1991 | OriginalPaper | Chapter
Desensitizing Control
Author : Univ.-Prof. Dr. Alexander Weinmann
Published in: Uncertain Models and Robust Control
Publisher: Springer Vienna
Included in: Professional Book Archive
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Consider the plant 1$${\rm{\dot x(t) = A(p)x(t) + B(p)u(}}t){\rm{B}} \in {R^{nxm}},{\rm{p}} \in {{\rm{R}}^{{n_p}}}$$ where A(p) and B(p) are matrix-valued functions of a slowly varying parameter vector p. Hence, x(t) depends on p . The subscript 0 denotes the nominal values. Assume that a quadratic performance has to be minimized 2$$I = \int_0^\infty {[{x^T}(t)Qx(t) + {{\rm{u}}^T}} (t){\rm{Ru}}(t)]dt$$ and the optimal control variable u(t) is 3$${{\rm{u}}^ \star }(t) = Kx(t) = - {R^{ - 1}}{B_0}Px(t)$$