This paper deals with the LQG control problem of flexible structures. Since the solution to this problem is given by infinite dimension equations, an approximation scheme is necessary to find an implementable control law. Here a Galerkin approach is used. The novelty of the paper is the successful use of the eigenfunctions of the system instead of usual splines to build up finite dimensional approximating subspaces. By using the Trotter-Kato theorem, it is proved that the state of the system evolving when the approximating input is applied converges in L2 norm to the state evolving when the optimal one is applied.
Manes, C., Palumbo, P., Pepe, P. (2015). An approximation scheme for the LQG control of flexible structures. In European Control Conference, ECC 1999 - Conference Proceedings (pp.1393-1398). Piscataway (New Jersey) : Institute of Electrical and Electronics Engineers Inc. [10.23919/ecc.1999.7099506].
An approximation scheme for the LQG control of flexible structures
Palumbo, P
;
2015
Abstract
This paper deals with the LQG control problem of flexible structures. Since the solution to this problem is given by infinite dimension equations, an approximation scheme is necessary to find an implementable control law. Here a Galerkin approach is used. The novelty of the paper is the successful use of the eigenfunctions of the system instead of usual splines to build up finite dimensional approximating subspaces. By using the Trotter-Kato theorem, it is proved that the state of the system evolving when the approximating input is applied converges in L2 norm to the state evolving when the optimal one is applied.
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