A trustregion interior point approach to fixed-order control applied to the benchmark system (2003)
| Venue: | European Journal of Control |
| Citations: | 1 - 0 self |
BibTeX
@ARTICLE{Hol03atrustregion,
author = {C. W. J. Hol and C. W. Scherer and E. G. Van Der Meché and O. H. Bosgra},
title = {A trustregion interior point approach to fixed-order control applied to the benchmark system},
journal = {European Journal of Control},
year = {2003}
}
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Abstract
The computation of optimal H ∞ controllers with a pre-scribed order is motivated by real-time implementation on systems with a very high sampling rate. In this paper we present a nonlinear SDP approach to the H ∞ fixed-order synthesis problem. The algorithm is an extension of a primal predictor-corrector method to nonconvex problems. To avoid wrong step directions the usual Newton steps in the corrector are replaced by a curved line-search. The predictor steps are based on Dikin elliposids of a “convexified ” domain. The method converges, under mild conditions, to a point that satisfies the first order necessary conditions. We compared the method with two other methods for fixed-order control: a posteriori reduction and the cone complementarity method. We computed for all three methods 6th order controllers for a 27th order plant of an active suspension system. The interior point method computes a controller which has slightly larger closed-loop H∞-norm than the full order controller. Results of experiments show that the controller computed with the interior point method practically achieved the control objectives.
Keyphrases
trustregion interior point approach benchmark system interior point method full order controller fixed-order synthesis problem first order necessary condition order controller 27th order plant predictor step cone complementarity method dikin elliposids fixed-order control nonlinear sdp approach method converges posteriori reduction convexified domain usual newton step primal predictor-corrector method pre-scribed order active suspension system wrong step direction optimal controller curved line-search real-time implementation closed-loop norm mild condition
