Dinkelbach Approach to Solving a Class of Fractional Optimal Control Problems

We consider optimal control problems with functional given by the ratio of two integrals (fractional optimal control problems). In particular, we focus on a special case with affine integrands and linear dynamics with respect to state and control. Since the standard optimal control theory cannot be used directly to solve a problem of this kind, we apply Dinkelbach’s approach to linearize it. Indeed, the fractional optimal control problem can be transformed into an equivalent monoparametric family { P q } of linear optimal control problems. The special structure of the class of problems considered allows solving the fractional problem either explicitly or requiring straightforward classical numerical techniques to solve a single equation. An application to advertising efficiency maximization is presented

A global optimization approach to fractional optimal control

In this paper, we consider a fractional optimal control problem governed by system of linear differential equations, where its cost function is expressed as the ratio of convex and concave functions. The problem is a hard nonconvex optimal control problem and application of Pontriyagin's principle does not always guarantee finding a global optimal control. Even this type of problems in a finite dimensional space is known as NP hard. This optimal control problem can, in principle, be solved by Dinkhelbach algorithm [10]. However, it leads to solving a sequence of hard D.C programming problems in its finite dimensional analogy. To overcome this difficulty, we introduce a reachable set for the linear system. In this way, the problem is reduced to a quasiconvex maximization problem in a finite dimensional space. Based on a global optimality condition, we propose an algorithm for solving this fractional optimal control problem and we show that the algorithm generates a sequence of local optimal controls with improved cost values. The proposed algorithm is then applied to several test problems, where the global optimal cost value is obtained for each case

Spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron at low values of x and Q^2

We present a precise measurement of the deuteron longitudinal spin asymmetry A_1^d and of the deuteron spin-dependent structure function g_1^d at Q^2 < 1 GeV^2 and 4*10^-5 < x < 2.5*10^-2 based on the data collected by the COMPASS experiment at CERN during the years 2002 and 2003. The statistical precision is tenfold better than that of the previous measurement in this region. The measured A_1^d and g_1^d are found to be consistent with zero in the whole range of x.Comment: 17 pages, 10 figure

Observation of a J^PC = 1-+ exotic resonance in diffractive dissociation of 190 GeV/c pi- into pi- pi- pi+

The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the pi- pi- pi+ final state using a 190 GeV/c pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420000 events taken at values of the squared 4-momentum transfer t' between 0.1 and 1 GeV^2/c^2. The well-known resonances a1(1260), a2(1320), and pi2(1670) are clearly observed. In addition, the data show a significant natural parity exchange production of a resonance with spin-exotic quantum numbers J^PC = 1-+ at 1.66 GeV/c^2 decaying to rho pi. The resonant nature of this wave is evident from the mass-dependent phase differences to the J^PC = 2-+ and 1++ waves. From a mass-dependent fit a resonance mass of 1660 +- 10+0-64 MeV/c^2 and a width of 269+-21+42-64 MeV/c^2 is deduced.Comment: 7 page, 3 figures; version 2 gives some more details, data unchanged; version 3 updated authors, text shortened, data unchange

Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs

We present a determination of the gluon polarization Delta G/G in the nucleon, based on the helicity asymmetry of quasi-real photoproduction events, Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarized muon beam scattered on a polarized 6-LiD target. The helicity asymmetry for the selected events is = 0.002 +- 0.019(stat.) +- 0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3 (GeV}/c)^2.Comment: 10 pages, 3 figure

The Deuteron Spin-dependent Structure Function g1d and its First Moment

We present a measurement of the deuteron spin-dependent structure function g1d based on the data collected by the COMPASS experiment at CERN during the years 2002-2004. The data provide an accurate evaluation for Gamma_1^d, the first moment of g1d(x), and for the matrix element of the singlet axial current, a0. The results of QCD fits in the next to leading order (NLO) on all g1 deep inelastic scattering data are also presented. They provide two solutions with the gluon spin distribution function Delta G positive or negative, which describe the data equally well. In both cases, at Q^2 = 3 (GeV/c)^2 the first moment of Delta G is found to be of the order of 0.2 - 0.3 in absolute value.Comment: fits redone using MRST2004 instead of MRSV1998 for G(x), correlation matrix adde

Measurement of the Longitudinal Spin Transfer to Lambda and Anti-Lambda Hyperons in Polarised Muon DIS

The longitudinal polarisation transfer from muons to lambda and anti-lambda hyperons, D_LL, has been studied in deep inelastic scattering off an unpolarised isoscalar target at the COMPASS experiment at CERN. The spin transfers to lambda and anti-lambda produced in the current fragmentation region exhibit different behaviours as a function of x and xF . The measured x and xF dependences of D^lambda_LL are compatible with zero, while D^anti-lambda_LL tends to increase with xF, reaching values of 0.4 - 0.5. The resulting average values are D^lambda_LL = -0.012 +- 0.047 +- 0.024 and D^anti-lambda_LL = 0.249 +- 0.056 +- 0.049. These results are discussed in the frame of recent model calculations.Comment: 13 pages, 7 figure

Measurement of the charged-pion polarisability

The COMPASS collaboration at CERN has investigated pion Compton scattering, $\pi^-\gamma\rightarrow \pi^-\gamma$, at centre-of-mass energy below 3.5 pion masses. The process is embedded in the reaction $\pi^-\mathrm{Ni}\rightarrow\pi^-\gamma\;\mathrm{Ni}$, which is initiated by 190\,GeV pions impinging on a nickel target. The exchange of quasi-real photons is selected by isolating the sharp Coulomb peak observed at smallest momentum transfers, $Q^2<0.0015$\,(GeV/$c$)$^2$. From a sample of 63\,000 events the pion electric polarisability is determined to be $\alpha_\pi\ =\ (\,2.0\ \pm\ 0.6_{\mbox{\scriptsize stat}}\ \pm\ 0.7_{\mbox{\scriptsize syst}}\,) \times 10^{-4}\,\mbox{fm}^3$under the assumption$\alpha_\pi=-\beta_\pi$, which relates the electric and magnetic dipole polarisabilities. It is the most precise measurement of this fundamental low-energy parameter of strong interaction, that has been addressed since long by various methods with conflicting outcomes. While this result is in tension with previous dedicated measurements, it is found in agreement with the expectation from chiral perturbation theory. An additional measurement replacing pions by muons, for which the cross-section behavior is unambigiously known, was performed for an independent estimate of the systematic uncertainty.Comment: Published version: 9 pages, 3 figures, 1 tabl

A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target

New high precision measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarised 6LiD target are presented. The data were taken in 2003 and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. Both the Collins and Sivers asymmetries turn out to be compatible with zero, within the present statistical errors, which are more than a factor of 2 smaller than those of the published COMPASS results from the 2002 data. The final results from the 2002, 2003 and 2004 runs are compared with naive expectations and with existing model calculations.Comment: 40 pages, 28 figure

Measurement of the Spin Structure of the Deuteron in the DIS Region

We present a new measurement of the longitudinal spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron in the range 1 GeV^2 < Q^2 < 100 GeV^2 and 0.004< x <0.7. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarised muon beam and a large polarised 6-LiD target. The results are in agreement with those from previous experiments and improve considerably the statistical accuracy in the region 0.004 < x < 0.03.Comment: 10 pages, 6 figures, subm. to PLB, revised: author list, Fig. 4, details adde