Simple robust control laws for robot manipulators. Part 2: Adaptive case

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control

Exotic-Hadron Signature by Constituent-Counting Rule in Perturbative QCD

We explain a method to find internal quark configurations of exotic hadron candidates by using the constituent counting rule. The counting rule was theoretically predicted in perturbative QCD for hard exclusive hadron reactions, and it has been tested in experiments for stable hadrons including compound systems of hadrons such as the deuteron, $^3$H, and $^3$He. It indicates that the cross section scales as $d\sigma /dt \sim 1/s^{n-2}$, where $s$ is the center-of-mass energy squared and $n$ is the total number of constituents. We apply this method for finding internal configurations of exotic hadron candidates, especially $\Lambda (1405)$. There is a possibility that $\Lambda (1405)$ could be five-quark state or a $\bar K N$ molecule, and scaling properties should be different between the ordinary three-quark state or five-quark one. We predict such a difference in $\pi^- + p \to K^0 + \Lambda (1405)$, and it could be experimentally tested, for example, at J-PARC. On the other hand, there are already measurements for $\gamma + p \to K^+ + \Lambda (1405)$ as well as the ground $\Lambda$ in photoproduction reactions. Analyzing such data, we found an interesting indication that $\Lambda (1405)$ looks like a five-quark state at medium energies and a three-quark one at high energies. However, accurate higher-energy measurements are necessary for drawing a solid conclusion, and it should be done at JLab by using the updated 12 GeV electron beam. Furthermore, we discuss studies of exotic hadron candidates, such as $f_0 (980)$ and $a_0 (980)$, in electron-positron annihilation by using generalized distribution amplitudes and the counting rule. These studies should be possible as a KEKB experiment.Comment: 6 pages, LaTeX, 10 eps files, to be published in JPS Conf. Proc., Proceedings of the 14th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2016), July 25-30, 2016, Kyoto, Japa

Coupled-channel study of gamma p --> K+ Lambda

A coupled-channel (CC) approach has been developed to investigate kaon photoproduction on the nucleon. In addition to direct K+ Lambda production, our CC approach accounts for strangeness production including K+ Lambda final state interactions with both pi0 p and pi+ n intermediate states. Calculations for the gamma p --> K+ Lambda reaction have been performed, and compared with the recent data from SAPHIR, with emphasis on the CC effects. We show that the CC effects are significant at the level of inducing 20% changes on total cross sections; thereby, demonstrating the need to include pi N channels to correctly describe the gamma p --> K+ Lambda reaction.Comment: 12 pages, 6 eps figures, uses elsart.cls, submitted to Phys.Lett.B; v2: added paragraph in section

Exotic order in simple models of bosonic systems

We show that simple Bose Hubbard models with unfrustrated hopping and short range two-body repulsive interactions can support stable fractionalized phases in two and higher dimensions, and in zero magnetic field. The simplicity of the constructed models advances the possibility of a controlled experimental realization and novel applications of such unconventional states.Comment: 4 pages, 4 figure

Berry's phase for coherent states of Landau levels

The Berry phases for coherent states and squeezed coherent states of Landau levels are calculated. Coherent states of Landau levels are interpreted as a result of a magnetic flux moved adiabatically from infinity to a finite place on the plane. The Abelian Berry phase for coherent states of Landau levels is an analog of the Aharonov- Bohm effect. Moreover, the non-Abelian Berry phase is calculated for the adiabatic evolution of the magnetic field B.Comment: 4 pages, 1 figur

Light cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench

We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled. We find that on short time scales the relative phase shows "light cone" like dynamics and creates a metastable superfluid state, which can be supercritical. We also demonstrate similar light cone dynamics for the transverse field Ising model. On longer time scales the supercritical state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We study this effect both numerically using truncated Wigner approximation and analytically within a newly suggested time dependent renormalization group approach (RG). In particular, within RG we show that there are two possible fixed points for the real time evolution corresponding to the superfluid and normal steady states. So depending on the initial conditions and the microscopic parameters of the Hamiltonian the system undergoes a non-equilibrium phase transition of the Kosterlitz-Thouless type. The time scales for the vortex unbinding near the critical point are exponentially divergent, similar to the equilibrium case.Comment: 14 pages, 10 figure

Finite Temperature Behavior of the ν=1\nu=1 Quantum Hall Effect in Bilayer Electron Systems

An effective field theoretic description of $\nu=1$ bilayer electron systems stabilized by Coulomb repulsion in a single wide quantum well is examined using renormalization group techniques. The system is found to undergo a crossover from a low temperature strongly correlated quantum Hall state to a high temperature compressible state. This picture is used to account for the recent experimental observation of an anomalous transition in bilayer electron systems (T. S. Lay, {\em et al.} Phys. Rev. B {\bf 50}, 17725 (1994)). An estimate for the crossover temperature is provided, and it is shown that its dependence on electron density is in reasonable agreement with i the experiment.Comment: Corrected typos, and changed content, 5 pages and 2 figures, accepted in Phys. Rev.

Edge states in Open Antiferromagnetic Heisenberg Chains

In this letter we report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes $S=1/2, 1,3/2,2$ using the density-matrix renormalization group (DMRG) method initiated by White. For integer spin chains, we find that edge states with spin magnitude $S_{edge}=S/2$ exist, in agreement with Valence-Bond-Solid model picture. For half-integer spin chains, we find that no edge states exist for $S=1/2$ spin chain, but edge state exists in $S=3/2$ spin chain with $S_{edge}=1/2$, in agreement with previous conjecture by Ng. Strong finite size effects associated with spin dimmerization in half-integer spin chains will also be discussed.Comment: 4 pages, RevTeX 3.0, 5 figures in a separate uuencoded postscript file. Replaced once to enlarge the acknowlegement