On convex parameterization of robust control design for minimizing (conditional) performance at risk
Author(s) -
Wang Qian
Publication year - 2007
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1292
Subject(s) - probabilistic logic , mathematical optimization , parametric statistics , robust control , linear matrix inequality , conditional probability distribution , mathematics , convexity , probability distribution , probabilistic design , convex optimization , percentile , computer science , regular polygon , control system , engineering , statistics , engineering design process , mechanical engineering , geometry , electrical engineering , financial economics , economics
Abstract This paper introduces performance at risk and conditional performance at risk as design metrics for the formulation of robust control design. These two metrics are used to characterize the high percentile or tail distribution of a performance specification when system uncertain parameters are random variables described by statistical distributions. The probabilistic robust control design is then formulated as a minimization problem with respect to the ( conditional ) performance at risk or as a constrained problem in terms of them. Performance specifications in terms of the high percentile or tail distribution are more stringent than that are defined in terms of the average (mean) value, which are often used in current literature for probabilistic robust control. Furthermore, the convexity of the conditional performance at risk does not have particular requirements on the underlying distribution of uncertain parameters; thus, convex optimization can be applied to the probabilistic robust control with respect to uncertain parameters with general distributions. The proposed probabilistic robust approach is applied to search solutions to linear matrix inequality containing random parametric uncertainties as well as to design a stabilizing controller for polynomial vector fields subject to random parametric uncertainties. Copyright © 2007 John Wiley & Sons, Ltd.