that exhibits the prototypical Rayleigh-Bernard convective instability. The fluid is enclosed between two cylinders, heated from above, and cooled from below, which makes its motion unstable for a large enough Rayleigh number. We design an stabilizing output feedback boundary control law for a realistic collocated setup, with actuation and measurements located at the outer boundary. Actuation is through rotation (direct velocity actuation) and heat flux (heating or cooling) of the outer cylinder, while measurements of friction and temperature are obtained at the same boundary. Though only a linearized version of the plant is considered in the design, an extensive closed loop simulation study of the nonlinear model shows that our design works for reasonably large initial conditions. A highly accurate approximation to the control kernels and observer output injection gains is found in closed form.