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# Algebraic Riccati equations arising in boundary/point control: A review of theoretical and numerical results Part I: Continuous case

Chapter

## Abstract

Consider the following optimal control problem: Given the dynamical system minimize the quadratic functional over all u ∈ L

$$ {y_t} = Ay + Bu;\quad y\left( 0 \right) = {y_0} \in y $$

(1.1)

$$ J\left( {u,y} \right) = \int\limits_0^\infty {\left[ {||RY\left( t \right)||\frac{2}{Z} + ||u\left( t \right)||\frac{2}{U}} \right]} dt $$

(1.2)

_{2}(0, ∞, U), with y solution of (1.1) due to u.## Keywords

Optimal Control Problem Riccati Equation Hyperbolic Equation Regularity Result Abstract Setting## Preview

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