Optimal Control of Variational Inequalities

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.