Augmented gradient flows for on-line robust pole assignment via state and output feedback

Jiang, Danchi; Wang, Jun

doi:10.1016/s0005-1098(01)00200-x

Cited by 28 publications

(12 citation statements)

References 15 publications

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“…As shown in [12], suppose T is a transformation of the state vector xðtÞ ¼ TxðtÞ (10) such that the pair (B,A) is transformed into the vector companion form ðB;ÃÞ, as defined in [11]B…”

Section: Synthesismentioning

confidence: 99%

“…In particular, parameterizations of state feedback [10,[12][13][14] and output feedback controllers [1][2][3][4][5][6][7][8][9][10][14][15][16][17][18][19][20][21][22] have received much attention in recent years. The problem of eigenvalue assignment by static output feedback is rather a more difficult problem than that of state feedback, but is more crucial in most practical systems since state measurements may not be always possible.…”

Section: Introductionmentioning

confidence: 99%

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A parametric approach for eigenvalue assignment by static output feedback

Karbassi

Saadatjou

2009

Journal of the Franklin Institute

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Section: Synthesismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A parametric approach for eigenvalue assignment by static output feedback

Karbassi

Saadatjou

2009

Journal of the Franklin Institute

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“…Neurodynamic optimization offers a promising computation method for solving the robust pole assignment problems. Some investigations on developing neurodynamic optimization approaches to robust pole assignment have been carried out [17], [18], [33]- [36].…”

Section: Introductionmentioning

confidence: 99%

Neurodynamics-based robust pole assignment for synthesizing second-order control systems via output feedback based on a convex feasibility problem reformulation

Wang

Yan

2014

2014 IEEE International Symposium on Innovations in Intelligent Systems and Applications (INISTA) Proceedings

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A neurodynamic optimization approach is proposed for robust pole assignment problem of second-order control systems via output feedback. With a suitable robustness measure serving as the objective function, the robust pole assignment problem is formulated as a quasi-convex optimization problem with linear constraints. Next, the problem further is reformulated as a convex feasibility problem. Two coupled recurrent neural networks are applied for solving the optimization problem with guaranteed optimality and exact pole assignment. Simulation results are included to substantiate the effectiveness of the proposed approach.

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“…Various neurodynamic optimization approaches have been widely developed with guaranteed optimality, expended applicability, improved convergence properties, and reduced model complexity, e.g., [10], [11], [14], [15], [18], [21], [27]- [29], [34], [36]- [38]. There have been some investigations on developing neurodynamic optimization approaches to robust pole assignment [12], [13], [16], [17], [19], [26]. Especially, [12] achieved robust approximate pole assignment for secondorder systems using neural network computation.…”

Section: Introductionmentioning

confidence: 99%

Neurodynamics-based robust eigenstructure assignment for second-order descriptor systems

Yan²,

Wang³

2014

2014 International Joint Conference on Neural Networks (IJCNN)

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In this paper, a neurodynamic optimization approach is proposed for robust eigenstructure assignment problem of second-order descriptor systems via state feedback control. With a novel robustness measure serving as the objective function, the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem. Two coupled recurrent neural networks are applied for solving the optimization problem with guaranteed optimality and exact pole assignment. Simulation results are included to substantiate the effectiveness of the proposed approach. I. INTRODUCTIONEigenstructure assignment is a vitally important problem in linear control systems design. Since poles (eigenvalues) and their associated eigenvectors of a closed-loop system greatly impact on the control performance such as the stability condition and the convergence speed, pole assignment is an effective approach to place poles of the close-loop system at any desired locations on the complex plane via a state feedback law with appropriate gains. In practice, robust control is more desirable as the systems cannot be precisely modeled or the systems are subject to parameter uncertainties. The robust pole assignment problem is to find the feedback gains such that the robustness of the eigensystem is optimized. Kautsky et al. [20] first formulated the robust pole (eigenstructure) assignment by means of minimizing the spectral condition number of the eigenvector matrix. Alternative robustness measures and various optimization approaches in linear control systems design were widely investigated [22], [24]-[26], [32], [35], [41]. Second-order linear systems constitute an important class of systems, as they can capture the dynamic behaviors of many natural phenomena. There exist numerous applications in various fields, such as vibration and structural analysis, spacecraft control and robotics control [1], [2], [7]. Furthermore, as second-order systems can be viewed as special cases of highorder systems, synthesis approach to second-order systems may be applied for higher-order systems. A few results on robust pole assignment in second-order linear systems are available in the literature [3], [5], [8], [9], [23], [30]. In specific, [30]proposed a robustness measure for second-order control by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. However, most existing algorithms cannot guarantee the achievement of global optimality due to the complexity and nonconvexity of the applied measures. In addition, most proposed methods are not applicable for on-line computing.Neurodynamic optimization based on recurrent neural networks is competent for solving optimization problems in

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Augmented gradient flows for on-line robust pole assignment via state and output feedback

Cited by 28 publications

References 15 publications

A parametric approach for eigenvalue assignment by static output feedback

A parametric approach for eigenvalue assignment by static output feedback

Neurodynamics-based robust pole assignment for synthesizing second-order control systems via output feedback based on a convex feasibility problem reformulation

Neurodynamics-based robust eigenstructure assignment for second-order descriptor systems

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