Given a smooth finite-dimensional state space system which is linear in the input, its input-output map can be represented by a Chen-Fliess series, namely, a weighted sum of iterated integrals of the input's compo...
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ISBN:
(数字)9781665467469
ISBN:
(纸本)9781665467469
Given a smooth finite-dimensional state space system which is linear in the input, its input-output map can be represented by a Chen-Fliess series, namely, a weighted sum of iterated integrals of the input's component functions. The objective of this paper is to propose a generalized notion of a Chen-Fliess series for infinite-dimensional systems. The basic idea is to replace the real field of series coefficients with a ring of linear operators which act on the iterated integrals. The specific goals are to provide sufficient conditions for convergence of this generalized series and to exercise the theory on two specific examples: the transport equation and second-order hyperbolic partial differential equations. It will be shown in these examples that the generalized Chen-Fliess series under suitable conditions yields solutions that converge pointwise to the known classical solutions.
An experimental implementation of a rapid active control strategy for flexible structures combined with a modal filter for state reconstruction is presented. The control law, which builds upon Komornik's original ...
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An experimental implementation of a rapid active control strategy for flexible structures combined with a modal filter for state reconstruction is presented. The control law, which builds upon Komornik's original idea, is designed so as to achieve an arbitrarily large decay rate of the energy of the system, at the price of solving once and for all a well-conditioned small-size linear system, instead of a Riccati equation. It is applied to a slender beam. The fundamental ideas and properties of this simple but efficient strategy are explained. The emphasis is put on the practical implementation and on the experimental results, which show an important increase of the apparent modal damping even for values of the resulting gain that do not generate spill-over. The proposed feedback outperforms the standard LQ control. The actual behaviour of the closed-loop system is accurately predicted by a complete electro-mechanical model that accounts for the identified dynamics of the shaker. (C) 2003 Published by Elsevier Ltd.
Double general orthogonal polynomials are used for the analysis, and the parameters estimation of linear distributed systems. The formulating of algorithms for analyzing and for estimating the parameters of linear dis...
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Double general orthogonal polynomials are used for the analysis, and the parameters estimation of linear distributed systems. The formulating of algorithms for analyzing and for estimating the parameters of linear distributed systems are straightforward and convenient for digital computation. Illustrative examples are given to demonstrate the availability of the proposed method
Optimal modal feedback control laws are synthesized from the modal equations which are obtained by eigenfunction expansion of the diffusion equation systems with space-independent control, boundary control, and distri...
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Optimal modal feedback control laws are synthesized from the modal equations which are obtained by eigenfunction expansion of the diffusion equation systems with space-independent control, boundary control, and distributed control. Comparison between the modal feedback control laws and distributed feedback control laws are discussed. The results also indicate proper quadrature performance criteria for the synthesis of the distributed feedback control laws.
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