Second order necessary and sufficient optimality conditions for bang-bang control problems in a very general form have been obtained in Milyutin and Osmolovskii (1998). These conditions require the positive (semi)-definiteness of a certain quadratic form on the finite-dimensional critical cone. Using a suitable transformation via a linear matrix ODE, Maurer and Osmolovskii (2003, 2004) have dev...

In this paper, we derive some sufficient second order optimality conditions for control problems of partial differential equations (PDEs) when the cost functional does not involve the usual quadratic term for the control or higher nonlinearities for it. Though not always, in this situation the optimal control is typically bang-bang. Two different control problems are studied. The second differs...

A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of...

We compare four spacecraft attitude control laws that require no prior modeling of the spacecraft mass distribution. All four control laws are based on rotation matrices, which provide a singularityfree attitude representation and unwinding-free operation without discontinuous switching. We apply these control laws to motion-to-rest and motion-to-spin maneuvers. Simulation results are given to ...

This paper proposes a Model Predictive Control (MPC) algorithm for the solution of a robust control problem for continuous-time systems. Discontinuous feedback strategies are allowed in the solution of the min-max problems to be solved. The use of such strategies allows MPC to address a large class of nonlinear systems, including among others nonholonomic systems. Robust stability conditions to...

While in the first paper of this series of two, optimal jacket fluid temperature control profiles have been derived for a family of dispersive tubular chemical reactors, the performance of these optimal profiles is further assessed in this second part. First, the performance of the optimal bang-bang control is compared with that of a more easily implementable constant jacket fluid temperature a...

We study the dissipative dynamics of a qubit that is afflicted by classical random telegraph noise and is subject to dynamical decoupling. We derive exact formulas for the qubit dynamics at arbitrary working points in the limit of infinitely strong control pulses bang-bang control , and we investigate in great detail the efficiency of the dynamical decoupling techniques for both Gaussian and no...

We propose and analyze an inexact version of the modified subgradient (MSG) algorithm, which we call the IMSG algorithm, for nonsmooth and nonconvex optimization over a compact set. We prove that under an approximate, i.e. inexact, minimization of the sharp augmented Lagrangian, the main convergence properties of the MSG algorithm are preserved for the IMSG algorithm. Inexact minimization may a...

In order to avoid wheel slippage or mechanical damage during the mobile robot navigation, it is necessary to smoothly change driving velocity or direction of the mobile robot. This means that dynamic constraints of the mobile robot should be considered in the design of path tracking algorithm. In the study, a path tracking problem is formulated as following a virtual target vehicle which is ass...

In the second order analysis of infinite dimension optimization problems, we have to deal with the so-called two-norm discrepancy. As a consequence of this fact, the second order optimality conditions usually imply local optimality in the L∞ sense. However, we have observed that the L local optimality can be proved for many control problems of partial differential equations. This can be deduced...