الفهرس 
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Abstract
sis presented here describes a framework for optimal control by nonlinear ing via a parameterization of multi-input eigenvalue assignment, which only for distinct open and closed-loop eigenvalues but also for the case of open and closed-loop eigenvalues. This framework is used to develop a fJ,nd effective algorithm based on iterative optimization that can solve several
’,multivariable control problems. The algorithm is tlsed for designing a state matrix which minimizes objective functions based on the Frobenius norm of
dback gain and/or the condition number of the c.losed-loop system state for specified closed-loop eigenvalue placement. The developed algorithm commercially available routines based on easy-to-use NAG routine for unconstrained optimization which are supported by error indicators. These
s do not require the first derivatives of the objective function to be explicitly The effects of basing the above algorithm upon more sophisticated
rehensive) routines than the easy-to-use routines are demonstrated. These
es have additional parameters to the easy-to-use routines to allow the enced user to improve the efficienr:y of the optimization by tuning it to a
ular problem. The use of such routines is to experimentally validate the use of sy-to-use routines and to seek better solutions to the ill-conditioned problems.
;mgorithm was tested on five test problems using routines for both Quasi-Newton
:nonlinear least-squares optimization. Each with approximate and then accurate ”rs;on at each iteration. The algorithm presented is used to show by examples that
.. izing the product of condition number of the closed-loop system and the state
ack gain may result in a controller which is more robust to rounding errors in
elements of the gain matrix than the controller which minimizes condition number e for the closed-loop system. The test problems indicate that, for robust control, ... may be more desirable to minimize the product of condition number and gain, .. ther than condition number alone.