Numerical Approximation for the Infinite-Dimensional Discrete-Time Optimal Linear-Quadratic Regulator Problem | Zendy

J. S. Gibson | Zendy; I. G. Rosen | Zendy

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Numerical Approximation for the Infinite-Dimensional Discrete-Time Optimal Linear-Quadratic Regulator Problem

Author(s) -

J. S. Gibson,

I. G. Rosen

Publication year - 1988

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/0326025

Subject(s) - mathematics , linear quadratic regulator , optimal control , hilbert space , semigroup , finite element method , quadratic equation , linear system , convergence (economics) , rate of convergence , mathematical analysis , mathematical optimization , geometry , physics , economics , thermodynamics , economic growth , channel (broadcasting) , engineering , electrical engineering

An abstract approximation framework is developed for the finite and infinite horizon discrete-time linear-quadratic regulator problems for systems whose state dynamics are described by a linear semigroup of operators on an infinite-dimensional Hilbert space. The schemes included in the framework yield finite-dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

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