This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R/sub 2/ to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate t...
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This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R/sub 2/ to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large-scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.
We followup on a suggestion from Bullo and Lewis concerning the importance of geometric homogeneity for mechanicalsystems. It is shown that controllability results for a large class of mechanicalsystems with drift c...
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ISBN:
(纸本)0780379241
We followup on a suggestion from Bullo and Lewis concerning the importance of geometric homogeneity for mechanicalsystems. It is shown that controllability results for a large class of mechanicalsystems with drift can be recovered by considering a class of nonlinear dynamicalsystems satisfying certain homogeneity conditions.
This papers applies a recently developed "generalized averaging theory" to construct stabilizing feedback control laws for underactuated driftless systems. These controls exponentialy stabilize in the averag...
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This papers applies a recently developed "generalized averaging theory" to construct stabilizing feedback control laws for underactuated driftless systems. These controls exponentialy stabilize in the average;the actual system may orbit around the average. Conditions for which the orbit collapses to the averaged trajectory are given. An example validates the theory, demonstrating its utility.
The series expansion methods were synthesized for nonlinear time-varying vector fields. The exponentially stabilizing controllers for underactuated nonlinear systems were also constructed. The algorithms for feedback ...
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The series expansion methods were synthesized for nonlinear time-varying vector fields. The exponentially stabilizing controllers for underactuated nonlinear systems were also constructed. The algorithms for feedback control of underactuated driftless controlsystems was constructed by using averaging theory.
This paper uses a recently developed generalized averaging theory to develop stabilizing control laws for a large class of nonlinear systems with drift. These control laws exponentially stabilize in the average.
This paper uses a recently developed generalized averaging theory to develop stabilizing control laws for a large class of nonlinear systems with drift. These control laws exponentially stabilize in the average.
Based on a recently developed "generalized averaging theory," we present a generic approach for the design of stabilizing feedback controllers for biomimetic locomotive systems. The control laws exponentiall...
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Based on a recently developed "generalized averaging theory," we present a generic approach for the design of stabilizing feedback controllers for biomimetic locomotive systems. The control laws exponentially stabilize in the average, and they apply to a very wide class of systems. Two examples are given: a "kinematic biped" that demonstrates how our theory handles discontinuities, and the snakeboard, which is an underactuated mechanical system with drift.
We followed-up a suggestion from Bullo and Lewis concerning the importance of geometric homogeneity for mechanicalsystems, that shows the controllability results for a large class of mechanicalsystems with drift can...
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We followed-up a suggestion from Bullo and Lewis concerning the importance of geometric homogeneity for mechanicalsystems, that shows the controllability results for a large class of mechanicalsystems with drift can be recovered by considering a class of nonlinear dynamicalsystems satisfying certain homogeneity conditions.
Based on a recently developed "generalized averaging theory", we present a generic approach for the design of stabilizing feedback controller for biomimetic locomotive systems. The control laws exponentially...
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Based on a recently developed "generalized averaging theory", we present a generic approach for the design of stabilizing feedback controller for biomimetic locomotive systems. The control laws exponentially stabilize in the average, and they apply to a very wide class of systems. Two examples are given: a "kinematic biped" that demonstrates how our theory handles discontinuities, and the snakeboard, which is an underactuated mechanical system with drift.
This paper uses a recently developed generalized averaging theory [P.A. Vela and J.W. Burdick, 2003] to develop stabilizing control laws for a large class of nonlinear systems with drift. These control laws exponentia...
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This paper uses a recently developed generalized averaging theory [P.A. Vela and J.W. Burdick, 2003] to develop stabilizing control laws for a large class of nonlinear systems with drift. These control laws exponentially stabilize in the average.
The complexity inherent in gene regulatory network models, as well as their nonlinear nature make them difficult to analyze or validate/invalidate using conventional tools. Combining ideas from robust control theory, ...
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ISBN:
(纸本)0780379241
The complexity inherent in gene regulatory network models, as well as their nonlinear nature make them difficult to analyze or validate/invalidate using conventional tools. Combining ideas from robust control theory, real algebraic geometry, optimization and semi-definite programming, SOSTOOLS provides a promising framework to answer these robustness and model validation questions algorithmically. We adopt these tools in the study of the heat shock response in bacteria. For this purpose, we use a reduced order model of the bacterial heat stress response. We study the robust stability properties of this system to parametric uncertainty, and address the model validation/invalidation problem by proving the necessity for the existence of certain feedback loops to reproduce the known time behavior of the system.
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