CONTROL OF NONLINEAR DYNAMICS: WHERE DO MODELS FIT IN?

Abstract

Several control design techniques applied to nonlinear dynamics and chaos assume that a model of the uncontrolled dynamics is available. The extent to which the controller performance is influenced by the model largely depends on many factors such as control effort and the control objective. It is suggested that model quality and control gains, which are strongly related to the control effort, define an uncertainty region in state space around the goal dynamics. For the unrealistic, but frequently assumed case in which model accuracy and admissible control effort are unlimited and there is no noise, the uncertainty region reduces to zero. But what happens when the model is realistically inaccurate, the maximum control effort is limited and the system state is observed with some noise? The objective of this paper is to discuss some issues related to model-based control techniques for nonlinear dynamical systems and to try to shed some light on questions like: How does model accuracy influence control performance? How can model inaccuracies be compensated for in the design? Which limits exist for such compensation? Extensive simulations are carried out and the results suggest that the requirements on nonlinear models might be different if the final objective is the reconstruction of nonlinear dynamics or controller design, and that even linear models can be used in some control design problems.