TY - GEN

T1 - Constrained ℋ∞ mixed-sensitivity optimization for stable infinite-dimensional plants

T2 - 2006 American Control Conference

AU - Cifdaloz, Oguzhan

AU - Rodriguez, Armando

PY - 2006/12/1

Y1 - 2006/12/1

N2 - This paper shows how ℋ∞ near-optimal finite-dimensional compensators may be designed for stable linear time invariant (LTI) infinite dimensional plants subject to convex constraints. The infinite dimensional plant is approximated by a finite dimensional approximant. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity ℋ∞ optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated infinite dimensional optimization problem from to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed sensitivity ℋ∞ control system design problems, subgradient concepts are used to directly accommodate time-domain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Convergence results are presented. An illustrative example for a thermal diffusion process is also provided.

AB - This paper shows how ℋ∞ near-optimal finite-dimensional compensators may be designed for stable linear time invariant (LTI) infinite dimensional plants subject to convex constraints. The infinite dimensional plant is approximated by a finite dimensional approximant. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity ℋ∞ optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated infinite dimensional optimization problem from to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed sensitivity ℋ∞ control system design problems, subgradient concepts are used to directly accommodate time-domain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Convergence results are presented. An illustrative example for a thermal diffusion process is also provided.

UR - http://www.scopus.com/inward/record.url?scp=34047213310&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047213310&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:34047213310

SN - 1424402107

SN - 9781424402106

T3 - Proceedings of the American Control Conference

SP - 1009

EP - 1014

BT - Proceedings of the 2006 American Control Conference

Y2 - 14 June 2006 through 16 June 2006

ER -