This paper addresses the cheap version of the classical linear quadratic (LQ) optimal control problem for continuous-time systems. The approach herein considered differs from those presented in literature, since it consists of applying the tools of the geometric control theory to the Hamiltonian system. In this way, it is possible to compute the stabilizing state-feedback gain achieving optimality by using standard geometric algorithms, whenever the initial state satisfies a suitable necessary and sufficient condition for solvability, also stated in geometric terms.
Prattichizzo, D., G., M., L., N. (2004). A Straightforward Approach to the Cheap LQ Problem for Continuous-Time Systems in Geometric Terms. In Proc. 43rd IEEE Conference on Decision and Control, 2004, CDC (pp.2262-2266). IEEE [10.1109/CDC.2004.1430385].
A Straightforward Approach to the Cheap LQ Problem for Continuous-Time Systems in Geometric Terms
PRATTICHIZZO, DOMENICO;
2004-01-01
Abstract
This paper addresses the cheap version of the classical linear quadratic (LQ) optimal control problem for continuous-time systems. The approach herein considered differs from those presented in literature, since it consists of applying the tools of the geometric control theory to the Hamiltonian system. In this way, it is possible to compute the stabilizing state-feedback gain achieving optimality by using standard geometric algorithms, whenever the initial state satisfies a suitable necessary and sufficient condition for solvability, also stated in geometric terms.
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https://hdl.handle.net/11365/20156
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