Decentralized stabilization and pole assignment for general proper systems

Davison, E.J.; Chang, Tsung-Hui

doi:10.1109/9.53544

Cited by 143 publications

(191 citation statements)

References 22 publications

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“…holds for every permutation (j 1 , j 2 , ..., j ν ) of the set {1, 2, ..., ν} and p ∈ {1, ..., ν − 1} [13].…”

Section: Assumptionmentioning

confidence: 99%

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Decentralized Implementation of Centralized Controllers for Interconnected Systems

Lavaei

2012

IEEE Trans. Automat. Contr.

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Given a centralized controller associated with a linear time-invariant interconnected system, this paper is concerned with designing a parameterized decentralized controller such that the state and input of the system under the obtained decentralized controller can become arbitrarily close to those of the system under the given centralized controller, by tuning the controller's parameters. To this end, a twolevel decentralized controller is designed, where the upper level captures the dynamics of the centralized closed-loop system, and the lower level is an observed-based sub-controller designed based on the new notion of structural initial value observability. The proposed method can decentralize every generic centralized controller, provided the interconnected system satisfies very mild conditions. The efficacy of this work is elucidated by some numerical examples.

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“…holds for every permutation (j 1 , j 2 , ..., j ν ) of the set {1, 2, ..., ν} and p ∈ {1, ..., ν − 1} [13].…”

Section: Assumptionmentioning

confidence: 99%

“…Several methods have been proposed in the literature to find the DFMs of a system [12], [13], [14]. The notion of quotient fixed modes (QFM) was subsequently introduced in [15] to investigate the stabilizability of a system with respect to all (nonlinear and time-varying) decentralized controllers.…”

mentioning

confidence: 99%

Decentralized Implementation of Centralized Controllers for Interconnected Systems

Lavaei

2012

IEEE Trans. Automat. Contr.

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“…According to [10], a (centralized) controllable and observable mode is a DFM of the system S if and only if there exist a permutation of f1; 2; . .…”

Section: A Matrix Rank Checkingmentioning

confidence: 99%

“…The following definition was presented in [7] for strictly proper systems and generalized in [10] for proper systems. …”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…It was also shown in [12] that the DFMs of any system can be found by checking the transmission zeros of a set of artificial systems derived from the original system. An algorithm was presented in [10] to identify the DFMs of a system by computing the rank of a set of matrices. Unfortunately, the number of systems whose transmission zeros need to be checked in [12] and the number of matrices whose ranks are to be computed in [10] depend exponentially on the number of subsystems of the original system.…”

Section: Introductionmentioning

confidence: 99%

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Time Complexity of Decentralized Fixed Mode Verification

Sojoudi

Lavaei

Aghdam

2011

Structurally Constrained Controllers

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971choose the initial condition of the original system to ensure the boundedness of the trajectory x(t). Taking the initial condition and observer gain as x(0) = (00:4; 1; 00:7; 00:5) T ,x(0) = 0, L = (l 1 ; l 2 ) with l1 = (4; 4; 0; 0) T , l2 = (0; 0; 4; 4) T , we have the simulation result in Fig. 1. Simulation demonstrates local error dynamics stability and the ease of implementation of the observer using multiple time scales. Control, vol. 2, no. 3, pp. 176-192, 1996. Time Complexity of Decentralized Fixed-Mode Verification Javad Lavaei and Somayeh SojoudiAbstract-Given an interconnected system, this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct DFMs (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This note provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem.

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Approximate nonlinear output regulation based on the universal approximation theorem

Wang

Huang

Yau

2000

Int. J. Robust Nonlinear Control

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The regulator equations arising from the nonlinear output regulation problem are a set of mixed partial and algebraic equations. Due to the nonlinear nature, it is difficult to obtain the exact solution of the regulator equations. This paper presents an approximation method for solving the regulator equations based on a class of feedforward neural networks. It is shown that a three‐layer neural network can solve the regulator equations up to a prescribed arbitrarily small error, and this small error can be translated into a guaranteed steady‐state tracking error for the closed‐loop system. The method has led to an effective approach to approximately solving the nonlinear output regulation problem. Copyright © 2000 John Wiley & Sons, Ltd.

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Decentralized stabilization and pole assignment for general proper systems

Cited by 143 publications

References 22 publications

Decentralized Implementation of Centralized Controllers for Interconnected Systems

Decentralized Implementation of Centralized Controllers for Interconnected Systems

Time Complexity of Decentralized Fixed Mode Verification

Approximate nonlinear output regulation based on the universal approximation theorem

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