# A deterministic affine-quadratic optimal control problem

• Volume: 20, Issue: 3, page 633-661
• ISSN: 1292-8119

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## Abstract

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A deterministic affine-quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the optimal control is unique which leads to the differentiability of the value function. Therefore, the value function satisfies the corresponding Hamilton–Jacobi–Bellman equation in the classical sense, and the optimal control admits a state feedback representation. Under some additional conditions, it is shown that the value function is actually twice differentiable and the so-called quasi-Riccati equation is derived, whose solution can be used to construct the state feedback representation for the optimal control.

## How to cite

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Wang, Yuanchang, and Yong, Jiongmin. "A deterministic affine-quadratic optimal control problem." ESAIM: Control, Optimisation and Calculus of Variations 20.3 (2014): 633-661. <http://eudml.org/doc/272934>.

@article{Wang2014,
abstract = {A deterministic affine-quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the optimal control is unique which leads to the differentiability of the value function. Therefore, the value function satisfies the corresponding Hamilton–Jacobi–Bellman equation in the classical sense, and the optimal control admits a state feedback representation. Under some additional conditions, it is shown that the value function is actually twice differentiable and the so-called quasi-Riccati equation is derived, whose solution can be used to construct the state feedback representation for the optimal control.},
author = {Wang, Yuanchang, Yong, Jiongmin},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {affine quadratic optimal control; dynamic programming; Hamilton–Jacobi–Bellman equation; quasi-Riccati equation; state feedback representation; affine-quadratic optimal control problem; Hamilton-Jacobi-Bellman equation},
language = {eng},
number = {3},
pages = {633-661},
publisher = {EDP-Sciences},
title = {A deterministic affine-quadratic optimal control problem},
url = {http://eudml.org/doc/272934},
volume = {20},
year = {2014},
}

TY - JOUR
AU - Wang, Yuanchang
AU - Yong, Jiongmin
TI - A deterministic affine-quadratic optimal control problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2014
PB - EDP-Sciences
VL - 20
IS - 3
SP - 633
EP - 661
AB - A deterministic affine-quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the optimal control is unique which leads to the differentiability of the value function. Therefore, the value function satisfies the corresponding Hamilton–Jacobi–Bellman equation in the classical sense, and the optimal control admits a state feedback representation. Under some additional conditions, it is shown that the value function is actually twice differentiable and the so-called quasi-Riccati equation is derived, whose solution can be used to construct the state feedback representation for the optimal control.
LA - eng
KW - affine quadratic optimal control; dynamic programming; Hamilton–Jacobi–Bellman equation; quasi-Riccati equation; state feedback representation; affine-quadratic optimal control problem; Hamilton-Jacobi-Bellman equation
UR - http://eudml.org/doc/272934
ER -

## References

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