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Time suboptimal feedback control of systems described by linear parabolic partial differential equations
Author(s) -
Wong Kin Tuck,
Luus Rein
Publication year - 1982
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660030206
Subject(s) - mathematics , partial differential equation , orthogonal collocation , optimal control , parabolic partial differential equation , control theory (sociology) , scalar (mathematics) , linear quadratic gaussian control , linear quadratic regulator , quadratic equation , differential equation , mathematical optimization , collocation method , mathematical analysis , ordinary differential equation , computer science , control (management) , geometry , artificial intelligence
Feedback control for systems described by linear parabolic partial differential equations is considered from a time suboptimal point of view. A scalar quadratic function representing the deviation from a desired distribution is first formulated, and the rate of approach to the target is maximized by minimizing this quadratic function at each time step. An orthogonal collocation technique enables an accurate low‐order lumped parameter model to be constructed. A direct search optimization can then be used to obtain the optimal quadratic function and, subsequently, the optimal feedback gain matrix for control. The resulting control applied to a diffusion process takes the system to the target rapidly and in a stable manner.