Abstract
We consider control problems for the variational inequality describing a single degree of freedom elasto-plastic oscillator. We are particularly interested in finding the critical excitation, i.e., the lowest energy input excitation that drives the system between the prescribed initial and final states within a given time span. This is a control problem for a state evolution described by a variational inequality. We obtain Pontryagin’s necessary condition of optimality. An essential difficulty lies with the non continuity of adjoint variables.
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