Abstract We consider an optimal control problem governed by an elliptic quasivariational inequality with unilateral constraints. We associate to a new optimal control problem obtained by perturbing the state inequality (including the set of constraints and the nonlinear operator) and the cost functional, as well. Then, we provide sufficient conditions which guarantee the convergence of solutions of Problem to a solution of Problem The proofs are based on convergence results for elliptic quasivariational inequalities, obtained by using arguments of compactness, lower semicontinuity, monotonicity, penalty and various estimates. Finally, we illustrate the use of the abstract convergence results in the study of optimal control associated with two boundary value problems. The first one describes the equilibrium of an elastic body in frictional contact with an obstacle, the so-called foundation. The process is static and the contact is modeled with normal compliance and unilateral constraint, associated to a version of Coulomb’s law of dry friction. The second one describes a stationary heat transfer problem with unilateral constraints. For the two problems we prove existence, uniqueness and convergence results together with the corresponding physical interpretation.

中文翻译：

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椭圆拟变分不等式控制的最优控制问题的收敛结果

摘要 我们考虑由具有单边约束的椭圆拟变分不等式支配的最优控制问题。我们与通过扰动状态不等式（包括约束集和非线性算子）和成本函数获得的新最优控制问题相关联。然后，我们提供了保证问题解收敛到问题解的充分条件。证明是基于椭圆拟变分不等式的收敛结果，通过使用紧致性、下半连续性、单调性、惩罚和各种估计的参数获得。最后，我们说明了抽象收敛结果在与两个边值问题相关的最优控制研究中的使用。第一个描述了弹性体与障碍物摩擦接触的平衡，即所谓的基础。该过程是静态的，接触建模为法向顺应性和单边约束，与库仑干摩擦定律的一个版本相关联。第二个描述了单边约束的固定传热问题。对于这两个问题，我们证明了存在性、唯一性和收敛性结果以及相应的物理解释。