An Akaike State-Space Controller for RBF-ARX Models

Radial basis function autoregressive with exogenous inputs (RBF-ARX) models have been shown to be useful in modeling the nonlinear behavior of a variety of complex systems. In particular, Peng et al. have shown how the RBF-ARX model may be used to model the selective catalytic reduction (SCR) process for real data from a thermal power plant, and have simulated control of the plant using the generalized predictive control (GPC) method of Clarke et al. very effectively. However, the GPC approach requires constrained nonlinear optimization at each control step, which is time-consuming and computationally very expensive. Here, in place of the GPC approach, the authors use a variation of the Kalman state-space approach to control, which involves only the solution of a set of Riccati equations at each step. As is well known, the usual Kalman state-space representation breaks down when we need to control a system depending on inputs extending several lags into the past, but to avoid this problem, we have used the state-space approach of Akaike and Nakagawa. Although this was originally developed for the linear case, here we show how the representation may be extended for use with the nonlinear RBF-ARX model. The straightforward tuning procedure is illustrated by several examples. Comparisons with the GPC method also show the effectiveness and computational efficiency of the Akaike state-space controller method. The robustness of the method is demonstrated by showing how the RBF-ARX model fitted to one data sequence from the SCR process may be used to construct a high performance controller for other sequences taken from the same process. Akaike state-space control may also be easily extended to the multi-input-multi-output case, making it widely applicable in practice.