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  • 1
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    In:  Other Sources
    Publication Date: 2019-06-28
    Description: The authors revealed several important eigen properties of the stabilizing solutions of the two H-infinity Riccati equations and their product. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H-infinity norm. Two examples are used to illustrate the algorithms.
    Keywords: CYBERNETICS
    Type: In: IEEE Conference on Decision and Control, 30th, Brighton, United Kingdom, Dec. 11-13, 1991, Proceedings. Vol. 2 (A93-13001 02-63); p. 1927-1932.
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  • 2
    Publication Date: 2019-06-28
    Description: The authors investigated some properties of the solutions to H-infinity Riccati equations which play a key role in the state approach to H-infinity optimization problem. The structure of the gamma-domain for the Riccati solutions has been described. There are two kinds of lower bounds for the solutions to exist and to be positive semidefinite respectively. A quadratically convergent algorithm for computing the lower bound is discussed.
    Keywords: CYBERNETICS
    Type: In: 1992 American Control Conference, 11th, Chicago, IL, June 24-26, 1992, Proceedings. Vol. 2 (A93-22776 07-63); p. 1147, 1148.
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  • 3
    Publication Date: 2019-07-12
    Keywords: CYBERNETICS
    Type: Journal of Guidance, Control, and Dynamics (ISSN 0731-5090); 15; 4 Ju; 944-952
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  • 4
    Publication Date: 2019-07-13
    Description: The two-Riccati-equation method solution to a standard H(infinity) control problem can be used to characterize all possible stabilizing optimal or suboptimal H(infinity) controllers if the optimal or suboptimal H(infinity) norm is available in the literature. An iterative algorithm for computing the optimal H(infinity) norm is proposed. The algorithm employs fixed-point, double secant and bisection to guarantee a super linear convergence.
    Keywords: CYBERNETICS
    Type: IEEE Conference on Decision and Control; Dec 05, 1990 - Dec 07, 1990; Honolulu, HI; United States
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  • 5
    Publication Date: 2019-07-13
    Description: The two-Riccati-equation method was employed to design an H(infinity) optimal controller for a four-block problem. An iterative scheme was used to reduce gamma to a number which is very close to the optimum. However, as gamma is close to the optimum, the elements of the state-space realization of the controller will approach infinity. It is demonstrated that the numerical difficulty is caused by the restriction of the controller being strictly proper. This difficulty can easily be removed if one is allowed to have a proper controller with a direct feed-through term.
    Keywords: CYBERNETICS
    Type: IEEE Conference on Decision and Control; Dec 05, 1990 - Dec 07, 1990; Honolulu, HI; United States
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  • 6
    Publication Date: 2019-07-13
    Description: In this paper, step-by-step procedures of applying the H-infinity theory to robust control systems design are given. The objective of the paper is to eliminate the possible difficulties a control engineer may encounter in applying H-infinity control theory and to clear up some misconceptions about H-infinity theory like high-gain controller and numerical obstacles, etc. An efficient algorithm is used to compute the optimal H-infinity norm. The Glover and Doyle (1988) controller formulas are slightly modified and used to construct an optimal controller without any numerical difficulties.
    Keywords: CYBERNETICS
    Type: AIAA PAPER 91-2686 , AIAA Guidance, Navigation and Control Conference; Aug 12, 1991 - Aug 14, 1991; New Orleans, LA; United States
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