Optimal Control of Distributed Systems with Conjugation Conditions

1. Front Matter

   Pages i-xvi

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2. Control of Systems Described by Elliptic-Type Partial-Differential Equations under Conjugation Conditions

   Pages 1-62

3. Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation under Conjugation Conditions

   Pages 63-98

4. Control of a System Described by a One-Dimensional Quartic Equation under Conjugation Conditions

   Pages 99-132

5. Control of a System Described by a Two-Dimensional Quartic Equation under Conjugation Conditions

   Pages 133-170

6. Control of a System Described by a Parabolic Equation under Conjugation Conditions

   Pages 171-202

7. Control of a System Described by a Parabolic Equation in the Presence of Concentrated Heat Capacity

   Pages 203-238

8. Control of a System Described by a Pseudoparabolic Equation under Conjugation Conditions

   Pages 239-271

9. Control of a System Described by a Hyperbolic Equation under Conjugation Conditions

   Pages 273-306

10. Control of a System Described by a Pseudohyperbolic Equation under Conjugation Conditions

    Pages 307-340

11. Optimal Control of a Deformed Complicated Solid Body State

    Pages 341-372

12. Back Matter

    Pages 373-383

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At present, in order to resolve problems of ecology and to save mineral resources for future population generations, it is quite necessary to know how to maintain nature arrangement in an efficient way. It is possible to achieve a rational nature arrangement when analyzing solutions to problems concerned with optimal control of distributed systems and with optimization of modes in which main ground medium processes are functioning (motion of liquids, generation of temperature fields, mechanical deformation of multicomponent media). Such analysis becomes even more difficult because of heterogeneity of the region that is closest to the Earth surface, and thin inclusions/cracks in it exert their essential influence onto a state and development of the mentioned processes, especially in the cases of mining. Many researchers, for instance, A.N. Tikhonov - A.A. Samarsky [121], L. Luckner - W.M. Shestakow [65], Tien-Mo Shih, K.L. Johnson [47], E. Sanchez-Palencia [94] and others stress that it is necessary to consider how thin inclusions/cracks exert their influences onto development of these processes, while such inclusions differ in characteristics from main media to a considerable extent (moisture permeability, permeability to heat, bulk density or shear strength may be mentioned). Xll An influence exerted from thin interlayers onto examined processes is taken into account sufficiently adequately by means of various constraints, namely, by the conjugation conditions [4, 8, 10, 15, 17-20, 22-26, 38, 44, 47, 52, 53, 68, 76, 77, 81, 83, 84, 90, 95, 96-100, 112-114, 117, 123].

• differential equation
• distributed systems
• hyperbolic equation
• optimal control
• partial differential equations

From the reviews of the first edition:

"The book is devoted to a special class of linear-quadratic optimal control problems governed by partial differential equations … . the book gives a clear enough understanding of properties of optimal control problems for the basic cases of nonstandard conjugation conditions (including controls) on the interface between the two domains." (Uldis Raitums, Zentralblatt MATH, Vol. 1080, 2006)

• National Academy of Science of Ukraine, Ukraine

  Naum Z. Shor

• Glushkov Institute of Cybernetics, Ukraine

  Ivan V. Sergienko, Vasyl S. Deineka

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