In the present paper we shall see that philosophizing on the specific nature of Linear-Quadratic optimal Control Problems (LQCPs) yields several a priori statements that are valid for the entire set of these problems. For instance, the real symmetric matrix that represents the optimal cost for a particular LQCP necessarily is a rank minimizing solution of the diSSipation inequality (DI). Since,...

This paper introduces a subclass of Hamiltonian control systems motivated by mechanical models. Some problems of time-optimal control are studied, and results on singular trajectories are obtained.

This paper is a survey on some recent aspects and developments in stochastic control theory. We discuss the two main historical approaches, Bellman’s optimality principle and Pontryagin’s maximum principle, and their modern exposition with viscosity solutions and backward stochastic differential equations. Some original proofs are presented in a unifying context including degenerate singular co...

We consider general singular control problems for random fields given by a stochastic partial differential equation (SPDE). We show that under some conditions the optimal singular control can be identified with the solution of a coupled system of SPDE and a reflected backward SPDE (RBSPDE). As an illustration we apply the result to a singular optimal harvesting problem from a population whose d...

in this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $dsubset mathbb{r}^{n}$ with smooth boundary‎. ‎we give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of caffarelli and friedman regarding the representation of functions whose ...

A general optimal control problem for ABS is formulated and analyzed, with the elimination of excessive slip and reduction of braking distance taken into account. Analytical formulas for singular optimal solutions are derived. These results are applied to a simple laboratory model of ABS. The results of simulations are compared with those obtained by a gain-scheduling approach. Copyright © 2005...

In this paper, we consider the minimum-time reorientation problem of an axi-symmetric rigid spacecraft with two independent control torques mounted perpendicular to the spacecraft symmetry axis. The objective is to reorient the spacecraft from an initial attitude, with some angular velocity, to a nal attitude with a certain angular velocity in minimum time. All possible control structures, incl...