An MDL-based Hammerstein recurrent neural network for control applications

This paper presents an efficient control scheme using a Hammerstein recurrent neural network (HRNN) based on the minimum description length (MDL) principle for controlling nonlinear dynamic systems. In the proposed control approach, an unknown system is first identified by the MDL-based HRNN, which consists of a static nonlinear model cascaded by a dynamic linear model and can be expressed in a state-space representation. For high-accuracy system modeling, we have developed a self-construction algorithm that integrates the MDL principle and recursive recurrent learning algorithm for constructing a parsimonious HRNN in an efficient manner. To ease the control of the system, we have established a nonlinearity eliminator that functions as the inverse of the static nonlinear model to remove the global nonlinear behavior of the unknown system. If the system modeling and the inverse of the nonlinear model are accurate, the compound model, the unknown system cascaded with the nonlinearity eliminator, will behave like the linear dynamic model. This assumption turns the task of complex nonlinear control problems into a simple feedback linear controller design. Hence, well-developed linear controller design theories can be applied directly to achieve satisfactory control performance. Computer simulations on unknown nonlinear system control problems have successfully validated the effectiveness of the proposed MDL-based HRNN and its control scheme as well as its superiority in control performance.