Some computational issues in optimal control by nonlinear programming |
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Authors: | T J Owens J F Marsh |
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Affiliation: | (1) Control Engineering Centre, Department of Electrical Engineering and Electronics, Brunel University of West London, UB8 3PH Uxbridge, Middlesex, UK |
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Abstract: | The Roppenecker 11] parameterization of multi-input eigenvalue assignment, which allows for common open- and closed-loop eigenvalues, provides a platform for the investigation of several issues of current interest in robust control. Based on this parameterization, a numerical optimization method for designing a constant gain feedback matrix which assigns the closed-loop eigenvalues to desired locations such that these eigenvalues have low sensitivity to variations in the open-loop state space model was presented in Owens and O'Reilly 8]. In the present paper, two closely related numerical optimization methods are presented. The methods utilize standard (NAG library) unconstrained optimization routines. The first is for designing a minimum gain state feedback matrix which assigns the closed-loop eigenvalues to desired locations, where the measure of gain taken is the Frobenius norm. The second is for designing a state feedback matrix which results in the closed-loop system state matrix having minimum condition number. These algorithms have been shown to give results which are comparable to other available algorithms of far greater conceptual complexity. |
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Keywords: | Nonlinear programming multivariable control systems |
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