### Abstract

A new concept in nonlinear control methods, called the Relaxed State-Dependent Riccati Equation (RSDRE) technique, is introduced in the current paper. This concept is derived from the State-Dependent Riccati Equation (SDRE) technique, which is known as one of the well defined nonlinear controllers. By gridding the states and obtaining representative states, the control gains can be obtained in advance of applying them to systems. Hence, the RSDRE technique is similar to the LQR technique in local state block and can be treated as a discretized SDRE technique in all of the state regions. The RSDRE technique has the same characteristics as the SDRE technique: it has nonlinear, sub-optimal, and robust control. Moreover, this technique can overcome some of the main drawbacks of the SDRE technique, specifically the computational burden in calculating the values of the optimal control gain matrix and the possibility of being unable to solve the algebraic Riccati equation in real-time for some internal or external problems. Examples of attitude controls for inverted pendulum and satellite attitude control systems are presented to show the effectiveness of the RSDRE technique.

Original language | English |
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Title of host publication | The F. Landis Markley Astronautics Symposium - Advances in the Astronautical Sciences |

Subtitle of host publication | Proceedings of the American Astronautical Society F. Landis Markley Astronautics Symposium |

Pages | 585-603 |

Number of pages | 19 |

Volume | 132 |

Publication status | Published - 2008 Dec 1 |

Event | American Astronautical Society F. Landis Markley Astronautics Symposium - Cambridge, MD, United States Duration: 2008 Jun 29 → 2008 Jul 2 |

### Other

Other | American Astronautical Society F. Landis Markley Astronautics Symposium |
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Country | United States |

City | Cambridge, MD |

Period | 08/6/29 → 08/7/2 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*The F. Landis Markley Astronautics Symposium - Advances in the Astronautical Sciences: Proceedings of the American Astronautical Society F. Landis Markley Astronautics Symposium*(Vol. 132, pp. 585-603)

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*The F. Landis Markley Astronautics Symposium - Advances in the Astronautical Sciences: Proceedings of the American Astronautical Society F. Landis Markley Astronautics Symposium.*vol. 132, pp. 585-603, American Astronautical Society F. Landis Markley Astronautics Symposium, Cambridge, MD, United States, 08/6/29.

**The Relaxed State-Dependent Riccati Equation Technique : Concept and applications.** / Chang, Insu; Park, Sang Young; Choi, Kyu Hong.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The Relaxed State-Dependent Riccati Equation Technique

T2 - Concept and applications

AU - Chang, Insu

AU - Park, Sang Young

AU - Choi, Kyu Hong

PY - 2008/12/1

Y1 - 2008/12/1

N2 - A new concept in nonlinear control methods, called the Relaxed State-Dependent Riccati Equation (RSDRE) technique, is introduced in the current paper. This concept is derived from the State-Dependent Riccati Equation (SDRE) technique, which is known as one of the well defined nonlinear controllers. By gridding the states and obtaining representative states, the control gains can be obtained in advance of applying them to systems. Hence, the RSDRE technique is similar to the LQR technique in local state block and can be treated as a discretized SDRE technique in all of the state regions. The RSDRE technique has the same characteristics as the SDRE technique: it has nonlinear, sub-optimal, and robust control. Moreover, this technique can overcome some of the main drawbacks of the SDRE technique, specifically the computational burden in calculating the values of the optimal control gain matrix and the possibility of being unable to solve the algebraic Riccati equation in real-time for some internal or external problems. Examples of attitude controls for inverted pendulum and satellite attitude control systems are presented to show the effectiveness of the RSDRE technique.

AB - A new concept in nonlinear control methods, called the Relaxed State-Dependent Riccati Equation (RSDRE) technique, is introduced in the current paper. This concept is derived from the State-Dependent Riccati Equation (SDRE) technique, which is known as one of the well defined nonlinear controllers. By gridding the states and obtaining representative states, the control gains can be obtained in advance of applying them to systems. Hence, the RSDRE technique is similar to the LQR technique in local state block and can be treated as a discretized SDRE technique in all of the state regions. The RSDRE technique has the same characteristics as the SDRE technique: it has nonlinear, sub-optimal, and robust control. Moreover, this technique can overcome some of the main drawbacks of the SDRE technique, specifically the computational burden in calculating the values of the optimal control gain matrix and the possibility of being unable to solve the algebraic Riccati equation in real-time for some internal or external problems. Examples of attitude controls for inverted pendulum and satellite attitude control systems are presented to show the effectiveness of the RSDRE technique.

UR - http://www.scopus.com/inward/record.url?scp=62949183409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62949183409&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780877035480

VL - 132

SP - 585

EP - 603

BT - The F. Landis Markley Astronautics Symposium - Advances in the Astronautical Sciences

ER -