Bounded Control Operators: Control Inside the Domain

Part of the Systems & Control: Foundations & Applications book series (SCFA)


In this chapter we consider the dynamical system governed by the equation
$$ \left\{ \begin{gathered} x'(t) = Ax(t) + Bu(t),t \geqslant 0, \hfill \\ x(0) = x_0 \in H, \hfill \\ \end{gathered} \right. $$
where A: D(A) ⊂ HH, B: UH are linear operators defined on the Hilbert spaces H (state space) and U (control space), respectively. x is the state and u the control of the system. We shall also consider another Hilbert space Y, the space of observations. The inner product and norm in H, U, and Y will be denoted by (·, ·) and | · |. Whenever confusion is possible a subscript H, U or Y will be added.


Classical Solution Riccati Equation Mild Solution Analytic Semigroup Optimal Pair 
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© Birkhäuser Boston 2007

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