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\({\mathcal H}^\infty\)-optimal control for a class of reaction-diffusion equations. (English) Zbl 0643.93033

The paper investigates the control of laminar combustion processes represented by a class of one-dimensional, nonlinear, reaction-diffusion equations. The control objective is to regulate the spatial location of a propagation flame front dynamically by varying the fuel-air velocity. It is shown that when viewed from an input-output perspective, the problem is equivalent to the control of a system consisting of linear elements and a single time-varying nonlinear element. The system is controlled using a linear compensator that is designed based on an \({\mathcal H}^{\infty}\) (minimax) optimality criterion.
Reviewer: J.Dzielski

MSC:

93C20 Control/observation systems governed by partial differential equations
80A32 Chemically reacting flows
93C10 Nonlinear systems in control theory
35B37 PDE in connection with control problems (MSC2000)
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
30D55 \(H^p\)-classes (MSC2000)
46E15 Banach spaces of continuous, differentiable or analytic functions
93B50 Synthesis problems
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References:

[1] DZIELSKI , J. E. , and NAGURKA , M. L. , 1985 , Position control of a one-dimensional flame front . Technical Report, Department of Mechanical Engineering, Carnegie-Mellon University .
[2] FLAMM , D. S. , and MITTER , S. K. , 1986 , HSensitivity minimization for delay systems : Part I. Laboratory for Information and Decision Systems, Report LIDS-P-1513 , Massachusetts Institute of Technology .
[3] DOI: 10.1109/TAC.1985.1103860 · Zbl 0647.93010 · doi:10.1109/TAC.1985.1103860
[4] DOI: 10.1109/TAC.1985.1103825 · Zbl 0576.93022 · doi:10.1109/TAC.1985.1103825
[5] DOI: 10.1016/0010-2180(57)90016-0 · doi:10.1016/0010-2180(57)90016-0
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[7] WILLIAMS F. A., Combustion Theory (1965)
[8] DOI: 10.1109/TAC.1981.1102603 · Zbl 0474.93025 · doi:10.1109/TAC.1981.1102603
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