We are currently experiencing intermittent issues impacting performance. We apologize for the inconvenience.
By Topic

Infinite-dimensional convex optimization in optimal and robust control theory

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Young, P.M. ; Dept. of Electr. Eng., Colorado State Univ., Fort Collins, CO, USA ; Dahleh, M.A.

Many engineering problems can be shown to be equivalent to solving semidefinite programs (SPs), i.e., convex optimization problems involving linear matrix inequalities (LMIs). Powerful computation tools are available for such problems in the finite-dimensional case. However, the problems arising in optimal and robust control theory are often infinite dimensional, and so adequate computation tools are not available. The key to tackling such problems with finite computation tools is to have a primal-dual formulation of the problem without duality gap. In this paper we study infinite-dimensional SPs and present a lifting technique to recast SPs as parameterized linear programs (LPs). This enables the wealth of theoretical tools available for infinite-dimensional LPs to be extended to infinite-dimensional SPs. In particular, we develop some new sufficient conditions for the lack of a duality gap for infinite-dimensional SPs and give an exact characterization of the primal and dual problems for these cases. Both primal and dual problems are formed as infinite-dimensional SP problems, with finite truncations to each giving upper and lower bounds, respectively, on the exact solution to the infinite-dimensional problem. Thus, these results can form the basis of practical computation schemes for infinite-dimensional problems, which require only finite-dimensional computation tools. To illustrate the power of these tools we apply the results to two previously unsolved optimization problems, namely minimizing the l1 norm of a closed-loop system subject to bounds on the frequency response magnitude at a finite number of points and/or bounds on the H2 norm

Published in:

Automatic Control, IEEE Transactions on  (Volume:42 ,  Issue: 10 )