Analysis and Optimization of Systems pp 339-355 | Cite as

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

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## 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 M^{2}. 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## Preview

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