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On reachability of parallel-flow heat exchanger equations with boundary inputs. (English) Zbl 1119.93015

This paper is concerned with the problem of reachability for parallel flow two-fluid heat exchanger equations with boundary inputs. It is shown that the boundary control system is well defined in the sense of [R. F. Curtain and H. Zwart, An introduction to infinite-dimensional linear systems theory. Texts in Applied Mathematics. 21. (New York), NY: Springer-Verlag. (1995; Zbl 0839.93001)] and that it is reachable. The proof gives a concrete expression of the corresponding controls. This is possible since the author obtains an explicit solution of the considered system through the method of characteristics. This representation of the solution allows a very clear analysis of the reachability problem. A reachable subspace is given for the case where only one boundary input is added to the system.

MSC:

93B03 Attainable sets, reachability
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
93C20 Control/observation systems governed by partial differential equations

Citations:

Zbl 0839.93001
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References:

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[2] R. F. Curtain and H. J. Zwart, An introduction to infinite-dimensional linear systems theory , Texts in Applied Mathematics, vol. 21, Springer-Verlag, New York, 1995. · Zbl 0839.93001
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