A Structure Exploiting Preprocessor for Semidefinite Programs Derived From the Kalman-Yakubovich-Popov Lemma

• Semidefinite programs derived from the Kalman-Yakubovich-Popov (KYP) lemma are quite common in control and signal processing applications. The programs are often of high dimension which makes them hard or impossible to solve with general-purpose solvers. Here we present a customized preprocessor, KYPD, that utilizes the inherent structure of this particular optimization problem. The key to an efficient implementation is to transform the optimization problem into an equivalent semidefinite program. This equivalent problem has much fewer variables and the matrices in the linear matrix inequality constraints are of low rank. KYPD can use any primal-dual solver for semidefinite programs as an underlying solver.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Keyword

Kalman-Yakubovich-Popov (KYP) lemma

Semidefinite programs (SDPs)

TECHNOLOGY

TEKNIKVETENSKAP

Automatic control

Reglerteknik

Publication and Content Type

ref (subject category)

art (subject category)