Quasi-polynomial Representation-based Control of Mechanical Systems

A simple kinematic model of a differential steering mobile robot is investigated using a nonlinear technique based on the quasi-polynomial representation of the dynamical model. Dynamical systems can be embedded in the generalized Lotka-Volterrs (or quasi-polynomial) form under mild conditions. Quasi-polynomial systems are good candidates for a general nonlinear system representation, since their global stability analysis is equivalent to the feasibility of a linear matrix inequality. The stabilizing quasi-polynomial state feedback controller design problem is equivalent to the feasibility of a bilinear matrix inequality. The classical stabilizing state feedback problem for quasi-polynomial systems was extended with the ability of tracking time-dependent reference signals. It is shown that the stabilizing quasi-polynomial controller design is equivalent to a bilinear matrix inequality. The results are applied to the model of the differential steering mobile robot. The goal reaching quasi-polynomial controller is shown to be a special kind of proportional state feedback.