The evenly convex hull of a given set is the intersection of all the open halfspaces which contain such set (hence the convex hull is contained in the evenly convex hull). This paper deals with finite dimensional line...
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The evenly convex hull of a given set is the intersection of all the open halfspaces which contain such set (hence the convex hull is contained in the evenly convex hull). This paper deals with finite dimensional linear systems containing strict inequalities and (possibly) weak inequalities as well as equalities. The number of inequalities and equalities in these systems is arbitrary (possibly infinite). For such kind of systems a consistency theorem is provided and those strict inequalities (weak inequalities, equalities) which are satisfied for every solution of a given system are characterized. Such results are formulated in terms of the evenly convex hull of certain sets which depend on the coefficients of the system. (c) 2005 Elsevier B.V. All rights reserved.
The evenly convex hull of a given set is the intersection of all the open halfspaces which contain such set (hence the convex hull is contained in the evenly convex hull). This paper deals with finite dimensional line...
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The evenly convex hull of a given set is the intersection of all the open halfspaces which contain such set (hence the convex hull is contained in the evenly convex hull). This paper deals with finite dimensional linear systems containing strict inequalities and (possibly) weak inequalities as well as equalities. The number of inequalities and equalities in these systems is arbitrary (possibly infinite). For such kind of systems a consistency theorem is provided and those strict inequalities (weak inequalities, equalities) which are satisfied for every solution of a given system are characterized. Such results are formulated in terms of the evenly convex hull of certain sets which depend on the coefficients of the system. (c) 2005 Elsevier B.V. All rights reserved.
A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most resu...
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A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most results for .E-convex functions and E-convex programming in [1] are not true by six counter examples.
This paper considers optimization of rotor system design using stability and vibration response criteria. The initial premise of the study is that the effect of certain design changes can be parametrized in a rotor dy...
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This paper considers optimization of rotor system design using stability and vibration response criteria. The initial premise of the study is that the effect of certain design changes can be parametrized in a rotor dynamic model through their influence on the system matrices obtained by finite element modeling. A suitable vibration response measure is derived by considering an unknown,axial distribution of unbalanced components having bounded magnitude. It is shown that the worst-case unbalanced response is given by an absolute row-sum norm of the system frequency response matrix. The minimization of this norm is treated through the formulation of a set of linear matrix inequalities that can also incorporate design parameter constraints and stability criteria. The formulation can also be extended to cover uncertain or time-varying system dynamics arising, for example, due to speed-dependent bearing coefficients or gyroscopic effects. Numerical solution of the matrix inequalities is tackled using an iterative method that involves standard. convex optimization routines. The method is applied in a case study that considers the optimal selection of bearing support stiffness and damping levels to minimize the worst-case vibration of a flexible rotor over a finite speed range. The main restriction in the application of the method is found to be the slow convergence of the numerical routines that occurs with high-order models and/or high problem complexity.
Generalized Disjunctive programming (GDP) has been introduced recently as an alternative to mixed-integer programming for representing discrete/continuous optimization problems. The basic idea of GDP consists of repre...
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Generalized Disjunctive programming (GDP) has been introduced recently as an alternative to mixed-integer programming for representing discrete/continuous optimization problems. The basic idea of GDP consists of representing these problems in terms of sets of disjunctions in the continuous space, and logic propositions in terms of Boolean variables. In this paper we consider GDP problems involving convex nonlinear inequalities in the disjunctions. Based on the work by Stubbs and Mehrotra [ 21] and Ceria and Soares [ 6], we propose a convex nonlinear relaxation of the nonlinear convex GDP problem that relies on the convex hull of each of the disjunctions that is obtained by variable disaggregation and reformulation of the inequalities. The proposed nonlinear relaxation is used to formulate the GDP problem as a Mixed-Integer Nonlinear programming (MINLP) problem that is shown to be tighter than the conventional "big-M" formulation. A disjunctive branch and bound method is also presented, and numerical results are given for a set of test problems.
In this paper, a method is proposed for synthesizing sets of stabilizing controllers of strictly proper, delay-free, Single Input, Single Output Linear Time Invariant (LTI) plants directly from their empirical frequen...
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In this paper, a method is proposed for synthesizing sets of stabilizing controllers of strictly proper, delay-free, Single Input, Single Output Linear Time Invariant (LTI) plants directly from their empirical frequency response data and from some coarse information about them. The coarse information that is required is the following: the number of non minimum phase zeros of the plant and the frequency range beyond which the phase response of the LTI plant does not change appreciably and the amplitude response goes to zero. It is assumed that the LTI plant does not have purely imaginary zeros or poles. The method of synthesizing stabilizing controllers involves the use of generalized Hermite-Biehler theorem for rational functions for counting the roots and the use of recently developed Sum-of- Squares techniques for checking the non-negativity of a polynomial in an interval through the Markov-Lucaks theorem. The method does not require an explicit analytical model of the plant that must be stabilized or the order of the plant, rather, it only requires an empirical frequency response data of the plant. The method also allows for measurement errors in the frequency response of the plant.
Projection type neural network for optimization problems has advantages over other networks for fewer parameters , low searching space dimension and simple structure. In this paper, by properly constructing a Lyapunov...
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Projection type neural network for optimization problems has advantages over other networks for fewer parameters , low searching space dimension and simple structure. In this paper, by properly constructing a Lyapunov energy function, we have proven the global convergence of this network when being used to optimize a continuously differentiable convex function defined on a closed convex set. The result settles the extensive applicability of the network. Several numerical examples are given to verify the efficiency of the network.
Numerous controllers have been proposed based on linear Hill's equations for satellite formation control. To date, most of these controllers assumed that the system model is well defined, and the disturbances are ...
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ISBN:
(纸本)0780393953
Numerous controllers have been proposed based on linear Hill's equations for satellite formation control. To date, most of these controllers assumed that the system model is well defined, and the disturbances are small. Previous studies have failed to consider the problem of disturbance rejection. In this paper, H/sub /spl infin// controllers are designed for disturbance attenuation based on linear Hill's equations. The goal is to design a state-feedback control law which minimizes the H/sub /spl infin// norm of transfer function from disturbance to the regulated outputs, which guarantee stable for the closed-loop system. The problem is reduced to a convex optimization involving linear matrix inequalities (LMIs). The proposed robust controllers are evaluated in simulation. The simulation results demonstrate that the proposed controllers are capable of controlling the satellite formation system more precisely than LQR under various perturbations.
This paper investigates the problem of stabilization for a Takagi-Sugeno (T-S) fuzzy system with nonuniform uncertain sampling. The sampling is not required to be periodic, and the only assumption is that the distance...
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ISBN:
(纸本)0780393953
This paper investigates the problem of stabilization for a Takagi-Sugeno (T-S) fuzzy system with nonuniform uncertain sampling. The sampling is not required to be periodic, and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound. By using the input delay approach, the T-S fuzzy system with variable uncertain sampling is transformed into a continuous-time T-S fuzzy system with a delay in the state. A new condition guaranteeing asymptotic stability of the closed-loop sampled-data system is derived by a Lyapunov approach plus the free weighting matrix technique. Based on this stability condition, two procedures for designing state-feedback control laws are given: one casts the controller design into a convex optimization by introducing some over design, and the other utilizes the cone complementarity linearization (CCL) idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality (LMI) constraints, which can be readily solved using standard numerical software.
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