| Abstract: |
| For a nonlinear impulsive control system we introduce a notion of
generalized solution x associated to a control u whose total
variation is bounded on [0,t] for every t < T but possibly unbounded on
[0,T], and prove existence, consistency with classical solutions and
well-posedness of this solution. It provides the natural setting for
controllability questions and for some non-coercive optimal control
problems, where chattering phenomena at the final time are expected.
More in general, it is well suited to describe the evolution of
control systems subject to a train of impulses where no a-priori
bounds on the number and the amplitude of the impulses are imposed. |
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