Probabilistic Robust Control Design of Polynomial Vector Fields

Research output: Contribution to journalConference articlepeer-review


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 languageEnglish (US)
Pages (from-to)2447-2452
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2003
Event42nd IEEE Conference on Decision and Control - Maui, HI, United States
Duration: Dec 9 2003Dec 12 2003

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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