Sampled-data Control of a Class of Nonlinear Flat Systems With Application to Unicycle Trajectory Tracking

Abstract

In this paper we propose a flatness-based nonlinear sampled-data control approach for the trajectory tracking of nonlinear differentially flat systems that can be expressed in cascade form. The nonlinear sampled-data control method relies on the flatness property for the generation of appropriate trajectories, with the design of one-step predictive control laws, and on controller discretization by means of an averaging-like method. In the paper we demonstrate that the causality problem that might arise in the implementation is avoided by using an estimator based on numerical integration techniques of sufficiently high order. Stability-like properties are proved. Numerical simulations show that the proposed sampled-data control law offers the best closed-loop performance when compared with nonlinear direct digital design for the trajectory tracking of a rotorcraft-like UAV modeled as the unicycle. The synthesis of the nonlinear sampled-data control law takes advantage of the feedback linearizability property of the unicycle model. Furthermore, the proposed nonlinear sampled-data control does not rely on approximated discretization techniques and is computed from exponentially convergent steering trajectories that result from the stabilization of the linearized unicycle model.