### Abstract

This paper presents a probabilistic approach to the design of robust controllers for nonlinear systems, in particular, polynomial vector fields in the presence of parametric uncertainty. The objective of the design is to minimize the system's probability of instability subject to the uncertainty described by statistical distributions. Based on the convexity property of a recently proposed stability criterion, which could be viewed as a dual to Lyapunov's second theorem, the probabilistic robust control problem for polynomial vector fields is formulated into a stochastic convex optimization problem. Stochastic gradient algorithms are used to search a generally parameterized nonlinear control law that minimizes the probability of instability.

Original language | English (US) |
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Pages (from-to) | 2447-2452 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 3 |

State | Published - Dec 1 2003 |

Event | 42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: Dec 9 2003 → Dec 12 2003 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

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*Proceedings of the IEEE Conference on Decision and Control*, vol. 3, pp. 2447-2452.

**Probabilistic Robust Control Design of Polynomial Vector Fields.** / Wang, Qian.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Probabilistic Robust Control Design of Polynomial Vector Fields

AU - Wang, Qian

PY - 2003/12/1

Y1 - 2003/12/1

N2 - This paper presents a probabilistic approach to the design of robust controllers for nonlinear systems, in particular, polynomial vector fields in the presence of parametric uncertainty. The objective of the design is to minimize the system's probability of instability subject to the uncertainty described by statistical distributions. Based on the convexity property of a recently proposed stability criterion, which could be viewed as a dual to Lyapunov's second theorem, the probabilistic robust control problem for polynomial vector fields is formulated into a stochastic convex optimization problem. Stochastic gradient algorithms are used to search a generally parameterized nonlinear control law that minimizes the probability of instability.

AB - This paper presents a probabilistic approach to the design of robust controllers for nonlinear systems, in particular, polynomial vector fields in the presence of parametric uncertainty. The objective of the design is to minimize the system's probability of instability subject to the uncertainty described by statistical distributions. Based on the convexity property of a recently proposed stability criterion, which could be viewed as a dual to Lyapunov's second theorem, the probabilistic robust control problem for polynomial vector fields is formulated into a stochastic convex optimization problem. Stochastic gradient algorithms are used to search a generally parameterized nonlinear control law that minimizes the probability of instability.

UR - http://www.scopus.com/inward/record.url?scp=1542648856&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542648856&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:1542648856

VL - 3

SP - 2447

EP - 2452

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -