A classical method for solving the variational inequality problem is the projection algorithm. We show that existing convergence results for this algorithm follow from one given by Gabay for a splitting algorithm for finding a zero of the sum of two maximal monotone operators. Moreover, we extend the projection algorithm to solve any monotone affine variational inequality problem. When applied ...

Abstract This work studies receding-horizon control of discrete-time switched linear systems subject to polytopic constraints for the continuous states and inputs. The objective is approximate optimal strategy cases in which online computation intractable due necessity solving mixed-integer quadratic programs each discrete time instant. proposed approach builds upon an approximated finite-horiz...

We consider an optimal control problem governed by elliptic variational inequality of the second kind. The is discretized linear finite elements for state and a discrete approach control. Based on quadratic growth condition we derive nearly priori error estimates. Moreover, establish order sufficient optimality conditions that ensure condition. These are rather restrictive, but allow us to cons...

This paper deals with the optimal quadratic control problem for non Gaussian discrete-time linear stochastic systems from the perspective of imprecise probabilities. The adopted philosophy is to use a convex set of probability distributions to characterize the imprecision in the knowledge about the probabilistic relationships present in the system to be controlled. In particular, an uncertain s...

The study of linear control problems with exponential-ofquadratic cost function was initiated in Jacobson (1973) where the author studies discrete-time and continuoustime state feedback problems. The discrete-time linear output feedback problems with exponential-of-quadratic cost function is studied in Whittle (1981). Bensousssan and Schuppen (1985) studied the continuous-time output feedback p...

This paper deals with the robust -control of discrete-time L# Markovian jump linear systems. It is assumed that both the state and jump variables are available to the controller. Uncertainties satisfying some norm bounded conditions are considered on the parameters of the system. An upperbound for the -control L# problem is derived in terms of an LMI optimization problem. For the case in which ...

In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available...