### Abstract

This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is based upon a set-oriented numerical approach. Using this approach, the codesign problem leads to a finite number of linear inequalities whose solutions define the feasible set of stabilizing controllers. We provide a proof of existence for a stochastic version of such a controller while the deterministic restriction is posed as the solution of a related integer programming problem. Mathematical programming techniques may be employed to obtain such controllers. Finally, an example is provided to illustrate the ideas.

Original language | English (US) |
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Title of host publication | Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC |

Pages | 1722-1727 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2007 |

Event | 46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0191-2216 |

### Other

Other | 46th IEEE Conference on Decision and Control 2007, CDC |
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Country | United States |

City | New Orleans, LA |

Period | 12/12/07 → 12/14/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC*(pp. 1722-1727). [4434956] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434956

}

*Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC.*, 4434956, Proceedings of the IEEE Conference on Decision and Control, pp. 1722-1727, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434956

**Nonlinear stabilization via control-Lyapunov measure.** / Vaidya, Umesh; Mehta, Prashant G.; Shanbhag, Vinayak V.

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

TY - GEN

T1 - Nonlinear stabilization via control-Lyapunov measure

AU - Vaidya, Umesh

AU - Mehta, Prashant G.

AU - Shanbhag, Vinayak V.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is based upon a set-oriented numerical approach. Using this approach, the codesign problem leads to a finite number of linear inequalities whose solutions define the feasible set of stabilizing controllers. We provide a proof of existence for a stochastic version of such a controller while the deterministic restriction is posed as the solution of a related integer programming problem. Mathematical programming techniques may be employed to obtain such controllers. Finally, an example is provided to illustrate the ideas.

AB - This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is based upon a set-oriented numerical approach. Using this approach, the codesign problem leads to a finite number of linear inequalities whose solutions define the feasible set of stabilizing controllers. We provide a proof of existence for a stochastic version of such a controller while the deterministic restriction is posed as the solution of a related integer programming problem. Mathematical programming techniques may be employed to obtain such controllers. Finally, an example is provided to illustrate the ideas.

UR - http://www.scopus.com/inward/record.url?scp=51349104128&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51349104128&partnerID=8YFLogxK

U2 - 10.1109/CDC.2007.4434956

DO - 10.1109/CDC.2007.4434956

M3 - Conference contribution

SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1722

EP - 1727

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

ER -