Download Control and Estimation of Distributed Parameter Systems: by H. T. Banks, S. C. Beeler, H. T. Tran (auth.), W. Desch, F. PDF

By H. T. Banks, S. C. Beeler, H. T. Tran (auth.), W. Desch, F. Kappel, K. Kunisch (eds.)

Consisting of sixteen refereed unique contributions, this quantity provides a various choice of fresh leads to keep watch over of allotted parameter structures. issues addressed contain - optimum regulate in fluid mechanics - numerical tools for optimum keep watch over of partial differential equations - modeling and keep watch over of shells - point set tools - mesh version for parameter estimation difficulties - form optimization complex graduate scholars and researchers will locate the e-book a very good consultant to the vanguard of keep watch over and estimation of dispensed parameter systems.

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Additional resources for Control and Estimation of Distributed Parameter Systems: International Conference in Maria Trost (Austria), July 15–21, 2001

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2. (49) 48 R. Becker and B. Vexler with a corresponding remainder term 1 R= ~J D"(Xh+ S(X-Xh))( X-X h,X-Xh,X-Xh)S(s - l)ds o (50) J 1 + P"(X" + s(X - x,,))(x - Xh, X - xh)sds. o Proof. 1) we write: J J J 1 M(x) - M(Xh) = M'(Xh + s(X - Xh))(X - xh)ds o 1 D(Xh + s(X - Xh))(X - x,,)ds P(Xh + s(X - Xh))(X - xh)ds. (51) o 1 + o We approximate the first integral by the trapezoidal rule , the second by the box rule and obtain 1 1 M(x) - M(Xh) = 2D(Xh)(X - Xh) + 2D(x)(x - Xh) + P(x)(x - Xh) + R, (52) with a corresponding remainder term J J 1 R = ~ D"(Xh + s(X - Xh))(X - Xh,X - Xh,X - Xh)S(S - l)ds o (53) 1 + P"(Xh + s(X - Xh))(X - Xh,X - xh)sds.

Th) can be written as: (54) This completes the proof. 2. A posteriori error estimation for parameter identification problems In this section we apply the above concept of a posteriori error estimation to parameter identification problems. Mesh Adaptation for Parameter Identification Problems 49 Corresponding to the parameter identification problem (2) we introduce the Lagrangian L in oder to derive optimality conditions, L(u,q,z) 1 21IC(u)112 + J(z) = (55) - a(u,q)(z), for u E V, q E Q and z E V.

29] K. D. Hammett , C. D. Hall, and D. B. Ridgely, Controllability Issues in Nonlinear State-Dependent Riccati Equation Control, Journal of Guidance, Control and Dynamics, 21 (1998) , 767- 773. [30] J . Markman and 1. N. Katz, An Iterative Algorithm for Solving Hamilton Jacobi Type Equations, preprint (1999). [31] W. L. Garrard, D. F. Enns, and S. A. Snell, Nonlinear Feedback Control of Highly Manoeuvrable Aircraft, International Journal of Control, 56 (1992) , 799-812. edu Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205 E-mail address: tran@control .

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