The Experts below are selected from a list of 35385 Experts worldwide ranked by ideXlab platform
Kazuhiro Sato - One of the best experts on this subject based on the ideXlab platform.
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Riemannian Optimal Model Reduction of Linear Second-Order Systems
IEEE Control Systems Letters, 2017Co-Authors: Kazuhiro SatoAbstract:This letter develops a structure preserving H2 Optimal Model reduction method of linear second-order systems. The Model reduction problem is formulated as an optimization problem on the product manifold of the two manifolds of symmetric positive definite matrices and two Euclidean manifolds. Reduced systems constructed by the Optimal solution preserve the structure of the original second-order system. A Riemannian metric of the manifold is chosen in such a way that the manifold is geodesically complete, i.e., the domain of the exponential map is the whole tangent space for all points on the manifold. The Riemannian gradient of the objective function is derived for solving the problem by using a Riemannian steepest descent method. The geodesic completeness of the manifold guarantees that all points generated by the steepest descent method are on the manifold, and thus, our method naturally preserves the second-order structure. Furthermore, we suggest how to choose an initial point in the proposed algorithm. The initial point is given by solving another optimization problem on the Stiefel manifold. As a result, we can expect that the value of the objective function at the initial point is relatively small. Numerical experiments illustrate that the proposed method can give a reduced system which is sufficiently close to the original system even if the dimension of the reduced system is small.
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A New H2 Optimal Model reduction method based on riemannian conjugate gradient method
2016 IEEE 55th Conference on Decision and Control (CDC), 2016Co-Authors: Hiroyuki Sato, Kazuhiro SatoAbstract:In this paper, a new optimization problem formulation of the H2 Optimal Model reduction problem is introduced and discussed. The optimization problem is shown to be a problem on a product manifold, which is a Riemannian submanifold of a Euclidean space. Geometry of the resultant optimization problem is investigated and the Riemannian conjugate gradient method for the problem is proposed. Solutions obtained by the proposed method realize stable reduced order systems if the original system satisfies a certain condition, which holds for example for dissipative systems. It is shown by numerical experiments that the proposed method is effective for large-scale problems.
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riemannian trust region methods for h2 Optimal Model reduction
Conference on Decision and Control, 2015Co-Authors: Hiroyuki Sato, Kazuhiro SatoAbstract:In this paper, the Riemannian trust-region method for the H2 Optimal Model reduction problem is proposed. The problem is regarded as optimization problems on the Stiefel and Grassmann manifolds and several geometric quantities of the problems are discussed to develop the Riemannian trust-region method. Numerical experiments show that the proposed methods can solve the H2 Optimal Model reduction problem effectively.
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CDC - Riemannian trust-region methods for H2 Optimal Model reduction
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Hiroyuki Sato, Kazuhiro SatoAbstract:In this paper, the Riemannian trust-region method for the H2 Optimal Model reduction problem is proposed. The problem is regarded as optimization problems on the Stiefel and Grassmann manifolds and several geometric quantities of the problems are discussed to develop the Riemannian trust-region method. Numerical experiments show that the proposed methods can solve the H2 Optimal Model reduction problem effectively.
Hiroyuki Sato - One of the best experts on this subject based on the ideXlab platform.
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A New H2 Optimal Model reduction method based on riemannian conjugate gradient method
2016 IEEE 55th Conference on Decision and Control (CDC), 2016Co-Authors: Hiroyuki Sato, Kazuhiro SatoAbstract:In this paper, a new optimization problem formulation of the H2 Optimal Model reduction problem is introduced and discussed. The optimization problem is shown to be a problem on a product manifold, which is a Riemannian submanifold of a Euclidean space. Geometry of the resultant optimization problem is investigated and the Riemannian conjugate gradient method for the problem is proposed. Solutions obtained by the proposed method realize stable reduced order systems if the original system satisfies a certain condition, which holds for example for dissipative systems. It is shown by numerical experiments that the proposed method is effective for large-scale problems.
