In this paper, we present a discussion of the proper orthogonal decomposition (POD) as applied to simulation and feedback control of the one dimensional heat equation. We provide two examples of input collections to which the POD process is applied. First, we apply POD directly to the nite element basis of linear B-splines. Next we additionally include time snapshots. We show that although the ...

For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...

We consider a fractional program with both linear and quadratic equation in numerator and denominator  having second order cone (SOC) constraints. With a suitable change of variable, we transform the problem into a  second order cone programming (SOCP)  problem.  For the quadratic fractional case, using a relaxation, the problem is reduced to a semi-definite optimization (SDO) program. The p...