By Eitan Altman, Tamer Başar, Naira Hovakimyan (auth.), Jerzy A. Filar, Vladimir Gaitsgory, Koichi Mizukami (eds.)
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Consider a system (E). Given y(> 0), find an output feedback controller (r) satisfying the following conditions (PI) and (P2), and characterize the domain Q satisfying condition (PI): (PI) The closed-loop system (E, f) is internally stable in a domain Q £; IRn x IRn that contains the equilibrium point (0, 0). 34 S. Sasaki and K. Uchida (P2) Whenever (X (0) , HO)) for all W E L 2p . = (0,0), thereexistssomep(> 0) and IIzll2 S yllwII2 3 Characterizations of Controllers Now assume that the structures 771 (~), 772(~), 773(~) of the controller (r) are already designed.
The study leads to original results not only in the infinite-dimensional case, but also for finite-dimensional systems with nonlinear outputs. Two examples included in this paper serve to illustrate the theory. The paper ends with two Appendices, containing some auxiliary results used in the main body of the paper. 1 Problem Formulation Consider a class of uncertain dynamical systems governed by the set of evolution equations x(t) = Ax(t) + Bu(t) + Dw(t), (10) x(to) = Xo, z(t) = f(x(t), u(t», where x(t) E X is the state, u(t) E V the control, w(t) E W the disturbance, and z(t) E Z the controlled output, with X, U, W, Z being real separable Hilbert spaces.
As in the nondelayed case, we see that for the case of sinusoidal measurement perturbations and noise, the attenuation is better under an H OO controller, whereas in the other cases the situation is reversed. 8 Concluding Remarks We have presented in this paper a control-theoretic approach to designing optimal rate-based flow controller. Using the Hoo-optimization based controller 26 E. Altman, T. ----. 5 -1 35 and N. 3 = 10, sinusoidal design theory that was developed in the last decade, we were able to handle very general measurement noise and interfering traffic: these may be bursty, nonstationary, nonergodic, higWy correlated, and even periodic.