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Special Issue on Nonsmooth Dynamical Systems: Analysis, Control and Optimization in Nonlinear Analysis: Hybrid Systems

Why a European Network for Nonsmooth Dynamics ?

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The goals of the European network for nonsmooth dynamics are :

  • to provide a cooperation platform for researchers specialized in nonsmooth dynamics
  • to promote the research focussed on nonsmooth dynamics and its applications
  • to improve networking activities (summer school, workshops or conferences)
  • to disseminate the knowledge from the academic community to industry

What is nonsmooth dynamics ?

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Nonsmooth dynamics is a research field which studies dynamical systems for which the state is not required to be a smooth (differentiable) function of time. The research field nonsmooth dynamics is very related to nonlinear dynamics (stability theory, bifurcation theory, chaos), non-smooth optimization and uses concepts of nonsmooth analysis, convex analysis and measure theory.

Famous examples of nonsmooth dynamics are
  • Nonsmooth mechanics. Due to possible impacts, the velocities of the mechanical system are even allowed to undergo jumps at certain time instants in order to fulfill kinematic restrictions. Consider for example a model of a rigid ball which falls on the ground. Just before the impact between ball and ground, the ball has non-vanishing pre-impact velocity. At the impact time instant, the velocity must jump to a post-impact velocity which is at least zero, as else penetration would occur. Nonsmooth mechanical models are often used in contact dynamics and plasticity theory.
  • Nonsmooth electrical circuits. Electrical circuits with ideal (or idealized) components are also standard examples of nonmsooth dynamical systems. The presence of diodes in circuits may imply unilateral constraints on currents and voltages, which in turn may imply state jumps
  • Control of nonsmooth systems and Nonsmooth Control Stability theory of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction are a subject of intense research. Sliding mode control is the most widespread type of nonsmooth control
  • Nonsmooth dynamical systems Nonsmooth dynamical systems in the large that can be found in Hybrid Systems, Computational Biology (gene networks), Economic models and finite automata