This text provides, in a unified framework, an updated treatment centered on the theory of optimal control with quadratic cost functional for abstract linear systems, with application to boundary/point control problems for partial differential equations (distributed parameter systems). It culminates with the analysis of differential and algebraic Riccati equations which arise in the pointwise feedback synthesis of the optimal pair. It incorporates the critical topics of optimal irregularity of solutions to mixed problems for partial differential equations, exact controlability, and uniform feedback stabilization. It covers the main results of the theory, as well as the authors' basic philosophy behind it. Moreover, it provides numerous illustrative examples of boundary/point control problems for partial differential equations, where the abstract theory applies. Both continuous theory and numerical approximation theory are included.
1. Introduction: Two abstract classes; statement of main problems.- 2. Abstract differential Riccati equation for the first class subject to the analyticity assumption (H.1)=(1.5).- 3. Abstract differential Riccati equations for the second class subject to the trace regularity assumption (H.2)=(1.6).- 4. Abstract differential Riccati equations for the second class subject to the regularity assumptions (H.2R)=(1.8).- 5. Abstract algebraic Riccati equations: Existence and uniqueness.- 6. Examples of partial differential equation problems satisfying (H.1).- 7. Examples of partial differential equation problems satisfying (H.2).- 8. Example of a partial differential equation problem satisfying (H.2R).- 9. Numerical approximations of the solution to the abstract differential and algebraic Riccati equations.- 10. Examples of numerical approximation for the classes (H.1) and (H.2).- 11. Conclusions.
Series: Lecture Notes in Control and Information Sciences
Number Of Pages: 165
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99
Weight (kg): 0.3