Ph.D. received on: 7/7/1997

E-mail: michele@dsi.unifi.it

Tutor: Prof. Roberto Genesio, Università degli Studi di Firenze

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Analysis and control of periodic solutions in nonlinear systems   ___________________________________________________________________________________________________________

Advisor:

Prof.  Roberto Genesio, Università degli Studi di Firenze

Summary:

This work deals with the analysis of periodic solutions in the class of nonlinear systems given by the scalar feedback interconnection of a linear dynamical time-invariant sub-system and a nonlinear (dynamical) one. More specifically, critical behaviors of such systems have been considered, when small perturbations of a nominal model  cause a bifurcation, that is, a structural modification of systems trajectories. The way different kinds of bifurcations are generated, such as period doubling, the onset of  quasi-periodic solutions, symmetry-breaking, etc., have been made clear assuming a model description in terms of subharmonic perturbation with respect to the frequency of the unperturbed periodic solution. This approach, based on harmonic balance techniques, gives a meaningful insight of complex phenomena which originate chaotic behaviors in many dynamical systems. The main result obtained consists in the determination in closed form of the approximating bifurcation boundaries in the parameter space, providing a general portrait of the structural stability features of the system under investigation.
The analysis in the frequency domain has then been employed to determine control techniques in order to avoid undesired complex dynamics in a certain region of the parameter space. In particular, due to an interest in minimal effort control strategies, techniques based on stabilization of periodic solution embedded in chaotic attractors have been considered.

 
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