منابع مشابه
Control of Partial Differential Equations
Evolution Equations 254 Let F be another Hilbert space (with scalar product and 255 norm denoted by the same symbols as for H), the so256 called control space, and let B : F ! H be a linear opera257 tor, that we will assume to be bounded for the time being. 258 Then, given T > 0 and u0 2 H, for all f 2 L2(0; T ; F) the 259 Cauchy problem 260 ( u0(t) D Au(t)C B f (t) t 0 u(0) D u0 (12) 261 has a...
متن کاملOptimal Control of Partial Differential Equations
1 Motivating Examples 4 1.1 Stationary Optimal Heating Problems . . . . . . . . . . . . . . . . . . . 4 1.1.1 General Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 Boundary Control . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.3 Distributed Control . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Transient Optimal Heating Problems . . . . . . . . . . ....
متن کاملFeedback modal control of partial differential equations
For hybrid systems in which control consists of selection from a discrete finite set of modes, a somewhat unfamiliar formulation is needed for analysis of the possibility of closed loop (feedback) control. We are here concerned to examine the desiderata for such feedback from the viewpoint of descriptive modeling of implementation in a PDE context. A principal result is global existence, in an ...
متن کاملAdvances in Control of Partial Differential Equations
s of the Invited Presentations 1. Roger W. Brockett, Division of Engineering and Applied Sciences, Harvard University The Influence of Continuum Dynamics on the Stabilization Problem The problem of stabilizing an unstable system by feedback is frequently encountered in applications of control. Although unsolved problems arise in a nonlinear setting, for controllable finite dimensional linear sy...
متن کاملAPPLICATION OF PARTIAL DIFFERENTIAL EQUATIONS IN SNOW MECHANICS
In the present work, failure of a snow slab is analyzed by accounting Normal mode criteria. The analysis has been extended to include residual stress into the model (in addition to body forces). Intensity of crack energy release rate, and displacement components have been derived and their values have been estimated. The obtained results have been compared with the existing snow slab failure mo...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2009
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.6451