By H. T. Banks, K. Ito, C. Wang (auth.), Wolfgang Desch, Franz Kappel, Karl Kunisch (eds.)
Read Online or Download Estimation and Control of Distributed Parameter Systems: Proceedings of an International Conference on Control and Estimation of Distributed Parameter Systems, Vorau, July 8–14, 1990 PDF
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Extra info for Estimation and Control of Distributed Parameter Systems: Proceedings of an International Conference on Control and Estimation of Distributed Parameter Systems, Vorau, July 8–14, 1990
Hampton, VA .. T. Banks and C. Wang, Optimal feedback control of infinite-dimensional parabolic evolution [BW] systems: approximation techniques, SIAM J. Control and Optim. 27 (1989), 1182-1219. [C] G. Chen, Energy decay estimates and exact boundary value controllability for wave equation in a bounded domain, J. Math. Pures Appl. 5 (1979), 249-274. [D] R. Datko, Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedback, SIAM J. Control and Opt.
Re (Ah)(F(h» = Re (h, A* F(h)}H. 3) we see (h, A* F(h)}H = Ao(h, F(h)}H = Aoh(F(h» = Aolhltr. + (h, (A* - Ao)F(h») H + (h, -RAO(A)h}H + ((A - Ao)RAO(A)h,RAO(A)h)H' so that Re (h, A* F(h)}H :::; Aolhltr. + (w - Ao)IRAO(A)hlk = (Ao +(w - Ao»)lhlt•. Henee Re (Ah, h}v. :::; wlhltr. for all h E H = dom A. Sinee H = dom A is dense in V*, we have that A - wI is dissipative. 7) (Ao - A)h = v*. \0 - A)h)(v) = v*(v) for all v E V. \0 - A*)v) H = (R>'o(A*)h,v)v. 7) is equivalent to: For v* E V*, there exists h E H so that F(v*) = R>'o(A*)h.
Since our main concern is to solve linear quadratic control problems using these approximation schemes, this observation should not substantially diminish the attractiveness of these two methods. T. Banks, W. J. Silcox, Active control of noise: A time domain approach, Proc. Conf. on Recent Advances in Active Control of Sound and Vibration, (VPISU, Blacksburg), April, 1991, pp. S43-S47. T. Banks and K. Kunisch, The linear regulator problemfor parabolic systems, SIAM J. Control and Opt. 22 (1984), 684-698.