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
Y1 - 2006
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.
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U2 - 10.1109/acc.2006.1655491
DO - 10.1109/acc.2006.1655491
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
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 14 June 2006 through 16 June 2006
ER -