7,286 research outputs found
Feedback control of unsupported standing in paraplegia. Part I: optimal control approach
This is the first of a pair of papers which describe an investigation into the feasibility of providing artificial balance to paraplegics using electrical stimulation of the paralyzed muscles. By bracing the body above the shanks, only stimulation of the plantarflexors is necessary. This arrangement prevents any influence from the intact neuromuscular system above the spinal cord lesion. Here, the authors extend the design of the controllers to a nested-loop LQG (linear quadratic Gaussian) stimulation controller which has ankle moment feedback (inner loops) and inverted pendulum angle feedback (outer loop). Each control loop is tuned by two parameters, the control weighting and an observer rise-time, which together determine the behavior. The nested structure was chosen because it is robust, despite changes in the muscle properties (fatigue) and interference from spasticity
Feedback control of unsupported standing in paraplegia. Part II: experimental results
For pt. I see ibid., vol. 5, no. 4, p. 331-40 (1997). This is the second of a pair of papers which describe an investigation into the feasibility of providing artificial balance to paraplegics using electrical stimulation of the paralyzed muscles. By bracing the body above the shanks, only stimulation of the plantar flexors is necessary. This arrangement prevents any influence from the intact neuromuscular system above the spinal cord lesion. Here, the authors present experimental results from intact and paraplegic subjects
Optimal control of ankle joint moment: Toward unsupported standing in paraplegia
This paper considers part of the problem of how to provide unsupported standing for paraplegics by feedback control. In this work our overall objective is to stabilize the subject by stimulation only of his ankle joints while the other joints are braced, Here, we investigate the problem of ankle joint moment control. The ankle plantarflexion muscles are first identified with pseudorandom binary sequence (PRBS) signals, periodic sinusoidal signals, and twitches. The muscle is modeled in Hammerstein form as a static recruitment nonlinearity followed by a linear transfer function. A linear-quadratic-Gaussian (LQG)-optimal controller design procedure for ankle joint moment was proposed based on the polynomial equation formulation, The approach was verified by experiments in the special Wobbler apparatus with a neurologically intact subject, and these experimental results are reported. The controller structure is formulated in such a way that there are only two scalar design parameters, each of which has a clear physical interpretation. This facilitates fast controller synthesis and tuning in the laboratory environment. Experimental results show the effects of the controller tuning parameters: the control weighting and the observer response time, which determine closed-loop properties. Using these two parameters the tradeoff between disturbance rejection and measurement noise sensitivity can be straightforwardly balanced while maintaining a desired speed of tracking. The experimentally measured reference tracking, disturbance rejection, and noise sensitivity are good and agree with theoretical expectations
Stability of Affine G-varieties and Irreducibility in Reductive Groups
Let be a reductive affine algebraic group, and let be an affine
algebraic -variety. We establish a (poly)stability criterion for points
in terms of intrinsically defined closed subgroups of , and
relate it with the numerical criterion of Mumford, and with Richardson and
Bate-Martin-R\"ohrle criteria, in the case . Our criterion builds on a
close analogue of a theorem of Mundet and Schmitt on polystability and allows
the generalization to the algebraic group setting of results of Johnson-Millson
and Sikora about complex representation varieties of finitely presented groups.
By well established results, it also provides a restatement of the non-abelian
Hodge theorem in terms of stability notions.Comment: 29 pages. To appear in Int. J. Math. Note: this version 4 is
identical with version 2 (version 3 is empty
Degenerations of LeBrun twistor spaces
We investigate various limits of the twistor spaces associated to the
self-dual metrics on n CP ^2, the connected sum of the complex projective
planes, constructed by C. LeBrun. In particular, we explicitly present the
following 3 kinds of degenerations whose limits of the metrics are: (a) LeBrun
metrics on (n-1) CP ^2$, (b) (Another) LeBrun metrics on the total space of the
line bundle O(-n) over CP ^1 (c) The hyper-Kaehler metrics on the small
resolution of rational double points of type A_{n-1}, constructed by Gibbons
and Hawking.Comment: 21 pages, 7 figures. V2: A new section added at the end of the
article. V3: Reference slightly update
Isothermic submanifolds of symmetric -spaces
We extend the classical theory of isothermic surfaces in conformal 3-space,
due to Bour, Christoffel, Darboux, Bianchi and others, to the more general
context of submanifolds of symmetric -spaces with essentially no loss of
integrable structure.Comment: 35 pages, 3 figures. v2: typos and other infelicities corrected
Deformation of LeBrun's ALE metrics with negative mass
In this article we investigate deformations of a scalar-flat K\"ahler metric
on the total space of complex line bundles over CP^1 constructed by C. LeBrun.
In particular, we find that the metric is included in a one-dimensional family
of such metrics on the four-manifold, where the complex structure in the
deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the
proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family
of a Hirzebruch surface stated in the last paragraph in the proof of Theorem
1.2, and fixed a relevant error in the proof. Also added a reference [24]
about Kuranishi family of Hirzebruch surface
Drinfeld-Manin Instanton and Its Noncommutative Generalization
The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM
formulism, which gives explicit general solutions of the ADHM constraints for
U(N) (N>=2k-1) k-instantons. For the N<2k-1 case, implicit results are given
systematically as further constraints, which can be used to the collective
coordinate integral. We find that this formulism can be easily generalized to
the noncommutative case, where the explicit solutions are as well obtained.Comment: 17 pages, LaTeX, references added, mailing address added,
clarifications adde
Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds
The precise relation between Kodaira-Spencer path integral and a particular
wave function in seven dimensional quadratic field theory is established. The
special properties of three-forms in 6d, as well as Hitchin's action
functional, play an important role. The latter defines a quantum field theory
similar to Polyakov's formulation of 2d gravity; the curious analogy with
world-sheet action of bosonic string is also pointed out.Comment: 31 page
Higher Spin Gravitational Couplings and the Yang--Mills Detour Complex
Gravitational interactions of higher spin fields are generically plagued by
inconsistencies. We present a simple framework that couples higher spins to a
broad class of gravitational backgrounds (including Ricci flat and Einstein)
consistently at the classical level. The model is the simplest example of a
Yang--Mills detour complex, which recently has been applied in the mathematical
setting of conformal geometry. An analysis of asymptotic scattering states
about the trivial field theory vacuum in the simplest version of the theory
yields a rich spectrum marred by negative norm excitations. The result is a
theory of a physical massless graviton, scalar field, and massive vector along
with a degenerate pair of zero norm photon excitations. Coherent states of the
unstable sector of the model do have positive norms, but their evolution is no
longer unitary and their amplitudes grow with time. The model is of
considerable interest for braneworld scenarios and ghost condensation models,
and invariant theory.Comment: 19 pages LaTe
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