Symbolic computations of nonlinear observability

Symbolic computations of nonlinear observability.

Observability is a very useful concept for determining whether the dynamics of complicated systems can be correctly reconstructed from a single (univariate or multivariate) time series. When the governing equations of dynamical systems are high-dimensional and/or rational, analytical computations of observability coefficients produce large polynomial functions with a number of terms that become...

Observability of Nonlinear Systems

Abstract. Observability of a general nonlinear system—given in terms of an ODE ẋ = f(x) and an output map y = c(x)—is defined as in linear system theory (i.e. if f(x) = Ax and c(x) = Cx). In contrast to standard treatment of the subject we present a criterion for observability which is not a generalization of a known linear test. It is obtained by evaluation of “approximate first integrals”. Th...

Symbolic Computations on Grids

Symbolic Synthesis of Observability Requirements for Diagnosability

Given a partially observable dynamic system and a diagnoser observing its evolution over time, diagnosability analysis formally verifies (at design time) if the diagnosis system will be able to infer (at runtime) the required information on the hidden part of the dynamic state. Diagnosability directly depends on the availability of observations, and can be guaranteed by different sets of sensor...

Observability of HIP Nonlinear Dynamics

We investigate observability of the nonlinear system equations describing the Hot Isostatic Pressing (HIP'ing) dynamic system. If the system is observable, then grain size may be estimated during the HIP'ing process without directly measuring it as an output of the system. Our results indicate that the system is observable. The problem of estimating the states and parameters of a nonlinear dyna...