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The standard regulator problem for systems with input delays. An approach through singular control theory. (English) Zbl 0815.49006
For the finite-dimensional state space system $\dot x= Ax+ \left\{\sum^ N_{i= 1} B_ i u(t- h_ i)+ \int^ 0_{-h} B(s) u(t+ s) ds\right\},$ where the novelty is in the introduction of “delays” in the control (modelling perhaps actuator-dynamics), the author considers the “infinite-horizon” LQR problem: $\min_ u \int^ \infty_ 0 [x(t), Qx(t)] dt+ \int^ \infty_ 0 [Ru(t), u(t)] dt,\quad R> 0,\quad Q\geq 0,$ and shows the existence of solution under appropriate “stabilizability” conditions, involving a generalized algebraic Riccati equation. The novelty in the technique of solution is the use of the so-called “singular” LQR problem, where $$R$$ as above is singular.

##### MSC:
 49J25 Optimal control problems with equations with ret. arguments (exist.) (MSC2000) 93C25 Control/observation systems in abstract spaces
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