On Event Triggered Trajectory Tracking for Control Affine Nonlinear Systems

In this paper we study an event based control algorithm for trajectory tracking in control affine nonlinear systems. The desired trajectory is modelled as the solution of a reference system with an exogenous input. It is assumed that the desired trajectory and the exogenous input to the reference system are uniformly bounded. Given a continuous-time controller that guarantees global uniform asymptotic tracking of the desired trajectory our algorithm provides an event based controller that not only guarantees semiglobal uniform ultimate boundedness of the tracking error, but also ensures non-accumulation of inter-execution times. In the special case that the derivative of the exogenous input to the reference system is also uniformly bounded, the proposed control algorithm can be used to design an ultimate bound that is arbitrarily small. The main ideas in the paper are illustrated through simulations of trajectory tracking by a nonlinear system.