TY - JOUR

T1 - Weighted H∞ mixed-sensitivity minimization for stable MIMO distributed-parameter plants

AU - Rodriguez, Armando

N1 - Funding Information:
This research was supported by Arizona State University FGIA grants 089-90 & 088-92, by an AFOSR RIA, by Research & Development Laboratories, and by Wright Laboratory, Eglin AFB.

PY - 1995

Y1 - 1995

N2 - This paper considers the problem of designing near-optimal finite-dimensional compensators for stable multiple-input multiple-output (MIMO) distributed-parameter plants. A weighted H∞ mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a 'natural' finite-dimensional optimization. Apriori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the distributed-parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. Although the proofs assume and exploit the fact that the plant can be approximated uniformly by finite-dimensional systems, it is indicated how compact approximants could be used. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The proofs and constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straightforward control design approach for a large class of MIMO distributed-parameter systems.

AB - This paper considers the problem of designing near-optimal finite-dimensional compensators for stable multiple-input multiple-output (MIMO) distributed-parameter plants. A weighted H∞ mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a 'natural' finite-dimensional optimization. Apriori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the distributed-parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. Although the proofs assume and exploit the fact that the plant can be approximated uniformly by finite-dimensional systems, it is indicated how compact approximants could be used. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The proofs and constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straightforward control design approach for a large class of MIMO distributed-parameter systems.

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U2 - 10.1093/imamci/12.3.219

DO - 10.1093/imamci/12.3.219

M3 - Article

AN - SCOPUS:33645436182

SN - 0265-0754

VL - 12

SP - 219

EP - 233

JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

IS - 3

ER -