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Quadratic Constraints (quadratic + constraint)
Selected AbstractsUpper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loadingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009J. J. Muńoz Abstract Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for Von Mises and Mohr,Coulomb plasticity criteria are written as a set of quadratic constraints, which permits one to solve the optimization problem using specific algorithms for Second-Order Conic Program (SOCP). From the stress field at the lower bound and the velocities at the upper bound, we construct a novel error estimate based on elemental and edge contributions to the bound gap. These contributions are employed in an adaptive remeshing strategy that is able to reproduce fan-type mesh patterns around points with discontinuous surface loading. The solution of this type of problems is analysed in detail, and from this study some additional meshing strategies are also described. We particularise the resulting formulation and strategies to two-dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature. Copyright © 2008 John Wiley & Sons, Ltd. [source] Robust ,2 -gain feedforward control of uncertain systems using dynamic IQCsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2009I. E. Köse Abstract We consider the problem of robust ,2 -gain disturbance feedforward control for uncertain systems described in the standard LFT form. We use integral quadratic constraints (IQCs) for describing the uncertainty blocks in the system. For technical reasons related to the feedforward problem, throughout the paper, we work with the duals of the constraints involved in robustness analysis using IQCs. We obtain a convex solution to the problem using a state-space characterization of nominal stability that we have developed recently. Specifically, our solution consists of LMI conditions for the existence of a feedforward controller that guarantees a given ,2 -gain for the closed-loop system. We demonstrate the effectiveness of using dynamic IQCs in robust feedforward design through a numerical example. Copyright © 2008 John Wiley & Sons, Ltd. [source] New IQC for quasi-concave nonlinearitiesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2001Alexandre Megretski Abstract A new set of integral quadratic constraints (IQC) is derived for a class of ,rate limiters', modelled as a series connections of saturation-like memoryless nonlinearities followed by integrators. The result, when used within the standard IQC framework (in particular, with finite gain/passivity-based argiments, Lyapunov theory, structured singular values, etc.), is expected to be widely useful in nonlinear system analysis. For example, it enables ,discrimination' between ,saturation-like' and ,deadzone-like' nonlinearities and can be used to prove stability of systems with saturation in cases when replacing the saturation block by another memoryless nonlinearity with equivalent slope restrictions makes the whole system unstable. In particular, it is shown that the L2 gain of a unity feedback system with a rate limiter in the forward loop cannot exceed \sqrt{2}. In addition, a new, more flexible version of the general IQC analysis framework is presented, which relaxes the homotopy and boundedness conditions, and is more aligned with the language of the emerging IQC software. Copyright © 2001 John Wiley & Sons, Ltd. [source] A smoothing Newton's method for the construction of a damped vibrating system from noisy test eigendataNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2009Zheng-Jian Bai Abstract In this paper we consider an inverse problem for a damped vibration system from the noisy measured eigendata, where the mass, damping, and stiffness matrices are all symmetric positive-definite matrices with the mass matrix being diagonal and the damping and stiffness matrices being tridiagonal. To take into consideration the noise in the data, the problem is formulated as a convex optimization problem involving quadratic constraints on the unknown mass, damping, and stiffness parameters. Then we propose a smoothing Newton-type algorithm for the optimization problem, which improves a pre-existing estimate of a solution to the inverse problem. We show that the proposed method converges both globally and quadratically. Numerical examples are also given to demonstrate the efficiency of our method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Robust H, control of an uncertain system via a strict bounded real output feedback controllerOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2009Ian R. Petersen Abstract This paper presents a new approach to the robust H, control of an uncertain system via an output feedback controller that is both stable and has an H, norm strictly less than a specified value. The uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints. The controller is designed to achieve absolute stabilization with a specified level of disturbance attenuation. The main result involves solving a state feedback version of the problem by solving an algebraic Riccati equation dependent on a set of scaling parameters. Then two further algebraic Riccati equations are solved, which depend on a further set of scaling parameters. The required controller is constructed from the Riccati solutions. 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