Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Unruh Radiation, Holography and Boundary Cosmology

A uniformly acclerated observer in anti-deSitter space-time is known to detect thermal radiation when the acceleration exceeds a critical value. We investigate the holographic interpretation of this phenomenon. For uniformly accelerated trajectories transverse to the boundary of the AdS space, the hologram is a blob which expands along the boundary. Observers on the boundary co-moving with the hologram become observers in cosmological space-times. For supercritical accelerations one gets a Milne universe when the holographic screen is the boundary in Poincare coordinates, while for the boundary in hyperspherical coordinates one gets deSitter spacetimes. The presence or absence of thermality is then interpreted in terms of specific classes of observers in these cosmologies.Comment: LaTeX, 35 pages, 3 figures. A reference is added and typos are correcte

Clean Time-Dependent String Backgrounds from Bubble Baths

We consider the set of controlled time-dependent backgrounds of general relativity and string theory describing ``bubbles of nothing'', obtained via double analytic continuation of black hole solutions. We analyze their quantum stability, uncover some novel features of their dynamics, identify their causal structure and observables, and compute their particle production spectrum. We present a general relation between squeezed states, such as those arising in cosmological particle creation, and nonlocal theories on the string worldsheet. The bubble backgrounds have various aspects in common with de Sitter space, Rindler space, and moving mirror systems, but constitute controlled solutions of general relativity and string theory with no external forces. They provide a useful theoretical laboratory for studying issues of observables in systems with cosmological horizons, particle creation, and time-dependent string perturbation theory.Comment: 38 pages, harvmac big, 6 figure

Red-shifts near black holes

A simple ordinary differential equation is derived governing the red-shifts of wave-fronts propagating through a non-stationary spherically symmetric space-time. Approach to an event horizon corresponds to approach to a fixed point; in general, the phase portrait of the equation illuminates the qualitative features of the geometry. In particular, the asymptotics of the red-shift as a horizon is approached, a critical ingredient of Hawking's prediction of radiation from black holes, are easily brought out. This asympotic behavior has elements in common with the universal behavior near phase transitions in statistical physics. The validity of the Unruh vacuum for the Hawking process can be understood in terms of this universality. The concept of surface gravity is extended to to non-stationary spherically symmetric black holes. Finally, it is shown that in the non-stationary case, Hawking's predicted flux of radiation from a black hole would be modified.Comment: 20 pages, plain Tex, IOP macros, 4 eps figures, accepted by CQ

Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum Calculations 5. ConclusionsComment: 56 pages, 2 figures, JHEP style, Invited review to appear in Living Reviews of Relativit

Optimal Active Control of a Wave Energy Converter

Abstract-This paper investigates optimal active control schemes applied to a point absorber wave energy converter within a receding horizon fashion. A variational formulation of the power maximization problem is adapted to solve the optimal control problem. The optimal control method is shown to be of a bang-bang type for a power take-off mechanism that incorporates both linear dampers and active control elements. We also consider a direct transcription of the optimal control problem as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard NLP solver. Since the system model is bilinear and the cost function is non-convex quadratic, the resulting optimization problem is not a convex quadratic program. Results will be compared with an optimal command latching method to demonstrate the improvement in absorbed power. Time domain simulations are generated under irregular sea conditions