Lie symmetries, observability and model transformation of nonlinear systems with unknown inputs - Shi, X; Chatzis, MN (European Association for Structural Dynamics, 2020)
This work investigates the use of Lie symmetries for assessing and improving the observability of dynamical systems under examined sensor setups. The framework of Lie symmetry is extended to account for unmeasured and hence unknown inputs. An efficient algorithm is developed to calculate the translation and scaling symmetries of nonlinear systems with unknown inputs. The use of the algorithm to assess the observability of a given nonlinear system is demonstrated, i.e. in theory whether it would be successful to identify the dynamic states, the parameters and the unknown inputs of the system from given measurements. The work further shows the potential application of the calculated symmetries for transforming the model of an unobservable system to an equivalent model with a minimum number of unobservable states and unknown inputs. The proposed method and algorithm are illustrated on the observability properties of a dynamical system with a Bouc-Wen nonlinearity.