Results 1  10
of
24
Well Posedness For Damped Second Order Systems With Unbounded Input Operators
 DIFFERENTIAL AND INTEGRAL EQUATIONS
, 1995
"... We consider damped second order in time systems such as those arising in structures with piezoceramic actuators and sensors. These systems are naturally formulated as abstract second order systems with unbounded nonhomogeneous term. Existence, uniqueness and continuous dependence of solutions in a ..."
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Cited by 24 (17 self)
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We consider damped second order in time systems such as those arising in structures with piezoceramic actuators and sensors. These systems are naturally formulated as abstract second order systems with unbounded nonhomogeneous term. Existence, uniqueness and continuous dependence of solutions in a weak or variational setting are given. A semigroup formulation is presented and conditions under which the variational solutions and semigroup solutions are the same are discussed.
Approximation in LQR Problems for Infinite Dimensional Systems With Unbounded Input Operators
, 1990
"... We present a variational framework based on sesquilinear forms for Galerkin approximation techniques for state feedback control in problems governed by infinite dimensional dynamical systems. Both parabolic and second order in time, hyperbolic partial differential equations with unbounded input and ..."
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Cited by 13 (6 self)
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We present a variational framework based on sesquilinear forms for Galerkin approximation techniques for state feedback control in problems governed by infinite dimensional dynamical systems. Both parabolic and second order in time, hyperbolic partial differential equations with unbounded input and unbounded observation operators are included as special cases of our treatment. 1 Introduction In this paper we discuss the linear quadratic regulator (LQR) problem for a class of (essentially parabolic) unbounded input or boundary control problems. A variational framework using sesquilinear forms is developed to treat Dirichlet and Neuman boundary control problems for parabolic equations and strongly damped elastic systems. Using such a framework, convergence of Galerkin approximations to solutions of Riccati equations is also established. The boundary control problem for parabolic systems has been studied extensively over the last two decades, inspired by the monograph of J.L. Lions [21] ...
Analytic semigroups: applications to inverse problems for flexible structures
 IN DIFFERENTIAL EQUATIONS WITH APPLICATIONS
, 1991
"... We present new convergence and stability results for least squares inverse problems involving systems described by analytic semigroups. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structur ..."
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Cited by 10 (9 self)
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We present new convergence and stability results for least squares inverse problems involving systems described by analytic semigroups. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data.
Computational issues in parameter estimation and feedback control problems for partial differential equation systems
 PHYSICA D
, 1992
"... We consider computational aspects of two problems governed by partial differential equations systems: (i) the computation of approximate Riccati feedback gains for LQR control problems, (ii) the estimation of parameters using methods based on approximate gradients computed via a costate algorithm. S ..."
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Cited by 10 (2 self)
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We consider computational aspects of two problems governed by partial differential equations systems: (i) the computation of approximate Riccati feedback gains for LQR control problems, (ii) the estimation of parameters using methods based on approximate gradients computed via a costate algorithm. Sufficient conditions for convergence of algorithms for these problems are discussed; in both cases, some type of adjoint or costate system convergence is required in addition to the expected system convergence. Examples are discussed that illustrate computational di#culties which may arise if only convergence of the approximate system holds (i.e., in the event costate convergence does not hold).
Modeling And Parameter Estimation For An Imperfectly Clamped Plate
 Computation and Control IV
, 1995
"... In this paper, the modeling of boundary conditions for an imperfectly clamped circular plate is discussed. This model is derived under the assumption that there is some variation in both the boundary displacement and slope when the plate oscillates. To account for this oscillation, boundary moment t ..."
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Cited by 9 (9 self)
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In this paper, the modeling of boundary conditions for an imperfectly clamped circular plate is discussed. This model is derived under the assumption that there is some variation in both the boundary displacement and slope when the plate oscillates. To account for this oscillation, boundary moment terms, involving parameters to be estimated through fittodata techniques, are included in the model. The wellposedness of the model is demonstrated and appropriate approximation techniques are outlined. Finally, under natural assumptions for this model and approximation scheme, results leading to parameter convergence are given. 1 Introduction An important consideration in the modeling of structural and structural acoustic systems involves the determination of appropriate boundary conditions for the vibrating structure. In many applications, the clamped nature of the structure leads to the use of clamped or fixed boundary conditions, in which case, it is assumed that zero displacements an...
