Optimal Design of Robust Controllers for Uncertain Discrete-Time Systems
I. K. Konstantopoulos and P. J. Antsaklis
International Journal of Control, Vol. 65, No. 1, pp. 71-91, September 1996.
Abstract -- This paper presents a fast algorithm for the design of robust
output feedback controllers for linear uncertain discrete-time systems. The
algorithm utilizes a version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS)
optimization method of conjugate directions and minimizes a performance index
that includes an LQR term to optimize performance and a robustness term based
on recently developed bounds. The minimization of only the robustness term
which corresponds to the maximization of the uncertainty bound is also studied.
The case of unstructured perturbations in $A$ has been the only one studied
in the robust controller design literature; the present algorithm introduces a
unified approach to both cases of unstructured and structured perturbations in
the matrices of a state-space model. For the special case of unstructured
perturbations in $A$ only, the algorithm is shown to improve considerably the
existing unstructured uncertainty bound. Several examples, including an
aircraft control system and a paper-machine head box, are presented to
illustrate the results.
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