Abstract
As in Chapter 2 of Part IV we consider a dynamical system governed by the following equation:
or equivalently
where x0 ∈ H and u ∈ L2(0,∞;U). We assume that
Clearly, if hypotheses \( (\mathcal{H}\mathcal{P})_\infty \) hold, then the hypotheses \( (\mathcal{H}\mathcal{P}) \) of Chapter 2 of Part IV are fulfilled with P0 = 0. If α ≤ 1/2, we will choose once and for all a number β belonging to ]1 − α/2, 1 − α/2[. We want to minimize the cost function:
over all controls u ∈ L2(0,∞;U) subject to the differential equation constraint (1.1). We say that the control u ∈ L2(0,∞;U) is admissible if J∞(u) < ∞. The definitions of optimal control, optimal state, and optimal pair are the same as in Chapter 1. When, for any x0 ∈ H, an admissible control exists, we say that (A,AD) is C-stabilizable.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2007 Birkhäuser Boston
About this chapter
Cite this chapter
(2007). Unbounded Control Operators: Parabolic Equations With Control on the Boundary. In: Representation and Control of Infinite Dimensional Systems. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4581-6_13
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4581-6_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4461-1
Online ISBN: 978-0-8176-4581-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)