Piecewise-smooth systems are common in applications, ranging from dry friction oscillators in mechanics, to power converters in electrical engineering, to neuron cells in biology. While the theory of stability and the control of such dynamical systems have been studied extensively, the conditions that trigger specific collective dynamics when many of such systems are interconnected in a network are not fully understood. The study of emergent behaviour, and in particular synchronization, has applicability in seismology, for what concerns the dynamics of neighbouring faults, in determining frequency consensus in power grids, in operating multi-body mechanical systems, and more. In the first part of this work we provide a series of sufficient conditions to assess global asymptotic state synchronization. Most notably, when the agents' dynamics satisfy the QUAD condition, an ordinary diffusive coupling is sufficient to achieve synchronization, even if the dynamics is discontinuous. In the case of more generic dynamics, we found that a further discontinuous coupling layer can be added to enforce convergence. Moreover, we show that the minimum threshold on the coupling gain associated to the new discontinuous communication protocol depends on the density of the sparsest cut in the graph. This quantity, which we named minimum density, plays a role very similar to that of the algebraic connectivity in the case of networks of smooth systems, in describing the relation between synchronizability and topology. In the second part of the thesis, we focus on specific applications of single PWS systems, and the unique challenges that emerge when particular domains are considered. In particular, we dealt with the design of control strategies to suppress undesired oscillations in the landing gear of an aeroplane and in a robotic set-up in contact with a moving belt. In addition, we expand the tools available to design observers for PWS systems through the use of contraction theory.
Analysis and Control of Piecewise-Smooth Systems and Networks
Coraggio, Marco
2020-01-01
Abstract
Piecewise-smooth systems are common in applications, ranging from dry friction oscillators in mechanics, to power converters in electrical engineering, to neuron cells in biology. While the theory of stability and the control of such dynamical systems have been studied extensively, the conditions that trigger specific collective dynamics when many of such systems are interconnected in a network are not fully understood. The study of emergent behaviour, and in particular synchronization, has applicability in seismology, for what concerns the dynamics of neighbouring faults, in determining frequency consensus in power grids, in operating multi-body mechanical systems, and more. In the first part of this work we provide a series of sufficient conditions to assess global asymptotic state synchronization. Most notably, when the agents' dynamics satisfy the QUAD condition, an ordinary diffusive coupling is sufficient to achieve synchronization, even if the dynamics is discontinuous. In the case of more generic dynamics, we found that a further discontinuous coupling layer can be added to enforce convergence. Moreover, we show that the minimum threshold on the coupling gain associated to the new discontinuous communication protocol depends on the density of the sparsest cut in the graph. This quantity, which we named minimum density, plays a role very similar to that of the algebraic connectivity in the case of networks of smooth systems, in describing the relation between synchronizability and topology. In the second part of the thesis, we focus on specific applications of single PWS systems, and the unique challenges that emerge when particular domains are considered. In particular, we dealt with the design of control strategies to suppress undesired oscillations in the landing gear of an aeroplane and in a robotic set-up in contact with a moving belt. In addition, we expand the tools available to design observers for PWS systems through the use of contraction theory.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
