Modeling and Control of Dynamical Systems with Nonlocal Operators

Dear Colleagues,

The nonlocal behavior of numerous dynamical systems, such as in diffusion processes, milling processes, data networks, transportation, plasma physics, Lévy processes, economics, flexible structures, continuum robots, etc., can be well-described using nonlocal operators. An operator acting on a function is local if its output at any arbitrary point only depends on the function values in a small neighborhood of the point. Otherwise, the operator is called nonlocal, like fractional derivatives, discrete delays, distributed delays, convolution integrals, integrodifferential operators, Volterra integral equations, stochastic processes, etc. The behavior of nonlocal dynamical systems is not intuitive, similar to the classic ones governed by ordinary differential equations. Moreover, adding these operators extends the inner dimension of the system to infinity, which makes their modeling and control difficult.

This Special Issue focuses on recent advances in modeling and control theory of dynamical systems with nonlocal operators. Topics of interest for the Special Issue include but are not limited to:

• Time-delay systems;
• Control theory for continuum systems;
• Fractional-order systems;
• Fractals and chaos;
• Volttera integrodifferential systems;
• Stochastic systems;
• Diffusion and random walk processes;
• Non-Markov processes;
• Computational methods for nonlocal operators.

Prof. Arman Dabiri
Guest Editor

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