Model Order Reduction Techniques from Mathematics to Innovative Applications

Dear Colleagues,

Model Order Reduction (MOR) is a multidisciplinary topic that has been of wide interest in the last forty years. MOR consists of the design of a lower order model with respect to that of an original system, where “order” indicates the minimum number of state variables that allow to successfully describe a considered real system. The topics arised when Large Scale Dynamical systems started to be considered fundamental in more fields. With this term we mean systems with a relevant number of internal variables, such as networks, biological processes, social systems, Very Large Scale Integration systems (VLSI) devices and each system that in order to be describe requies a number of state variables. Howerer the approximation of distributed systems, or of non integer order systems, often require a high number of variables. The mathematical tools to obtain simplified models from original one have been widely studied in the literature; moreover, it does not appear an unified scheme to get reduced order model systems. Indeed, it is not enough discussed in the the literature about the performance of the reduced order models respect the original ones and has not yet clearly identified quantities measuring their performances. The application of Model Reduction techniques is currently also due to network approaches that are continuously used to model complex systems, and to the achievements of complex devices, such as the Lab-on-a-Chip, Systems-on-a-Chip and the Systems-of-Systems areas.

The Special Issue will review the latest mathematical tools for MOR techniques, including their numerical recipes, innovative software tools that support modern MOR techniques, and advanced applications where does appear the active use of the Mathematics in obtaing Reduced Order Models for proposind advance robust control techniques.

The topics of the Special Issue include:

• New mathematical tools for Reduced Model Order;
• innovative methods to get reliable MOR in networks;
• guidelines to measure the performances of reduced order models;
• advanced applications in the area of integrated circuits, microfluidic devices, smart materials;
• MOR in the area of economic and financial systems;
• MOR for nonlinear complex systems.

Prof. Dr. Luigi Fortuna
Prof. Dr. Riccardo Caponetto
Guest Editors

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