A Fast MPC Algorithm Using Nonfeasible Active Set Methods

Model predictive control (MPC) is an optimization-based control framework which is attractive to industry both because it can be practically implemented and it can deal with constraints directly. One of the main drawbacks of MPC is that large MPC horizon times can cause requirements of excessive computational time to solve the quadratic programming (QP) minimization which occurs in the calculation of the controller at each sampling interval. This motivates the study of finding faster ways for computing the QP problem associated with MPC. In this paper, a new nonfeasible active set method is proposed for solving the QP optimization problem that occurs in MPC. This method has the feature that it is typically an order of magnitude faster than traditional methods. This work has been supported by the Canadian NSERC under Grant A4396.     

Large order expansion in perturbation theory

We investigate the large n behavior of the perturbation coefficients E_n for the ground state energy of the anharmonic oscillator, considered as a field theory in one space-time dimension. We combine the saddle point expansion for functional integrals introduced in this context by Lipatov with the dispersion relation (in coupling constant) used by Bender and Wu. The complete Feynman rules for the expansion in $\text{1}\text{n}$ are worked out, and we compute the first two terms, which agree with those computed by Bender and Wu using the WKB approximation. One feature of our analysis is a deformation of the integration contour in function space as one analytically continues in the coupling.     

Hypergeometric solution of the Stark-ladder effect in crystals

The motion of electrons in a crystal subjected to a linear electric field is studied by means of the molecular orbital method. The field perturbation of the resonance integrals, as well as the Coulomb ones, results in the Schroedinger equation being expressed as a hypergeometric difference equation, whose solution gives rise to the well-known Stark-ladder picture of the tilted energy band. It is found that the part played by the resonance integral perturbation is just as important as that of the Coulomb integral perturbation and, therefore, cannot be neglected as in earlier investigations.     

Shock compression of solids

This review contains a brief, comprehensive, critical assessment of the status of investigations concerning the response of solids to shock compression. Mechanical, metallurgical, electrical, optical and other phenomena occurring in substances subjected to shock pressures covering the range from about 0.1 to 6000 GPa are considered. Emphasis is placed on physical interpretation of observations peculiar to the shock environment and on the relationships among observations in the various areas of investigation.     

Measurement of the proton total reaction cross section for 159Tb, 181Ta and 197Au between 20 and 48 MeV

Proton total reaction cross sections have been measured for the nuclei ¹⁵⁹Tb, ¹⁸¹Ta and ¹⁹⁷Au at seven proton energies between 20 and 48 MeV using an attenuation technique. The experimentally determined energy dependence of the total reaction cross sections is compared with results obtained for black nucleus and optical model calculations.     

Two-electron theory of non-interacting surface and impurity states

Some earlier results in the Davison-Cheng two-electron theory of surface and impurity states are corrected. Although the surface spin state findings are only slightly modified, it is found that the inner and outer impurity spin states no longer always occur separately, but can in fact co-exist. After discussing the connection between the two-electron theory of monatomic crystals and the one-electron theory of diatomic crystals, the paper concludes by briefly outlining the recent developments in the one-electron theory of surface and impurity state interaction.