Correlation-Based Tuning of a Restricted-Complexity Controller for an Active Suspension System

A correlation-based controller tuning method is proposed for the ``Design and optimization of restricted-complexity controllers'' benchmark problem. The approach originally proposed for model following is extended to solve the disturbance rejection problem. The idea is to tune the controller parameters such that the closed-loop output be uncorrelated with the disturbance signal. Since perfect decorrelation between the closed-loop output and the disturbance signal is not attainable in the restricted-complexity controller design, the cross correlation between these two signals is minimized iteratively using the stochastic approximation method. Since control specifications can normally be expressed in terms of constraints on the sensitivity functions, a frequency-domain analysis of the criterion is performed. Straightforward implementation of the proposed approach on the active suspension system of the Automatic Control Laboratory of Grenoble (LAG) provides a 2nd-order controller that meets the control specifications very well

Iterative Correlation-Based Controller Tuning: Application to a Magnetic Suspension System

Iterative tuning of the parameters of a restricted-order controller using the data acquired in closed-loop operation seems to be a promising idea, especially for tuning PID controllers in industrial applications. In this paper, a new tuning approach based on decorrelation is proposed. The basic idea is to make the output error between the designed and achieved closed-loop systems uncorrelated with the reference signal. The controller parameters are calculated as the solution to correlation equations involving instrumental variables. Different choices of instrumental variables are proposed and compared via simulation. The stochastic properties of the correlation approach are compared with those of standard IFT using Monte-Carlo simulation. The proposed approach is also implemented on an experimental magnetic suspension system, and excellent performance using only a few real-time experiments is achieved

Kac-Moody symmetry in the light front of gauge theories

We discuss the emergence of a new symmetry generator in a Hamiltonian realisation of four-dimensional gauge theories in the flat space foliated by retarded (advanced) time. It generates an asymptotic symmetry that acts on the asymptotic fields in a way different from the usual large gauge transformations. The improved canonical generators, corresponding to gauge and asymptotic symmetries, form a classical Kac-Moody charge algebra with a non-trivial central extension. In particular, we describe the case of electromagnetism, where the charge algebra is the $\mathrm{U}(1)$ current algebra with a level proportional to the coupling constant of the theory, $\kappa=4\pi^2/e^2$. We construct bilinear generators yielding Virasoro algebras on the null boundary. We also provide a non-Abelian generalization of the previous symmetries by analysing the evolution of Yang-Mills theory in Bondi coordinates.Comment: 31 pages, no figures; in V2 text clarified and references adde

Control of an Active Suspension System as a Benchmark for Design and Optimization of Restricted Complexity Controllers

A benchmark problem for restricted complexity controller design is introduced. The objective is to design the lowest-order controller which meets the control specifications for an active suspension system. The input-output data of the plant are provided on the benchmark site and the final controllers are evaluated using the closed-loop data. Thirteen solutions proposed to solve the benchmark problem are briefly presented and classified in terms of methodology and compared with respect to their complexity and performance

Thermodynamics of Taub-NUT/Bolt-AdS Black Holes in Einstein-Gauss-Bonnet Gravity

We give a review of the existence of Taub-NUT/bolt solutions in Einstein Gauss-Bonnet gravity with the parameter $\alpha$ in six dimensions. Although the spacetime with base space $S^{2}\times S^{2}$ has curvature singularity at $r=N$, which does not admit NUT solutions, we may proceed with the same computations as in the $\mathbb{CP}^{2}$ case. The investigation of thermodynamics of NUT/Bolt solutions in six dimensions is carried out. We compute the finite action, mass, entropy, and temperature of the black hole. Then the validity of the first law of thermodynamics is demonstrated. It is shown that in NUT solutions all thermodynamic quantities for both base spaces are related to each other by substituting $\alpha^{\mathbb{CP}^{k}}=[(k+1)/k]\alpha^{S^{2} \times S^{2}\times >...S_{k}^{2}}$. So no further information is given by investigating NUT solution in the $S^{2}\times S^{2}$ case. This relation is not true for bolt solutions. A generalization of the thermodynamics of black holes to arbitrary even dimensions is made using a new method based on the Gibbs-Duhem relation and Gibbs free energy for NUT solutions. According to this method, the finite action in Einstein Gauss-Bonnet is obtained by considering the generalized finite action in Einstein gravity with an additional term as a function of $\alpha$. Stability analysis is done by investigating the heat capacity and entropy in the allowed range of $\alpha$, $\Lambda$ and $N$. For NUT solutions in $d$ dimensions, there exist a stable phase at a narrow range of $\alpha$. In six-dimensional Bolt solutions, metric is completely stable for $\mathcal{B}=S^{2}\times S^{2}$, and is completely unstable for $\mathcal{B}=\mathbb{CP}^{2}$ case.Comment: 19 pages, 3 figures, some Refs. are added, Fig 1 is replaced, and some corrections are don

Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity

The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton-Jacobi method to calculate the boundary counterterms necessary to remove the divergences and allow the study of the thermodynamics of Einstein-Gauss-Bonnet black holes.Comment: 21 pages, LaTe

Generalizing Galileons

The Galileons are a set of terms within four-dimensional effective field theories, obeying symmetries that can be derived from the dynamics of a 3+1-dimensional flat brane embedded in a 5-dimensional Minkowski Bulk. These theories have some intriguing properties, including freedom from ghosts and a non-renormalization theorem that hints at possible applications in both particle physics and cosmology. In this brief review article, we will summarize our attempts over the last year to extend the Galileon idea in two important ways. We will discuss the effective field theory construction arising from co-dimension greater than one flat branes embedded in a flat background - the multiGalileons - and we will then describe symmetric covariant versions of the Galileons, more suitable for general cosmological applications. While all these Galileons can be thought of as interesting four-dimensional field theories in their own rights, the work described here may also make it easier to embed them into string theory, with its multiple extra dimensions and more general gravitational backgrounds.Comment: 16 pages; invited brief review article for a special issue of Classical and Quantum Gravity. Submitted to CQ

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...Comment: 51 single column pages, 19 postscript figures, 2 tables, GRG tex style; minor corrections added; final version appearing in General Relativity and Gravitatio