
Accession Number : AD0685281
Title : ON EQUIVALENCE OF QUADRATIC LOSS FUNCTIONS.
Descriptive Note : Research rept.,
Corporate Author : GRUMMAN AIRCRAFT ENGINEERING CORP BETHPAGE N Y RESEARCH DEPT
Personal Author(s) : Kreindler,E. ; Hedrick,J. K.
Report Date : JAN 1969
Pagination or Media Count : 24
Abstract : When a linear, timeinvariant plant is optimized with respect to the performance index 1/2 the integral from zero to infinity of (x superscript TQx + u superscript TRu)dt, where x is the state vector and u the control, the optimal control can be expressed as a feedback law u =  Kx. Two pairs of matrices (Q,R) and(Qe,Re), yielding the same control law are equivalent. A necessary and sufficient condition is derived, in the singleinput case, for a symmetric nonnegative definite Q to be equivalent to a diagonal matrix Q*. This condition is satisfied by a plant described by equations in phasevariable canonical form, and a formula for Q* in terms of Q is given. It is shown that an equivalent Qe can be parameterized by exactly n nonnegative parameters. For the multiinput case, Qe and Re must contain at least nr parameters, where n and r are the dimensions of x and u, respectively. (Author)
Descriptors : (*CONTROL SYSTEMS, OPTIMIZATION), DIFFERENTIAL EQUATIONS, MATRICES(MATHEMATICS), FEEDBACK, STABILITY, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE