Regularization of chattering phenomena via bounded variation controls
Roberta Ghezzi (Università di Roma "Tor Vergata")
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Thu Apr 15, 20:00-21:00 (starts in 4 hours)
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Abstract: In control theory, chattering refers to fast oscillations of controls, such as accumulation of switchings in finite time. This behavior is rather typical, as it is the case for the class of single-input control-affine problems, and may be a serious obstacle to convergence of standard numerical methods to detect optimal solutions.

We propose a general regularization procedure, consisting of penalizing the cost functional with a total variation term. Under appropriate assumptions of small-time local controllability, we prove that the optimal cost and any optimal solution of the regularized problem converge respectively to the optimal cost and an optimal solution of the initial problem. Our approach is valid for general classes of nonlinear optimal control problems and applies to chattering phenomena appearing in constrained problems as well as to switching systems. We also quantify the error in terms of the rate of convergence of the sequence of switching times, for systems with regular time-optimal map.
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