ON EQUIVALENCE OF QUADRATIC LOSS FUNCTIONS.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1969
- Accession Number
- AD0685281
Entities
People
- E. Kreindler
- J. K. Hedrick
Organizations
- Grumman