• Structural Engineering and Mechanics
• /
• v.12 no.1
• /
• pp.35-50
• /
• 2001

A numerical methodology is presented in this paper for the geometrically non-linear analysis of slender uni-dimensional structural elements under unilateral contact constraints. The finite element method together with an updated Lagrangian formulation is used to study the structural system. The unilateral constraints are imposed by tensionless supports or foundations. At each load step, in order to obtain the contact regions, the equilibrium equations are linearized and the contact problem is treated directly as a minimisation problem with inequality constraints, resulting in a linear complementarity problem (LCP). After the resulting LCP is solved by Lemke's pivoting algorithm, the contact regions are identified and the Newton-Raphson method is used together with path following methods to obtain the new contact forces and equilibrium configurations. The proposed methodology is illustrated by two examples and the results are compared with numerical and experimental results found in literature.

• Nuclear Engineering and Technology
• /
• v.16 no.4
• /
• pp.181-194
• /
• 1984

The in-core fuel management problem was studied by use of the calculus of variations. Two functions of interest to a public power utility, the profit function and the cost function, were subjected to the constraints of criticality, the reactor turnup equations and an inequality constraint on the maximum allowable power density. The variational solution of the initial profit rate demonstrated that there are two distinct regions of the reactor, a constant power region and a minimum inventory or flat thermal flux region. The transition point between these regions is dependent on the relative importance of the profit for generating power and the interest charges for the fuel. The fuel cycle cost function was then used to optimize a three equal volume region reactor with a constant fuel enrichment. The inequality constraint on the maximum allowable power density requires that the inequality become an equality constraint at some points in the reactor. and at all times throughout the core cycle. The finite difference equations for reactor criticality and fuel burnup in conjunction with the equality constraint on power density were solved, and the method of gradients was used to locate an optimum enrichment. The results of this calculation showed that standard non-linear optimization techniques can be used to optimize a reactor when the inequality constraints are properly applied.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.1
• /
• pp.11-15
• /
• 1999

In this paper, a robust pole placement controller for time invariant linear systems with polytopic uncertainties is presented. The proposed controller is a fixed order output feedback controller which stabilizes the uncertain systems and satisfies the constraints on the closed-loop pole location. The proposed controller can be obtained by minimizing a certain nonlinear object function subject to linear matrix inequality constraints. An algorithm for solving the nonlinear optimization problem is also proposed.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10b
• /
• pp.1655-1658
• /
• 1991

This paper considers the design and analysis of one-step ahead optimal and adaptive controllers, under the restriction that a known constraint on the input amplitude is imposed. It is assumed that the discrete-time single-input, single-output system to be controlled is linear, except for inequality constraints on the input. The objective function to be minimized is an one-step quadratic function, where polynomial weights on the input and output are included. Both the known parameter and unknown parameter (indirect adaptive controller) cases are examined.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.32 no.4
• /
• pp.121-127
• /
• 1983

In this paper an efficient algorithm for Pontriagin's maximum principle is developed. Fletcher-Powell method is adopted as optimization technique which shows fast and stable convergence characteristics. Terminal constraints are alse considered by using Hestens' algorithm and penalty function method together. Control variable inequality constraints are also considered by using Gradient Projection technique combined with Flectcher-Powell method. Test experiment shows good and reliable results.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.33 no.6
• /
• pp.241-246
• /
• 1984

The power system scheduling process is formulated as an optimization problem with linear inequality constraints. AC Loadflow method is used for the problem solution and line losses are considered. The constraints under consiceration are generator power limits, load schedding limits and line capacity limits. In solving the objective function the Dual Relaxation method is adopted. Tests indicate that the method is practical for real time applications.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.40 no.4
• /
• pp.251-263
• /
• 2003

This paper presents matrix inequality conditions for Η$_2$control and Η$_2$controller design method of linear time-invariant descriptor systems with parameter uncertainties in continuous and discrete time cases, respectively. First, the necessary and sufficient condition for Η$_2$control and Η$_2$ controller design method are expressed in terms of LMI(linear matrix inequality) with no equality constraints in continuous time case. Next, the sufficient condition for Hi control and Η$_2$controller design method are proposed by matrix inequality approach in discrete time case. Based on these conditions, we develop the robust Η$_2$controller design method for parameter uncertain descriptor systems and give a numerical example in each case.

• Transactions on Control, Automation and Systems Engineering
• /
• v.2 no.1
• /
• pp.31-39
• /
• 2000

We present a robust and reliable H$\infty$ state-feedback controller design for linear uncertain systems, which have norm-bounded time-varying uncertainty in the state matrix, and their prespecified sets of actuators are susceptible to failure. These controllers should guarantee robust stability of the systems and H$\infty$ norm bound against parameter uncertainty and/or actuator failures. Based on the linear matrix inequality (LMI) approach, two state-feedback controller design methods are constructed by formulating to a set of LMIs corresponding to all failure cases or a single LMI that covers all failure cases, with an additional costraint. Effectiveness and geometrical property of these controllers are validated via several numerical examples. Furthermore, the proposed LMI frameworks can be applied to multiobjective problems with additional constraints.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.05a
• /
• pp.436-439
• /
• 2005

Dynamic contact of a cantilever beam with Sap at the end is discussed. The gap in a structure induces dynamic contact, and the contact problem is always accompanied by inequality constraints which mean that the solution of the structure with contact condition should satisfy variational inequality. Inequality, but, can be reduced to equality condition considering convex penalty function. In this paper, formulation of a beam with contact is derived using quasi convex penalty function. General coordinate solution which is needed to increase computational efficiency is applied. Nonlinear behavior of a beam with rigid and elastic contact condition was discussed.

• Journal of Information Processing Systems
• /
• v.13 no.2
• /
• pp.417-427
• /
• 2017

Power allocation is an important factor for cognitive radio networks to achieve higher communication capacity and faster equilibrium. This paper considers power allocation problem to each cognitive user to maximize capacity of the cognitive systems subject to the constraints on the total power of each cognitive user and the interference levels of the primary user. Since this power control problem can be formulated as a mixed-integer nonlinear programming (NP) equivalent to variational inequality (VI) problem in convex polyhedron which can be transformed into complementary problem (CP), we utilize modified projection method to solve this CP problem instead of finding NP solution and give a power control allocation algorithm with a subcarrier allocation scheme. Simulation results show that the proposed algorithm performs well and effectively reduces the system power consumption with almost maximum capacity while achieve Nash equilibrium.