131 research outputs found
In-domain control of a heat equation: an approach combining zero-dynamics inverse and differential flatness
This paper addresses the set-point control problem of a heat equation with
in-domain actuation. The proposed scheme is based on the framework of zero
dynamics inverse combined with flat system control. Moreover, the set-point
control is cast into a motion planing problem of a multiple-input, multiple-out
system, which is solved by a Green's function-based reference trajectory
decomposition. The validity of the proposed method is assessed through
convergence and solvability analysis of the control algorithm. The performance
of the developed control scheme and the viability of the proposed approach are
confirmed by numerical simulation of a representative system.Comment: Preprint of an original research pape
A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances
This note addresses input-to-state stability (ISS) properties with respect to
(w.r.t.) boundary and in-domain disturbances for Burgers' equation. The
developed approach is a combination of the method of De~Giorgi iteration and
the technique of Lyapunov functionals by adequately splitting the original
problem into two subsystems. The ISS properties in -norm for Burgers'
equation have been established using this method. Moreover, as an application
of De~Giorgi iteration, ISS in -norm w.r.t. in-domain disturbances
and actuation errors in boundary feedback control for a 1- {linear}
{unstable reaction-diffusion equation} have also been established. It is the
first time that the method of De~Giorgi iteration is introduced in the ISS
theory for infinite dimensional systems, and the developed method can be
generalized for tackling some problems on multidimensional spatial domains and
to a wider class of nonlinear {partial differential equations (PDEs)Comment: This paper has been accepted for publication by IEEE Trans. on
Automatic Control, and is available at
http://dx.doi.org/10.1109/TAC.2018.2880160. arXiv admin note: substantial
text overlap with arXiv:1710.0991
Input-to-State Stability with Respect to Boundary Disturbances for a Class of Semi-linear Parabolic Equations
This paper studies the input-to-state stability (ISS) properties based on the
method of Lyapunov functionals for a class of semi-linear parabolic partial
differential equations (PDEs) with respect to boundary disturbances. In order
to avoid the appearance of time derivatives of the disturbances in ISS
estimates, some technical inequalities are first developed, which allow
directly dealing with the boundary conditions and establishing the ISS based on
the method of Lyapunov functionals. The well-posedness analysis of the
considered problem is carried out and the conditions for ISS are derived. Two
examples are used to illustrate the application of the developed result.Comment: Manuscript submitted to Automatic
Flatness-based Deformation Control of an Euler-Bernoulli Beam with In-domain Actuation
This paper addresses the problem of deformation control of an Euler-Bernoulli
beam with in-domain actuation. The proposed control scheme consists in first
relating the system model described by an inhomogeneous partial differential
equation to a target system under a standard boundary control form. Then, a
combination of closed-loop feedback control and flatness-based motion planning
is used for stabilizing the closed-loop system around reference trajectories.
The validity of the proposed method is assessed through well-posedness and
stability analysis of the considered systems. The performance of the developed
control scheme is demonstrated through numerical simulations of a
representative micro-beam.Comment: Preprint of an original research wor
Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads
This paper addresses the boundary stabilization of a flexible wing model,
both in bending and twisting displacements, under unsteady aerodynamic loads,
and in presence of a store. The wing dynamics is captured by a distributed
parameter system as a coupled Euler-Bernoulli and Timoshenko beam model. The
problem is tackled in the framework of semigroup theory, and a Lyapunov-based
stability analysis is carried out to assess that the system energy, as well as
the bending and twisting displacements, decay exponentially to zero. The
effectiveness of the proposed boundary control scheme is evaluated based on
simulations.Comment: Published in Automatica as a brief pape
Boundary Control of a Nonhomogeneous Flexible Wing with Bounded Input Disturbances
This note deals with the boundary control problem of a nonhomogeneous
flexible wing evolving under unsteady aerodynamic loads. The wing is actuated
at its tip by flaps and is modeled by a distributed parameter system consisting
of two coupled partial differential equations. Based on the proposed boundary
control law, the well-posedness of the underlying Cauchy problem is first
investigated by resorting to the semigroup theory. Then, a Lyapunov-based
approach is employed to assess the stability of the closed-loop system in the
presence of bounded input disturbances.Comment: Published in IEEE Transactions on Automatic Control as a Technical
Not
A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances
In this paper, we introduce a weak maximum principle-based approach to
input-to-state stability (ISS) analysis for certain nonlinear partial
differential equations (PDEs) with boundary disturbances. Based on the weak
maximum principle, a classical result on the maximum estimate of solutions to
linear parabolic PDEs has been extended, which enables the ISS analysis for
certain {}{nonlinear} parabolic PDEs with boundary disturbances. To illustrate
the application of this method, we establish ISS estimates for a linear
reaction-diffusion PDE and a generalized Ginzburg-Landau equation with
{}{mixed} boundary disturbances. Compared to some existing methods, the scheme
proposed in this paper involves less intensive computations and can be applied
to the ISS analysis for a {wide} class of nonlinear PDEs with boundary
disturbances.Comment: 14 page
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