A computational approach to parameter identification of spatially distributed nonlinear systems with unknown initial conditions

In this paper, a high-precision algorithm for parameter identification of nonlinear multivariable dynamic systems is proposed. The proposed computational approach is based on the following assumptions: a) system is nonlinearly parameterized by a vector of unknown system parameters; b) only partial measurement of system state is available; c) there are no state observers; d) initial conditions are unknown except for measurable system states. The identification problem is formulated as a continuous dynamic optimization problem which is discretized by higher-order Adams method and numerically solved by a backward-in-time recurrent algorithm which is similar to the backpropagation-through-time (BPTT) algorithm. The proposed algorithm is especially effective for identification of homogenous spatially distributed nonlinear systems what is demonstrated on the parameter identification of a multi-degree-of-freedom torsional system with nonlinearly parameterized elastic forces, unknown initial velocities and positions measurement only.