Computational framework of lie symmetries of nonlinear systems with unmeasured inputs - Shi, X; Chatzis, M (International Society for Structural Health Monitoring of Intelligent Infrastructure, 2021)
This work proposes a novel framework for computing general Lie symmetries of nonlinear dynamical systems with unmeasured (unknown) inputs. Existing methods are typically oriented towards finding specific types of Lie symmetries with known forms, while often inputs are required to be fully measured. The main objective of the work is to relax both of the constraints. The obtained Lie symmetries from the framework provide an alternative path to approach the observability and identifiability properties of a dynamical system. Moreover, Lie symmetries imply the possible system identification results of states, parameters and unmeasured inputs for a given set of input-output measurements. Potential applications of Lie symmetries to model reduction and sensor placement in order for obtaining an equivalent observable and identifiable model are also important. In the end of this work, the computation and usage of Lie symmetries are demonstrated in detail using a suitably chosen engineering model with a displacement-proportional stiffness nonlinearity.