Control of limit cycles in hybrid dynamical systems

This work deals with limit cycle control for one particular class of hybrid dynamical systems (HDS): The cyclic switched systems. HDS were born because the traditional dynamical models were not able to describe complex behaviours (behaviours with discontinuities). From an application point of view, one important class of HDS depicts a cyclic behaviour in steady state. Its main characteristic is that a control that maintains the system on a desired operation point does not exist. However, this point can be obtained in average. Thus, a cycle is produced by switching among the system modes. A control law must satisfy stability and dynamical performance. Moreover, criteria related to the waveform must be verified. Some generic methods are studied. The proposed algorithms can be implemented in real-time. Approaches are based on an affine non-linear model whose control explicitly appears. Two control methods are considered: a predictive control and an optimal control. Since predictive control is a good choice for tracking, it maintains the system in a cycle. Optimal control yields solutions that can be applied to transients. Some experiments applied to the power converters are shown.