Determination of Periodic Trajectories of Dynamic Systems Subject to Switching Input Constraints

The present paper is concerned with the determination of periodic state trajectories of discrete-time dynamic systems resulting from the application of bidirectional on/off input sequences subject to switching constraints. The main contribution consists of characterizing the feasible input sequences and associated state trajectories in terms of a set of linear constraints involving integer variables. For practical purposes, the resulting solutions obtained by an integer linear solver can be evaluated in terms of engineering criteria such as amplitude or fuel expense in order to choose an appropriate trajectory to be used as target in a control law. A numerical example involving a double-integrator system is presented to illustrate the use of the proposed constraint formulation for the determination of feasible periodic state trajectories.