An efficient algorithm to test the observability of rational nonlinear systems with unmeasured inputs

This work proposes an efficient algorithm to examine the observability and identifiability of rational nonlinear systems in the presence of unmeasured and unknown inputs. The proposed algorithm allows for determining whether the dynamic states, unknown parameters and unmeasured inputs of a dynamical system can be, in theory, successfully identified from a given set of input–output measurements. The underlying theory of the algorithm is based on a further extension of the recently suggested extended Observability Rank Condition while focusing on rational instead of analytic nonlinearities. For the robust development of the algorithm, a power series based framework is established for computing the observability matrix efficiently. The occurring framework substantially alleviates the computational burden of the standard implementations of the extended Observability Rank Condition approaches, which allows for applications to real-world engineering systems that are often large and complex. Several examples of large-scale and high-complexity engineering structures are used to demonstrate the performance and capability of the algorithm. Furthermore, the proposed algorithm is used to investigate the feasibility of monitoring a sub-system that is independently separated from a full system under the introduction of additional unmeasured inputs.