The Continuous-Time Problem with Imperfect-State Measurements

  • Tamer Başar
  • Pierre Bernhard
Part of the Modern Birkhäuser Classics book series (MBC)


We now turn to the class of continuous-time problems originally formulated in Section 1.2, where the state variable is no longer available to the controller, but only a disturbance-corrupted linear output is. The system is therefore described by the following equations
$$\begin{array}{*{20}c} {\dot x\left( t \right) = \left( t \right)x\left( t \right) + B\left( t \right)u\left( t \right) + D\left( t \right)w\left( t \right),} & {x\left( 0 \right) = x_0 } \\ \end{array}$$
$$y\left( t \right) = C\left( t \right)x\left( t \right) + E\left( t \right)w\left( t \right)$$


Continuous Time Riccati Equation Auxiliary Problem Conjugate Point Optimal Controller 
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Copyright information

© Springer Science+Business Media New York 2008

Authors and Affiliations

  • Tamer Başar
    • 1
  • Pierre Bernhard
    • 2
  1. 1.Coordinated Science LaboratoryUniversity of IllinoisUrbanaUSA
  2. 2.Unité de Recherche Sophia-AntipolisINRIAValbonne CedexFrance

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