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We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the...
A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.
We discuss the null boundary controllability of a linear thermo-elastic plate. The method employs a smoothing property of the system of PDEs which allows the boundary controls to be calculated directly by solving two Cauchy problems.
In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.
The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input state” map in -norms is established. A structure of the reachable sets for arbitrary is studied. In general case, only the first component of the complete state may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....
The boundary control problem for the dynamical Lame system
(isotropic elasticity model) is considered. The continuity of
the “input → state" map in L2-norms is established. A structure of the
reachable sets for arbitrary T>0 is studied.
In general case, only the first component of the
complete state
may be controlled, an approximate controllability occurring in
the subdomain filled with the shear (slow) waves.
The controllability results are applied to the problem of the boundary
data continuation....
The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The purpose of this paper is to show that the method of controlled
Lagrangians and its Hamiltonian counterpart (based on the notion
of passivity) are equivalent under rather general hypotheses. We
study the particular case of simple mechanical control systems
(where the underlying Lagrangian is kinetic minus potential
energy) subject to controls and external forces in some detail.
The equivalence makes use of almost Poisson structures (Poisson
brackets that may fail to satisfy the Jacobi identity)...
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant.
The results are obtained by applying global perturbations of the domains
and exploiting analytic perturbation properties.
The work is motivated by two applications: an existence result for
the problem of maximizing the rate of...
Continuous multidimensional systems described by partial differential equations can be represented by discrete systems in a number of ways. However, the relations between the various forms of continuous, semi-continuous, and discrete multidimensional systems do not fit into an established framework like in the case of one-dimensional systems. This paper contributes to the development of such a framework in the case of multidimensional systems. First, different forms of partial differential equations...
The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem...
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