Robust LQR design for systems with probabilistic uncertainty
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© 2019 John Wiley & Sons, Ltd. 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.
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