2005 Fiscal Year Final Research Report Summary
Theoretical and Numerical Study on Sampled-Data Control of Parabolic Distributed Parameter Systems
| Project/Area Number |
16540111
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kagoshima University |
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Principal Investigator |
SANO Hideki Kagoshima University, Computing and Communications Center, Associate Professor, 学術情報基盤センター, 助教授 (70278737)
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| Project Period (FY) |
2004 – 2005
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| Keywords | parabolic system / unbounded output operator / sampled-data H∞ control / finite-dimensional controller / residual mode filter / hyperbolic system / exponential stability / observability, reachability |
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| Research Abstract |
This research is concerned with sampled-data H_∞ control of parabolic systems with unbounded output operators. Especially, the output operator is assumed to be (-L)^γ-bounded, where 0<γ<1/2. For example, diffusion systems with boundary control can be formulated as parabolic systems with output operators of such a type. For the parabolic system with an ideal sampler and a zero-order hold, the aim is to construct a finite-dimensional discrete-time stabilizing controller that makes the L^2 -induced norm of the feedback sampled-data system less than a given positive number. For that purpose, the infinite-dimensional continuous-time system is formulated as an infinite-dimensional discrete-time system by using a lifting technique and a variable transformation. Based on a reduced-order model with a finite-dimensional state space for the infinite-dimensional discrete-time system, a finite-dimensional controller containing a residual mode filter is designed to provide the desirable performance.
Moreover, systems whose axial dispersion coefficients are sufficiently small and can be neglected are treated as control objects. A parallel-flow heat exchanger with boundary inputs is described by two parabolic equations when the axial dispersion is taken into consideration. On the other hand, the parabolic equations become hyperbolic equations in the case where the axial dispersion can be neglected. In this research, the stability analysis is carried out, for the closed-loop system which consists of the hyperbolic system and an output feedback law. In addition, the dynamical analysis such as observability and reachability is performed for the hyperbolic system.
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