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Nonlinear Systems and Control

Research on nonlinear systems and control at the University of Rome La Sapienza has been active since the early 70s and, historically, has played a major role worldwide.

The geometric approach to nonlinear feedback design marked the beginning of a new area of research which, in the subsequent decades, has profoundly influenced the development of the entire field. The concepts of feedback equivalence and zero dynamics, their properties and implications are perhaps the most frequently used concepts in nonlinear feedback design. The natural evolution of the geometric approach from the study of systems evolving on Lie groups, with numerous applications to the control of spacecrafts and mobile robots, to robust regulation under state and output measurements feedback of systems possessing unstable zero dynamics, the use of filtered Lyapunov functions for robust stabilization, the control of networked systems in presence of limited information, till the control of nonlinear delayed systems, state estimators and optimal control for noisy systems with non-Gaussian noise and packet loss, stochastic delay identification. Analysis and design of real control systems integrating devices and computational procedures in a digital context involves ad-hoc methods. Nonlinear discrete-time and sampled data systems are the subjects of an investigation developed at La Sapienza from the early 80s, in a still active cooperation with the Laboratoire des Signaux et Systèmes of the French CNRS. The research activity has been focused on solving nonlinear control problems in discrete-time and on finding digital solutions to continuous-time control systems. One of the major outcomes of the investigation has been the settlement of an original approach, mixed by algebraic and geometric concepts, used either to prove the existence of solutions in discrete-time or to compute approximated solutions in the digital context. From the results on feedback linearization, stabilization, regulation, observer theory, new research lines are in the direction of hybrid, networked and Hamiltonian dynamics. Particular attention is devoted to the settlement of executable algorithms for computing the proposed solutions. Measurements devices, algorithms, data handling and transmission represent critical aspects in any distributed control problem. The number of devices, their location, the energy consumption, the data-communication links, the distributed data handling, multi-consensus, load balancing, and quality evaluation are nowadays classical concepts in this context. New issues deal with dynamic sensor networks, where mobile platforms are assimilated to intelligent devices, in which motion planning and control problems pose additional requirements and make harder the solution of the task. The full problem formulation as a high dimensional nonlinear dynamics is a challenging interdisciplinary area of research towards easier and cheaper solutions to problems like surveillance, monitoring, decentralized and distributed control. Problems under investigation in this field concern sensor and actuator devices, computation algorithms, local and global coordinated control, network communication protocols, data acquisition and fusion.

Epidemic modeling, analysis and control is a further research line developed by the group. The methodologies of mathematical modeling and system analysis are applied to the study of specific epidemic diseases, like the HIV/AIDS, the measles and, recently, the COVID-19. The research goes through the introduction of ad hoc models, identified by using real data, the characterization the Reproduction Number, together with its relation with the most significant epidemic parameters (contact rates, death rates, time constants of infections, etc), the definition of suitable optimal intervention policies along the possible control channels corresponding to vaccination, prevention with informative campagne, medication, quarantine and isolation (as in the recent COVID 19 emergency). The same kind of modeling analysis and control is successfully applied to computer viruses and cybersecurity. Extension of theoretical aspects (singular control) as well as of applications (dynamics on unemployment) of optimal control are also considered.

The applicative aspects of these research activities are carried out at the Systems and Control Laboratory, founded in 1995. Members of the Nonlinear Systems and Control group have been actively serving in the control community in technical committees and as associate editors for the major journals in the area and conference editorial boards as for both IEEE CSS, IFAC and EUCA.

The research activities, as testified by the scientific production, are developed in collaboration with several national and international institutes as the Laboratoire des Signaux et Systèmes (CNRS, Gif sur Yvette), IRCCyN (CNRS, Nantes), Fondazione Santa Lucia , Cosync Lab (Sapienza University of Rome) and the company BrainTrends, Istituto di Analisi dei Sistemi e Informatica (IASI- CNR) for the modeling, analysis and control of epidemiological models, Universidade do Porto, Centro di Sistemi di Elaborazione e Bio-Informatica (Campus Biomedico), McKelvey School of Engineering (Washington University of St. Louis). Those collaborations also encourage international research training and orientation, with PhD double degrees delivering, in the context of an ad hoc binational program ELISA, which involves Italian and French Institutions.

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