The energies of the excited states in very neutron-rich (42)Si and (41,43)P have been measured using in-beam gamma-ray spectroscopy from the fragmentation of secondary beams of (42,44)S at 39A MeV. The low 2(+) energy of (42)Si, 770(19) keV, together with the level schemes of (41,43)P, provides evidence for the disappearance of the Z=14 and N=28 spherical shell closures, which is ascribed mainly to the action of proton-neutron tensor forces. New shell model calculations indicate that (42)Si is best described as a well-deformed oblate rotor.
Abstract-In this note, we investigate the stability of hybrid systems in closed-loop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1, -norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory.Index Terms-Hybrid systems, Lyapunov stability, model predictive control (MPC), piecewise affine systems.
Min-Max model predictive control (MPC) is one of the few techniques suitable for robust stabilization of uncertain nonlinear systems subject to constraints. Stability issues as well as robustness have been recently studied and some novel contributions on this topic have appeared in the literature. In this survey, we distill from an extensive literature a general framework for synthesizing min-max MPC schemes with an a priori robust stability guarantee. Firstly, we introduce a general prediction model that covers a wide class of uncertainties, which includes bounded disturbances as well as state and input dependent disturbances (uncertainties). Secondly, we extend the notion of regional Input-to-State Stability (ISS) in order to fit the considered class of uncertainties. Then, we establish that the standard min-max approach can only guarantee practical stability. We concentrate our attention on two different solutions for solving this problem. The first one is based on a particular design of the stage cost of the performance index, which leads to a H ∞ strategy, while the second one is based on a dual-mode strategy. Under fairly mild assumptions both controllers guarantee Input-to-State Stability of the resulting closed-loop system. Moreover, it is shown that the nonlinear auxiliary control law introduced in [29] to solve the H ∞ problem can be used, for nonlinear systems affine in control, in all the proposed min-max schemes and also in presence of state independent disturbances. A simulation example illustrates the techniques surveyed in this article.
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