Journal ArticleDOI
Mixed H/sub 2//H/sub infinity / control: a convex optimization approach
TLDR
It is shown that in the state-feedback case one can come arbitrarily close to the optimal (even over full information controllers) mixed H/sub 2//H/sub infinity / performance measure using constant gain state feedback.Abstract:
The problem of finding an internally stabilizing controller that minimizes a mixed H/sub 2//H/sub infinity / performance measure subject to an inequality constraint on the H/sub infinity / norm of another closed-loop transfer function is considered. This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. Both the state-feedback and output-feedback problems are considered. It is shown that in the state-feedback case one can come arbitrarily close to the optimal (even over full information controllers) mixed H/sub 2//H/sub infinity / performance measure using constant gain state feedback. Moreover, the state-feedback problem can be converted into a convex optimization problem over a bounded subset of (n*n and n*q, where n and q are, respectively, the state and input dimensions) real matrices. Using the central H/sub infinity / estimator, it is shown that the output feedback problem can be reduced to a state-feedback problem. In this case, the dimension of the resulting controller does not exceed the dimension of the generalized plant. >read more
Citations
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References
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Journal ArticleDOI
State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Journal ArticleDOI
State-space formulae for all stabilizing controllers that satisfy and H ∞ norm bound and relations to risk sensitivity
Keith Glover,John Doyle +1 more
TL;DR: In this paper, the relationship between robust and stochastic control is established, giving an equivalence between robust control and control with respect to the Riccati Equation (RCE).
Journal ArticleDOI
LQG control with an H/sup infinity / performance bound: a Riccati equation approach
TL;DR: In this article, an LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered, and an algorithm is developed for the full-order design problem and illustrative numerical results are given.
Journal ArticleDOI
An algebraic Riccati equation approach to H ∞ optimization
Kemin Zhou,Pramod P. Khargonekar +1 more
TL;DR: In this article, the authors considered the general four-block H ∞ optimal control problem with the assumption that system states are available for feedback and showed that the optimal norm of the closed loop transfer function over all linear constant, i.e., non-dynamic, stabilizing state feedback laws can be characterized via an algebraic Riccati equation.