Optimal feedback control, linear first-order PDE systems, and obstacle problems

Optimal Control of Problems Governed by Obstacle

In this paper we investigate optimal control problems governed by variational inequalities. We give optimality conditions under classical assumptions using a dual regularized functional to interpret the Variational Inequality. 1. Introduction. In this paper we investigate optimal control problems governed by vari-ational inequalities of obstacle type. This problem has been widely studied during...

Optimal Control of Semilinear Elliptic Obstacle Problems

Optimal Control of Bilateral Obstacle Problems

We consider an optimal control problem where the state satisfies a bilateral elliptic variational inequality and the control functions are the upper and lower obstacles. We seek a state that is close to a desired profile and the H norms of the obstacles are not too large. Existence results are given and an optimality system is derived. A particular case is studied that need no compactness assum...

Characterization of optimal feedback for stochastic linear quadratic control problems

One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exactly to construct the desired feedbacks. To date, the same problem in the stochastic setting is only partially well-understood. In this paper, we establish the equivalence between...

First Order Conditions for Nonsmooth Discretized Constrained Optimal Control Problems

This paper studies first order conditions (Karush–Kuhn–Tucker conditions) for discretized optimal control problems with nonsmooth constraints. We present a simple condition which can be used to verify that a local optimal point satisfies the first order conditions and that a point satisfying the first order conditions is a global or local optimal solution of the optimal control problem.