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, time-invariant 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 single-input 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 phase-variable 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 multi-input 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