We consider a general linear control system and a general quadratic cost, where the state evolves continuously in time and the control is sampled, i.e., is piecewise constant over a subdivision of the time interval. This is the framework of a linear-quadratic optimal sampleddata control problem. As a first result, we prove that, as the sampling periods tend to zero, the optimal sampled-data con...

Abstract – In this paper we present a unified approach for optimal control and filtering of linear continuous-time singularly perturbed linear systems that facilitates complete and exact decomposition of optimal control and filtering tasks into pure-slow and pure-fast time scales. The presented methodology eliminates numerical ill-conditioning of the original singularly perturbed problems, intr...

Abstract: Both the linear moving horizon estimator and controller may be solved by solving a linear quadratic optimal control problem. A primal active set, a dual active set, and an interior point algorithm for solution of the linear quadratic optimal control problem are presented. The major computational effort in all these algorithms reduces to solution of certain unconstrained linear quadrat...