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Optimal control for linear systems with retarded state and observation and quadratic cost

  • Elena M. Fernandez-Berdaguer
  • E. Bruce Lee
Session 7 Distributed Parameter Systems
  • 138 Downloads
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 62)

Abstract

Stabilization (feedback control) of linear finite dimensional systems has long been based on the use of input-output models and ideas associated with equivalent systems. When such ideas are applied to the linear hereditary systems or other infinite dimensional systems new results appear which are significant in terms of controller synthesis and analysis.

Recently the input-output model in the hereditary situation was generalized by admitting delays in the observation (or reconstruction) of state type data. Also considerations of various categories of equivalent linear hereditary systems under, for example, the action of the feedback group has been undertaken. Each of these studies has led to new insights into the formulation of optimal control questions and questions of stabilizability.

Here we extend previous results on optimal control (quadratic formulation) of the linear hereditary systems. The main contribution is the extension of the optimal control theory to the infinite horizon case (with delayed observation) where questions of stability with the optimal controller become a significant issue in optimal synthesis.

The setting is the standard semigroup formulation in the Hilbert space M2. The main result is a characterization of the optimal stabilizing feedback controller in terms of the solution of a certain system of operator Riccati equations in the delayed cost formulation.

Keywords

Riccati Equation Admissible Control Quadratic Cost Controller Synthesis Linear Quadratic Optimal Control Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Elena M. Fernandez-Berdaguer
    • 1
  • E. Bruce Lee
    • 1
  1. 1.Department of Electrical EngineeringUniversity of MinnesotaMinneapolis

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