On the Continuous Dependence with Respect to Sampling of the Linear Quadratic Regulator Problem for Distributed Parameter Systems | Zendy

I. G. Rosen | Zendy; Chunming Wang | Zendy

Open Access

On the Continuous Dependence with Respect to Sampling of the Linear Quadratic Regulator Problem for Distributed Parameter Systems

Author(s) -

I. G. Rosen,

Chunming Wang

Publication year - 1992

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 - 10.1137/0330052

Subject(s) - mathematics , linear quadratic regulator , riccati equation , algebraic riccati equation , heat equation , sampling (signal processing) , rate of convergence , control theory (sociology) , optimal control , linear system , stability (learning theory) , quadratic equation , convergence (economics) , discrete time and continuous time , mathematical analysis , mathematical optimization , differential equation , control (management) , statistics , channel (broadcasting) , filter (signal processing) , economic growth , computer science , geometry , machine learning , computer vision , economics , engineering , management , electrical engineering

The convergence of solutions to the discrete- or sampled-time linear quadratic regulator problem and associated Riccati equation for infinite-dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite- and infinite-time horizon problems are studied. In the finite-time horizon case, strong continuity of the operators that define the control system and performance index, together with a stability and consistency condition on the sampling scheme are required. For the infinite-time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary or delay system, and a flexible beam are presented and discussed.

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