The TrotterKato theorem and approximation of PDEs
 Math. Comp
, 1998
"... Abstract. We present formulations of the TrotterKato theorem for approximation of linear C0semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equat ..."
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Cited by 6 (0 self)
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Abstract. We present formulations of the TrotterKato theorem for approximation of linear C0semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes ’ equation as illustrative examples. 1.
Design of Finitedimensional Controllers for Infinitedimensional Systems by Approximation
, 1994
"... Several difficulties in controller design for infinitedimensional systems arise from using an approximation for the state of the system. In this paper it is demonstrated that the graph topology is an appropriate framework in which to discuss convergence of approximations used for controller design. ..."
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Cited by 6 (2 self)
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Several difficulties in controller design for infinitedimensional systems arise from using an approximation for the state of the system. In this paper it is demonstrated that the graph topology is an appropriate framework in which to discuss convergence of approximations used for controller design. It is also shown that Galerkin type approximations to a large class of problems possess the required convergence properties and can be used to design controllers which will perform as designed when implemented on the original infinitedimensional system. An H1controller design problem is used to illustrate this approach. Key words: infinitedimensional systems, Galerkin approximations, coprime factorizations, control theory, graph topology 1 Introduction There are computational difficulties, apart from the theoretical problems, to designing controllers for systems whose dynamics are described by partial differential equations or integraldifferential equations. Consider the following on ...
Estimation of Material Parameters for Grid Structures
 J. MATH. SYSTEMS, ESTIM. CONTROL
, 1991
"... A numerical approximation scheme is developed for the identification of spatially varying stiffness parameters along with KelvinVoigt and viscous damping parameters in LoveKirchhoff models for the transverse vibrations of thin, flexible grids. The inverse problem is formulated as a least squares f ..."
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Cited by 5 (3 self)
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A numerical approximation scheme is developed for the identification of spatially varying stiffness parameters along with KelvinVoigt and viscous damping parameters in LoveKirchhoff models for the transverse vibrations of thin, flexible grids. The inverse problem is formulated as a least squares fit to data. Splinebased finite element approximations are used to solve the partial differential equation which describes the dynamics of the grid. Theoretical convergence results concerning the parameter estimates are obtained. Several numerical examples are discussed.
Analyticity and Riesz basis property of semigroups associated to damped vibrations
 J. Evol. Eq
, 2008
"... Second order equations of the form ¨z(t)+A0z(t)+D ˙z(t) = 0 are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of the operator matrix A = ˆ ˜ 0 I −A0 −D associated with the second order problem abov ..."
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Cited by 4 (0 self)
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Second order equations of the form ¨z(t)+A0z(t)+D ˙z(t) = 0 are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of the operator matrix A = ˆ ˜ 0 I −A0 −D associated with the second order problem above. We develop sufficient conditions for analyticity of the associated semigroup and for the existence of a Riesz basis consisting of eigenvectors and associated vectors of A in the phase space.
Model Reference Adaptive Control of Distributed Parameter Systems
 SIAM J. Control Optim
, 1995
"... A model reference adaptive control law is defined for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand triple of reflexive Banach and Hilbert spaces. The resulting nonlinear closed loop sys ..."
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Cited by 3 (0 self)
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A model reference adaptive control law is defined for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator defined with respect to a Gelfand triple of reflexive Banach and Hilbert spaces. The resulting nonlinear closed loop system is shown to be well posed. The tracking error is shown to converge to zero, and regularity results for the control input and the output are established. With an additional richness, or persistence of excitation assumption, the parameter error is shown to converge to zero as well. A finite dimensional approximation theory is developed. Examples involving both first (parabolic) and second (hyperbolic) order systems and linear and nonlinear systems are discussed, and numerical simulation results are presented. Supported in part by DFG. y Supported in part by the Air Force Office of Scientific Research under grant AFOSR F496209310198, and in part by NASA under grant NAG11600. z S...