Geodesic
A simple solution to the finite-horizon LQ problem with zero terminal state
Kybernetika, Tome 39 (2003) no. 4, p. [483].

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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.
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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     author = {Ntogramatzidis, Lorenzo},
     title = {A simple solution to the finite-horizon {LQ} problem with zero terminal state},
     journal = {Kybernetika},
     pages = {[483]},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {2003},
     mrnumber = {2024527},
     zbl = {1249.49048},
     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, p. [483]. http://geodesic.mathdoc.fr/item/KYB_2003__39_4_a5/