Reduced order modeling for systems with parametric uncertainty using proper generalized decomposition

In this work we have proposed a new technique of model order reduction for linear time invariant (LTI) systems with parametric uncertainty. The model order reduction method is based on proper generalized decomposition (PGD). Using PGD, the underlying state variable is expanded as a sum of separated functions of time and uncertain parameters. At first, the stochastic states of the LTI system is represented using PGD. Then equations to obtain the PGD basis functions are derived. Furthermore a state feedback structure for the control input is assumed where the gain is found by solving a minimum expectation linear quadratic regulator (LQR) problem. An algorithm is then proposed, from which the PGD basis functions and the control input gain are found. The proposed algorithm is then applied to control the angle of attack and pitch rate of a F-16 aircraft having uncertain parameters. It is found that the proposed technique based on PGD could successfully achieve the control objective for the current application.