State-Space Solution to Anisotropy-Based Stochastic H ∞ -Optimization Problem

Stochastic robust controller reduction by anisotropic balanced truncation

“…The normalized anisotropy-based stochastic H ∞ -optimization problem is characterized by some features making it different from the general-case problem introduced in [2]. To disclose these distinctions, let us briefly consider the statement and solution of the normalized problem given in more details in [6].…”

“…The stochastic approach to H ∞ optimization introduced in [1], [2] is based on using the anisotropic norm of a system as performance criterion. This approach combines the attractive features of robust control and information theories holding an intermediate position between H 2 /LQG and H ∞ problems.…”

“…Given a standard plant model and input mean anisotropy level, the anisotropy-based stochastic H ∞ problem consists in finding an output-feedback dynamic controller to internally stabilize the closed-loop system and minimize its anisotropic norm. The solution to this problem presented in [2] yields to the full-order controller, while it would be desirable to obtain also a reduced-order one.…”

State-Space Solution to Stochastic H∞-Optimization Problem With Uncertainty

“…The problem at the right-hand side of the last equality can be solved by using anisotropic technique developed in (Vladimirov et al, 1996). The frequency description of the worst shaping filter G 0 is given by the following proposition.…”

“…Anisotropy norm (Diamond P. et al, 2001) of the closed-loop transfer function is proposed to be the performance criterion. The controller design problem with such performance criterion was solved in (Vladimirov et al, 1996). Stochastic (anisotropybased) H ∞ -optimal controllers are located "between" H 2 -optimal and H ∞ -optimal controllers.…”