A simple solution to the finite-horizon LQ problem with zero terminal state

Lorenzo Ntogramatzidis

Kybernetika (2003)

  • Volume: 39, Issue: 4, page [483]-492
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Ntogramatzidis, Lorenzo. "A simple solution to the finite-horizon LQ problem with zero terminal state." Kybernetika 39.4 (2003): [483]-492. <http://eudml.org/doc/33658>.

@article{Ntogramatzidis2003,
abstract = {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.},
author = {Ntogramatzidis, Lorenzo},
journal = {Kybernetika},
keywords = {finite-horizon LQ problems; Hamiltonian system; Riccati differential equation; algebraic Riccati equation; optimal value of the quadratic cost; finite-horizon LQ problem; Hamiltonian system; Riccati equation; optimal value of the quadratic cost},
language = {eng},
number = {4},
pages = {[483]-492},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A simple solution to the finite-horizon LQ problem with zero terminal state},
url = {http://eudml.org/doc/33658},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Ntogramatzidis, Lorenzo
TI - A simple solution to the finite-horizon LQ problem with zero terminal state
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 4
SP - [483]
EP - 492
AB - 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.
LA - eng
KW - finite-horizon LQ problems; Hamiltonian system; Riccati differential equation; algebraic Riccati equation; optimal value of the quadratic cost; finite-horizon LQ problem; Hamiltonian system; Riccati equation; optimal value of the quadratic cost
UR - http://eudml.org/doc/33658
ER -

References

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  8. Kwakernaak H., Sivan R., Linear Optimal Control Systems, Wiley, New York 1972 Zbl0276.93001MR0406607
  9. Lewis F. L., Syrmos V., Optimal Control, Wiley, New York 1995 
  10. Marro G., Prattichizzo, D., Zattoni E., 10.1109/9.981727, IEEE Trans. Automat. Control 47 (2002), 1, 102–107 MR1879695DOI10.1109/9.981727
  11. Marro G., Prattichizzo, D., Zattoni E., A nested computational scheme for discrete-time cheap and singular LQ control, SIAM J. Control Optim. 2002 (to appear) 
  12. Marro G., Prattichizzo, D., Zattoni E., Previewed signal H 2 optimal decoupling by finite impulse response compensators, Kybernetika 38 (2002), 4, 479–492 MR1937142

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