On the Design of a Piecewise-constant Feedback Control for the Linear Regulator Problem |
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Page 30
... nonsingular , so that the set of Tj vectors Xk = ek k = 1 , τ j m form a basis of R TM m Only m - 1 of the basis vectors can lie in the null space of S , resulting in a contradiction . b ) m Since Y = Σ α.φ is a sum of nonsingular ...
... nonsingular , so that the set of Tj vectors Xk = ek k = 1 , τ j m form a basis of R TM m Only m - 1 of the basis vectors can lie in the null space of S , resulting in a contradiction . b ) m Since Y = Σ α.φ is a sum of nonsingular ...
Page 31
... nonsingular . < §¡ , §j > > denotes the inner product . Consider the expression f พ . = k [ e , [ Q + K ' WK ] [ dt . ( 79 ) This is a gram matrix of linearly independent vectors , and hence in positive definite . m Σ Wk = k = 1 Note ...
... nonsingular . < §¡ , §j > > denotes the inner product . Consider the expression f พ . = k [ e , [ Q + K ' WK ] [ dt . ( 79 ) This is a gram matrix of linearly independent vectors , and hence in positive definite . m Σ Wk = k = 1 Note ...
Page 37
... nonsingular Ai + 1 = GiFi ( 91 ) If A is symmetric and positive definite , then the LR algorithm of Rutishauser [ 15 ] is much more economical than the QR algorithm because the latter is only linearly con- vergent while the LR algorithm ...
... nonsingular Ai + 1 = GiFi ( 91 ) If A is symmetric and positive definite , then the LR algorithm of Rutishauser [ 15 ] is much more economical than the QR algorithm because the latter is only linearly con- vergent while the LR algorithm ...
Contents
Surface Modeling Algorithms | 2 |
Structure of the Suboptimal Feedback Control | 3 |
Structure Performance index | 13 |
13 other sections not shown
Common terms and phrases
accuracy approximation coefficient computed constraint algorithm contraction mapping CORN CORNELL CORNELL CORNELL FOUNDED CORNELL LIBRARY CORNELL CORNELL UNIVERSITY CORNELL UNIVERSITY CORNELL cost index denote distribution eigenvalues elements equation expressions EZRA EZRA CORNELL feedback control feedback gain matrix FOUNDED LIBRARY function gradient and Hessian Hessian p.d. HOSV implementation integral interpolation interval inverse iterations to solution Lemma LIBRARY LIBRARY LIBRARY UNIV LIBRARY UNIVERSITY linear regulator linear regulator problem matrix R(to method modified Hessian number of iterations number of switches OUNDED P(to parameters partial derivatives performance index piecewise-constant point quadrature polynomial positive definite Q+K'WK QR algorithm quadrature rate of convergence resulting Riccati feedback Riccati solution satisfy scheme second order second-variation switches 3 switches Taylor expansion technique Theorem A-2 thesis third-variation algorithm Tj+1 transition matrix UNIV CORNELL CORNELL UNIVERSITY CORNELL LIBRARY vector δι δλ δτ ττ