Tracking control for hybrid systems via embedding of known reference trajectories

We study the problem of designing controllers to track time-varying state trajectories for plants modeled as hybrid dynamical systems, which are systems with both continuous and discrete dynamics. The reference trajectories are given by functions that may exhibit jumps. The class of controllers considered are also modeled as hybrid systems. These are designed to guarantee stability of tracking and that the difference between the plant´s state and the reference trajectory converges to zero. Using recently developed tools for the study of asymptotic stability in hybrid systems, we recast the tracking problem as the problem of stabilizing a closed set and derive conditions for the design of tracking controllers for hybrid reference trajectories with the property that the jump times of the plant coincide with those of the given reference trajectories. The approach is illustrated in examples.