Dzielski, John E.; Nagurka, Mark L. \({\mathcal H}^\infty\)-optimal control for a class of reaction-diffusion equations. (English) Zbl 0643.93033 Int. J. Control 47, No. 6, 1947-1960 (1988). 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 Keywords:laminar combustion; one-dimensional, nonlinear, reaction-diffusion equations; propagation flame front; linear compensator; \({\mathcal H}^{\infty }\) (minimax) optimality criterion PDFBibTeX XMLCite \textit{J. E. Dzielski} and \textit{M. L. Nagurka}, Int. J. Control 47, No. 6, 1947--1960 (1988; Zbl 0643.93033) Full Text: DOI 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 [6] TAYLOR J. H., Nonlinear System Analysis and Synthesis 2 pp 365– (1980) [7] WILLIAMS F. A., Combustion Theory (1965) [8] DOI: 10.1109/TAC.1981.1102603 · Zbl 0474.93025 · doi:10.1109/TAC.1981.1102603 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.