Closed-loop nonlinear system identification via the vector optimal parameter search algorithm: Application to heart rate baroreflex control

The vector optimal parameter search (VOPS) and the constrained optimal parameter search (COPS) are recently developed algorithms for closed-loop linear system identification. We extend both algorithms to be applicable to a closed-loop nonlinear system, which is characterized by a vector nonlinear autoregressive model. Monte Carlo simulations of nonlinear closed-loop systems were performed to compare the performance of the VOPS to the widely utilized vector least squares (VLS), the COPS and the total least squares (TLS) approaches. The relative error and linear transfer functions are computed to determine the accuracy of each method. The comparative results show that both the VOPS and COPS algorithms provide far superior parameter estimates than does the VLS for all simulation examples considered. The TLS provides better estimates than the VOPS, COPS and VLS when there is only observation noise present in the data. However, the performance of the TLS degrades considerably when the data are corrupted by dynamic noise. The clinical applicability of the two extended methods is examined by applying them to a classical physiological closed-loop system, the heart rate baroreflex. It was found that while both control and blockade of parasympathetic system conditions are dominated by linear dynamics, more nonlinearity was observed in the latter. This observation is statistically supported by the calculation of the mutual information of the data and their surrogates.