摘要 :
This report summarizes recent research on the dynamics of nonlinear feedback systems. We are primarily interested in phase portraits of such systems and the ways in which these portraits depend on parameters. Because of this, we a...
展开
This report summarizes recent research on the dynamics of nonlinear feedback systems. We are primarily interested in phase portraits of such systems and the ways in which these portraits depend on parameters. Because of this, we are interested primarily in processes which have associated probability measures that are absolutely continuous with respect to Lebesgue measure. Such processes will have 'interesting' phase portraits. In this paper we note that the space of piecewise constant functions is invariant under the Perron-Frobenius operator associated with any piecewise affine function. We further show that this will imply the existence of a piecewise constant probability density which is invariant for a given piecewise affine mapping satisfying certain easily checked conditions. We address the 'inverse density problem:' given a density /rho/ defined on some region UCR/sup n/, is it possible to find a mapping F: U implies U which is ergodic on U and which admits /rho/ as an invariant density. We show that an ergodic interval map cascaded with a stable linear system will, under certain conditions, results in a system having a strange attractor. For one canonical such mapping, we calculate the fractal dimension of the resulting attractor as a function of the parameters in the linear system. 15 refs., 5 figs. (ERA citation 14:021576)
收起
摘要 :
General conclusions drawn concerning the effect of feedback on a common emitter amplifier are: Series feedback (1) Increases the low frequency input and output impedances of the transistor itself. (2) Decreases the voltage gain, c...
展开
General conclusions drawn concerning the effect of feedback on a common emitter amplifier are: Series feedback (1) Increases the low frequency input and output impedances of the transistor itself. (2) Decreases the voltage gain, current gain, and gain-bandwidth product of the amplifier. (3) Increases the upper cutoff frequency of the amplifier. (4) Decreases the sensitivity of the amplifier to changes in the transistor parameters; Shunt feedback (1) Decreases the low frequency input and output impedances of the transistor itself. (2) Decreases the voltage gain, current gain, and gain-bandwidth product of the amplifier. (3) Increases the upper cutoff frequency of the amplifier. (4) Decreases the sensitivity of the amplifier to changes in the transistor parameters. (Author)
收起
摘要 :
We study the fundamental properties of feedback for nonlinear, time-varying, multi-input, multi-output, distributed systems. The classical Black formula is generalized to the nonlinear case. Achievable advantages and limitations o...
展开
We study the fundamental properties of feedback for nonlinear, time-varying, multi-input, multi-output, distributed systems. The classical Black formula is generalized to the nonlinear case. Achievable advantages and limitations of feedback in nonlinear dynamical systems are classified and studied in five categories: desensitization, disturbance attenuation, linearizing effect, asymptotic tracking and disturbance attenuation, linearizing effect, asymptotic tracking and disturbance rejection, stabilization. Conditions under which feedback is beneficial for nonlinear dynamical systems are derived. Our results show that if the appropriate linearized inverse return difference operator is small, then the nonlinear feedback system has advantages over the open-loop system. Several examples are provided to illustrate the results.
收起
摘要 :
Preliminary results are presented on the use of observers for interpolation in constant-coefficient, linear, dynamic systems. Two sequential algorithms, which are termed fixed-point and fixed-lag interpolators and can be implement...
展开
Preliminary results are presented on the use of observers for interpolation in constant-coefficient, linear, dynamic systems. Two sequential algorithms, which are termed fixed-point and fixed-lag interpolators and can be implemented to operate in real time, are developed. Extensions to noisy dynamic systems and to reduced-order interpolators, and implications in feedback control are noted.
收起
摘要 :
The role of sensory feedback is a central question in understanding vertebrate locomotion. Sensory feedback related to movement of the body and its interaction with the environment is known to have profound effects on the central ...
展开
The role of sensory feedback is a central question in understanding vertebrate locomotion. Sensory feedback related to movement of the body and its interaction with the environment is known to have profound effects on the central pattern generator (CPG), the neural circuit responsible for generating the basic locomotor pattern. Conversely, the CPG controls muscle activation, leading to changes in body configurations as it interacts with the environment. We take two approaches to understanding the role of sensory feedback in locomotion: a control-theory approach and a CPG-based approach. In the control theory approach, we have developed a general method of computing the optimal local feedback control law given a model of the plant (the mapping from muscle activation to movement) and a cost rate function that penalizes muscle activation and rewards speed through the environment. The first step in this method is to the compute the optimal steady-state swimming pattern. In the CPG- based approach, we have investigated the role of sensory feedback in a simple closed-loop model in which a CPG produces a pattern of muscle activation which is modified by sensory feedback related to body curvature.
收起
