A Closed-Form Representation of Piecewise Defined Systems and their Integration with Iterative Learning Control

Hybrid dynamical systems have steadily grown in popularity over the last few decades because they ease the task of modeling complicated nonlinear systems. However, it can be challenging to apply pre-existing control strategies to hybrid systems. This is in part because hybrid systems have been difficult to represent in closed-form, which is necessary for executing the operations required for many controllers' synthesis. The primary contribution of this work is a general closed-form state space representation of piecewise defined systems, a class of hybrid systems. The utility of this representation is demonstrated via the first-ever application of iterative learning control to a hybrid system, which is accomplished without modifying the controller design to account for the system model's hybrid nature. Secondary contributions unrelated to system's hybrid nature, however, are made to the controller itself, formalizing it for application to systems of any relative degree, and enabling the direct application of Newton's method in the controller by using automatic differentiation in the learning function derivation.