From power converters to walking robots: analysis, bifurcations and control of piecewise-smooth circuits and systems

The tutorial will introduce the audience to the theory of discontinuity-induced bifurcations in nonlinear circuits and systems affected by switching, saturation and any other nonlinear effects that can be modeled as a discontinuous event at a macroscopic timescale. Bifurcations of fixed points in discrete-time maps will be discussed before introducing a systematic classification of other bifurcation phenomena in systems modeled by continuous-times models such as grazing bifurcations of limit cycles and sliding bifurcations. The theoretical derivations will be complemented by applications to switched circuits and systems, power electronic converters and vibro-impacting mechatronic devices. A combination of analytical tools will be presented to study these nonlinear phenomena that often occur in devices and circuits of practical interest. Current open problems and challenges will be highlighted both in the theory and the applications of discontinuity-induced bifurcations.