This paper considers an on-line technique for estimating the bounded state of a process described by a linear heat conduction equation. The estimation procedure generates a rationale for the optimal selection of the transducer measurement location within the spatial domain of the conductor. Approximate state estimation is accomplished by two independent procedures, linear programming and least squares, respectively. Appropriate a priori and a posteriori error estimates of the difference between the solution and its approximation are derived. The concept of quasi closed-loop control is introduced, and an extensive listing of related literature for distributed parameter observability and continuation problems is given following the References.

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