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  • 1
    Publication Date: 2011-08-19
    Description: Spaceflight offers the unique opportunity to study linear bioaccelerometers (vestibular maculas) in the virtual absence of a primary stimulus, gravitational acceleration. Combined morphological-physiological studies of maculas fixed in space and following flight should reveal macular adaptive responses to microgravity, and their time-course. Ground-based research, already begun, using computer-assisted, three-dimensional reconstructions of macular terminal fields will lead to development of computer models of functioning maculas. This research should continue in conjunction with physiological studies, including work with multichannel electrodes.
    Keywords: AEROSPACE MEDICINE
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  • 2
    Publication Date: 2013-08-31
    Description: Space flight offers the opportunity to study linear bioaccelerometers (vestibular maculas) in the virtual absence of a primary stimulus, gravitational acceleration. Macular research in space is particularly important to NASA because the bioaccelerometers are proving to be weighted neural networks in which information is distributed for parallel processing. Neural networks are plastic and highly adaptive to new environments. Combined morphological-physiological studies of maculas fixed in space and following flight should reveal macular adaptive responses to microgravity, and their time-course. Ground-based research, already begun, using computer-assisted, 3-dimensional reconstruction of macular terminal fields will lead to development of computer models of functioning maculas. This research should continue in conjunction with physiological studies, including work with multichannel electrodes. The results of such a combined effort could usher in a new era in understanding vestibular function on Earth and in space. They can also provide a rational basis for counter-measures to space motion sickness, which may prove troublesome as space voyager encounter new gravitational fields on planets, or must re-adapt to 1 g upon return to earth.
    Keywords: AEROSPACE MEDICINE
    Type: NASA. Lyndon B. Johnson Space Center, Spacelab Life Sciences 1: Reprints of Background Life Sciences Publications; p 261-271
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  • 3
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    In:  CASI
    Publication Date: 2019-06-28
    Description: Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables.
    Keywords: CYBERNETICS
    Type: NASA-TM-81323 , A-8990 , NAS 1.15:81323
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  • 4
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    In:  Other Sources
    Publication Date: 2019-07-13
    Description: This paper is presenting an overview of the theory of transformations from nonlinear systems to linear systems. Topics covered include (1) necessary and sufficient conditions for transformations to exist, (2) a method of constructing transformations (3) robustness in design (based on transformations theory) and Liapunov functions, (4) estimation theory, and (5) the relationship between transformation theory and 'nonlinear zeros'. Application of these results to automatic flight control is presented in another paper at this session.
    Keywords: CYBERNETICS
    Type: American Control Conference; Jun 14, 1982 - Jun 16, 1982; Arlington, VA
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  • 5
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    In:  Other Sources
    Publication Date: 2019-06-28
    Description: Necessary and sufficient conditions for a nonlinear system of equations to be locally equivalent, in a neighborhood of the origin in the real number system, to a controllable linear system are combined with several versions of the global inverse function theorem to define sufficient conditions for transforming the nonlinear system into a linear system. Additionally, a technique is introduced for developing a transformation under the assumptions that the columns of a controllability matrix span an n-dimensional space. Finally, the n-l form of the controllability matrix columns is demonstrated to be involutive
    Keywords: CYBERNETICS
    Type: IEEE Transactions on Automatic Control; AC-28; Jan. 198
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  • 6
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    In:  Other Sources
    Publication Date: 2019-07-12
    Description: The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.
    Keywords: CYBERNETICS
    Type: Circuits, Systems, and Signal Processing (ISSN 0278-081X); 5; 4 19; 419-433
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