Title :
H∞-control by state-feedback and fast algorithms for the computation of optimal H∞-norms
Author :
Scherer, Carsten
Author_Institution :
Math. Inst., Wurzburg Univ., West Germany
fDate :
10/1/1990 12:00:00 AM
Abstract :
The suboptimality of some parameter for H∞ -optimization by dynamic state-feedback is characterized in terms of the solvability of Riccati inequalities. This is done without restricting the finite zero structure of the plant. If there are no system zeros on the imaginary axis, the H∞-problem can be treated in a complete and satisfactory way. Explicit characterizations optimum to be achieved are provided, and a closed formula for the optimal value is derived in terms of the H∞-norm of some fixed transfer matrix. If the optimum is not attained, any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high-gain. A globally and quadratically convergent algorithm to compute the optimal value is proposed. This algorithm is generalized to the H∞-optimization problem by measurement feedback
Keywords :
control system analysis; feedback; optimal control; optimisation; poles and zeros; Riccati inequalities; dynamic state-feedback; optimal control; optimization; state-feedback; suboptimality; transfer matrix; zero structure; Eigenvalues and eigenfunctions; Frequency domain analysis; Game theory; H infinity control; Helium; Output feedback; Polynomials; Riccati equations; State feedback; Symmetric matrices;
Journal_Title :
Automatic Control, IEEE Transactions on