Geodesic
Linear Quadratic Control Problem With Fixed Final State for Discrete-Time Distributed Systems
International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 3, pp. 517-535.

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The problem considered is that of minimizing a quadratic cost functional for a discrete distributed system with fixed initial and final states. It is shown that under suitable controllability assumptions, there is a close relationship between this problem and that of exact controllability with minimization of a time-varying energy criterion. The HUM technique is then extended to treat the exact controllability problem in the time-varying case and applied to provide an explicit form for the optimal control and the optimal cost.
Keywords: exact controllability, feedback law, open loop, optimal control, quadratic control
Mots-clés : sterowność, prawo sprzężenia zwrotnego, sterowanie optymalne 
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     author = {Chraibi, L. and Karrakchou, J. and Ouansafi, A. and Rachik, M.},
     title = {Linear {Quadratic} {Control} {Problem} {With} {Fixed} {Final} {State} for {Discrete-Time} {Distributed} {Systems}},
     journal = {International Journal of Applied Mathematics and Computer Science},
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Chraibi, L.; Karrakchou, J.; Ouansafi, A.; Rachik, M. Linear Quadratic Control Problem With Fixed Final State for Discrete-Time Distributed Systems. International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 3, pp. 517-535. http://geodesic.mathdoc.fr/item/IJAMCS_2000_10_3_a3/