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Li, X. P.

Publications and source records attributed to Li, X. P..

7 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

On convexity of H-infinity Riccati solutions and its applications

The celebrated two-Riccati-equation 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 H-infinity norm or gamma, an upper bound of a suboptimal H-infinity norm, is given. In this note, some properties of these H-infinity Riccati solutions are revealed. 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 on the domain of interest. Based on these properties, a quadratically convergent algorithm is developed to compute the optimal H-infinity norm.

Li, X. P.↗
NASA NTRS1992

The structure of the gamma-domain for H-infinity Riccati solutions

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.

Li, X. P.↗
NASA NTRS1991

Robust control systems design by H-infinity optimization theory

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.

Chang, B. C.↗
NASA NTRS1991

On convexity of H-infinity Riccati solutions

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.

Li, X. P.↗
NASA NTRS1990

Design of an H(infinity) optimal controller by using DGKF's state-space formulas

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.

Chang, B. C.↗
NASA NTRS1990

Iterative computation of the optimal H(infinity) norm by using two-Riccati-equation method

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.

Chang, B. C.↗