Geodesic
A simple solution to the finite-horizon LQ problem with zero terminal state
Kybernetika, Tome 39 (2003) no. 4, pp. 483-492 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This short paper deals with the classical finite-horizon linear-quadratic regulator problem with the terminal state constrained to be zero, for both continuous and discrete-time systems. Closed-form expressions for the optimal state and costate trajectories of the Hamiltonian system, as well as the corresponding control law, are derived through the solutions of two infinite- horizon LQ problems, thus avoiding the use of the Riccati differential equation. The computation of the optimal value of the performance index, as a function of the initial state, is also presented.
This short paper deals with the classical finite-horizon linear-quadratic regulator problem with the terminal state constrained to be zero, for both continuous and discrete-time systems. Closed-form expressions for the optimal state and costate trajectories of the Hamiltonian system, as well as the corresponding control law, are derived through the solutions of two infinite- horizon LQ problems, thus avoiding the use of the Riccati differential equation. The computation of the optimal value of the performance index, as a function of the initial state, is also presented.
Classification : 49N10, 93C15
Keywords: finite-horizon LQ problems; Hamiltonian system; Riccati differential equation; algebraic Riccati equation; optimal value of the quadratic cost 
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     title = {A simple solution to the finite-horizon {LQ} problem with zero terminal state},
     journal = {Kybernetika},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_4_a5/}
}
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Ntogramatzidis, Lorenzo. A simple solution to the finite-horizon LQ problem with zero terminal state. Kybernetika, Tome 39 (2003) no. 4, pp. 483-492. http://geodesic.mathdoc.fr/item/KYB_2003_39_4_a5/

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