The author of this book made an attempt to create the general theory of optimization of linear systems (both distributed and lumped) with a singular control. The book touches upon a wide range of issues such as solvability of boundary values problems for partial differential equations with generalized right-hand sides, the existence of optimal controls, the necessary conditions of optimality, the controllability of systems, numerical methods of approximation of generalized solutions of initial boundary value problems with generalized data, and numerical methods for approximation of optimal controls. In particular, the problems of optimization of linear systems with lumped controls (pulse, point, pointwise, mobile and so on) are investigated in detail.

Inhalt

Preface. 1. Optimization of linear systems with generalized control. 2. General principles of investigation of linear systems with generalized control. 3. Numerical methods of optimization of linear systems with generalized control. 4. Parabolic systems. 5. Pseudo-parabolic systems. 6. Hyperbolic systems. 7. Pseudo-hyperbolic systems. 8. Systems with hyperbolic operator coefficients. 9. Sobolev systems. 10. Controllability of linear systems with generalized control. 11. Perspectives. References.