It is well known that three momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished using smooth feedback. If failure of one of the momentum wheel actuators occurs, we demonstrate that two momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrar...

submerged breakwaters are one of the shore protective structures. any discontinuity in these breakwaters causes changes on current parameters including speed and water surface profile. in this paper, discontinuous submerged breakwaters were modelled to investigate the changes in the wave and flow pattern.to investigate the phenomenon, three models including a shore with constant slope, a shore ...

We study the reach control problem for affine systems on simplices, and the focus is on cases when it is known that the problem is not solvable by continuous state feedback. In previous work we used the reach control indices to construct a (discontinuous) piecewise affine control that solves the problem. Here we investigate the extent to which time-varying feedbacks can be used. A simple time-v...

The formal extension of the conventional theory of dynamic programming to control problems with slow growth and a state constraint x 2 encounters two major drawbacks: on one hand the formal Hamiltonian may happen to be discontinuous; on the other hand, just as in the case of bounded controls, the imposition of a state constraint possibly gives rise to a discontinuous value function. On the cont...

We present a version of the Pontryagin Maximum Principle for control dynamics with a possibly non smooth, nonlipschitz and even discontinuous righthand side. The usual adjoint equation, where state derivatives occur, is replaced by an integrated form, containing only differentials of the reference flow maps. The resulting “integrated adjoint equation” leads to “adjoint vectors” that need not be...

In this paper we consider a parabolic optimal control problem with a pointwise (Dirac type) control in space, but variable in time, in two space dimensions. To approximate the problem we use the standard continuous piecewise linear approximation in space and the piecewise constant discontinuous Galerkin method in time. Despite low regularity of the state equation, we show almost optimal h2 + k ...