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riemannian trust region methods for h2 Optimal Model reduction
Conference on Decision and Control, 2015Co-Authors: Hiroyuki Sato, Kazuhiro SatoAbstract:In this paper, the Riemannian trust-region method for the H2 Optimal Model reduction problem is proposed. The problem is regarded as optimization problems on the Stiefel and Grassmann manifolds and several geometric quantities of the problems are discussed to develop the Riemannian trust-region method. Numerical experiments show that the proposed methods can solve the H2 Optimal Model reduction problem effectively.
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CDC - Riemannian trust-region methods for H2 Optimal Model reduction
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Hiroyuki Sato, Kazuhiro SatoAbstract:In this paper, the Riemannian trust-region method for the H2 Optimal Model reduction problem is proposed. The problem is regarded as optimization problems on the Stiefel and Grassmann manifolds and several geometric quantities of the problems are discussed to develop the Riemannian trust-region method. Numerical experiments show that the proposed methods can solve the H2 Optimal Model reduction problem effectively.
D.p. Atherton - One of the best experts on this subject based on the ideXlab platform.
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An Optimal Model reduction method for linear systems
1991 American Control Conference, 1991Co-Authors: D.p. AthertonAbstract:An Optimal Model reduction method is proposed. The method can be used to reduce single-input singe-output stable systems. An optimization criterion is defined which minimise the weightd variance of the error function between the output of the original system and the reduced order one when subjected to the same input signal. The accuracy of the reduction is often significantly improved compared with the results of other methods.
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An Optimal Model reduction method for closed-loop systems
[1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1991Co-Authors: D.p. AthertonAbstract:An Optimal Model reduction method is presented for closed-loop systems. The procedure is an iterative one in that one endeavours to find the best reduced Model of a given order so that the difference in the responses of the original closed-loop system and the closed-loop system with the reduced-order Model is minimized. Optimal Model reduction algorithms for a feedback system and a nonlinear feedback system are developed and examined. Illustrative examples are given to show the advantages of the Optimal Model reduction method for closed-loop systems presented.
D. Kennedy - One of the best experts on this subject based on the ideXlab platform.
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Simultaneous stabilization with near Optimal Model reference tracking
Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), 2001Co-Authors: D. Miller, D. KennedyAbstract:We consider the use of linear time-varying controllers for simultaneous stabilization and performance. We prove that for every finite set of plants, we can design a linear time-varying controller which provides not only closed loop stability, but also near Optimal Model reference tracking.
Yisheng Zhong - One of the best experts on this subject based on the ideXlab platform.
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Optimal Model matching with disturbance rejection for the non-minimum phase plants
1997 IEEE 6th International Conference on Emerging Technologies and Factory Automation Proceedings EFTA '97, 1997Co-Authors: Xudong Wu, Yisheng ZhongAbstract:The design problem of Optimal (or perfect) Model matching control system with minimal weighted sensitivity to disturbance is considered in this paper. A system is said to achieve Optimal (or perfect) Model matching control if the system is internally stable and the H/sub /spl infin//-norm of the difference between its closed-loop transfer function and that of the reference plant is minimized (or zero). So, the design of an Optimal Model matching control system leads to an H/sub /spl infin//-optimization problem. A controller achieving Optimal Model matching control still has free design parameters, which can be utilized to reduce the effect of external disturbances. The disturbance rejection problem is transferred into another weighted optimization problem with constraints which come from the Optimal Model matching design. A new method is proposed to solve the resulting two coupled H/sub /spl infin//-optimization problems by interpolation method.
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Robust Optimal Model matching for the non-minimum phase plants
Proceedings of the 36th IEEE Conference on Decision and Control, 1997Co-Authors: Xudong Wu, Yisheng ZhongAbstract:Robust Optimal (or perfect) Model matching problem for the linear time-variant systems is dealt with in this paper. A two-degree of freedom controller is used. For the case of the nonminimum phase plants with multiplicative perturbations, the problem of robust stability of closed-loop system under the conditions of Optimal Model matching is transferred into a constrained H/sub /spl infin// optimization problem. A new method for determining parameters of the controller is given, which involves solving an H/sub /spl infin// interpolation problem.
