A Novel Nonlinear Dynamical System Control Using Linear Controllers with Nonlinearity Eliminators

This paper presents a novel control design approach for controlling nonlinear dynamical systems using linear controllers with nonlinearity eliminators. Our control philosophy is to apply a divide-and-conquer strategy based on the assumption that an unknown system can be decomposed into two components: a static nonlinear model and a dynamic linear model. If the system modeling and the inverse of the nonlinear model are accurate, the compound model, the unknown system cascaded with the inverse model, will behave like the linear dynamic model. To effectively control such a linear model, well-developed linear control theory can directly be used in the feedback linear controller design. We first developed an ad hoc recurrent network structure that consists of a nonlinear model and a linear dynamic model. A fully automatic construction algorithm was devised to construct the recurrent structure. This algorithm integrates the order determination, parameter initialization and optimization, as well as the design procedure of the controller into a systematic framework. With this algorithm, the modeling and controller design procedures are totally exempted from trial-and-error approaches. Computer simulations on unknown system control problems have successfully validated the effectiveness of the proposed hybrid control scheme with superior control performance.