Premium
Robust LQR design for systems with probabilistic uncertainty
Author(s) -
Bhattacharya Raktim
Publication year - 2019
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.4548
Subject(s) - polynomial chaos , robustness (evolution) , mathematical optimization , probabilistic logic , robust control , optimization problem , nonlinear system , robust optimization , convex optimization , maximization , polynomial , mathematics , quadratic equation , computer science , control theory (sociology) , regular polygon , control (management) , monte carlo method , mathematical analysis , biochemistry , statistics , chemistry , physics , geometry , quantum mechanics , artificial intelligence , gene
Summary In this paper, we consider the design of robust quadratic regulators for linear systems with probabilistic uncertainty in system parameters. The synthesis algorithms are presented in a convex optimization framework, which optimize with respect to an integral cost. The optimization problem is formulated as a lower‐bound maximization problem and developed in the polynomial chaos framework. Two approaches are considered here. In the first approach, an exact optimization problem is formulated in the infinite‐dimensional space, which is solved approximately using polynomial‐chaos expansions. In the second approach, an approximate problem is formulated using a reduced‐order model and solved exactly. The robustness of the controllers from these two approaches are compared using a realistic flight control problem based on an F16 aircraft model. Linear and nonlinear simulations reveal that the first approach results in a more robust controller.