E-mail: giuseppe.notarstefano(at)unisalento.it

Home page: http://cor.unile.it/notarstefano

Tutors: Prof.  R. Frezza (Università di Padova), Prof.  F. Bullo (University of California Santa Barbara), Prof.  J. Hauser (University of Colorado Boulder)

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Optimization Strategies for Constrained Control Systems and Robotic Networks   ___________________________________________________________________________________________________________

Advisors: Prof.  R. Frezza (Università di Padova), Prof.  F. Bullo (University of California Santa Barbara), Prof.  J. Hauser (University of Colorado Boulder)

Summary of the thesis

In the first part of the work we develop a strategy to compute feasible trajectories of state-input constrained nonlinear control systems. This strategy is interesting itself in understanding the behavior of the system, especially in critical conditions, and represents a useful tool that can be used, in a receding horizon scheme, to perform trajectory tracking in presence of constraints. The strategy is based on a novel optimization technique, introduced by Hauser, to find a regularized solution for point-wise constrained optimization of trajectory functionals. We demonstrate the effectiveness of the proposed strategy. In particular, we prove that for suitable choice of the constraints, the solution of the regularized optimization problem exists. The novel concept of operating region is another contribution of the work. Its importance relies on the property of providing ``a priori'' a region where a control engineer can choose (feasible) trajectories that are ensured to be exponentially stabilizable. We prove some preliminary results in the direction of characterizing the operating region of nonlinear control-affine systems driven by (essentially) bounded inputs. The strategy for computation of feasible trajectories is applied to the PVTOL (Planar Vertical Take Off and Landing) aircraft, a simplified model of a real aircraft that captures the main features and challenges of the real model. In the second part of the work we study two different classes of constrained optimization problems for robotic networks. First, we address the connectivity maintenance problem in wireless networks of robotic agents with double integrator dynamics. We establish an existence theorem for this problem by defining a novel state-dependent graph. Also, we design a distributed ``flow-control'' algorithm to compute optimal connectivity-maintaining controls. Second, we identify a novel class of optimization problems, namely a networked version of abstract linear programming. For such problems we propose distributed algorithms for networks with various connectivity and/or memory constraints. Finally, we show how various minimum time formation control problems can be tackled through appropriate geometric examples of abstract linear programs.

 

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