Probabilistic robust control design of polynomial vector fields

• Published in: 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) Vol. 3; pp. 2447 - 2452 Vol.3
• Main Author: Qian Wang
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2003
• Subjects: Control systems; Nonlinear control systems; Nonlinear systems; Polynomials; Probability; Robust control; Robust stability; Statistical distributions; Stochastic processes; Uncertainty
• ISBN: 9780780379244; 0780379241
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2003.1272987

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.