Chang-Hee Won

Reliability-based measures of structural control robustness

Abstract Because of the uncertainty inherent in engineering structures, consistent probabilistic stability/performance measures are essential to accurately assessing and comparing the robustness of structural control systems. An approach is presented herein for calculating such probabilistic measures for a controlled structure. First and second order reliability methods (FORM/SORM) are shown to be appropriate for the required calculations. The concepts are illustrated through several examples of seismically excited structures with active protective systems.

Comparative study of various control methods for attitude control of a LEO satellite

Abstract A nonlinear attitude model of a satellite with thrusters, gravity torquers and a reaction wheel cluster is developed. Then the linearized version of this satellite attitude model is derived for the attitude hold mode. For comparison purposes, various control methods are considered for attitude control of a satellite. We consider a proportional derivative controller which is actually used in the remote sensing satellite, KOMPSAT. Then a comparison is made with an H2 controller, an H∞ controller, and a mixed H 2 H ∞ controller. The analysis and numerical studies show that the proportional derivative controllers performance is limited in the sense that the pitch angle cannot approach zero. The simulations also show that among three control methods (H2 control, H∞ control, and mixed H2/H∞ control) H2 control has the fastest response time, H∞ control has the slowest and mixed H2/H∞ control has an intermediate value. On the other hand, H∞ control used least amount of control effort while H2 control required the most.

Topology Preserving Relaxation Labeling for Nonrigid Point Matching

This paper presents a relaxation labeling process with the newly defined compatibility measure for solving a general nonrigid point matching problem. In the literature, there exists a point matching method using relaxation labeling; however, the compatibility coefficient takes a binary value of zero or one depending on whether a point and a neighbor have corresponding points. Our approach generalizes this relaxation labeling method. The compatibility coefficient takes n-discrete values which measure the correlation between point pairs. In order to improve the speed of the algorithm, we use a diagram of log distance and polar angle bins to compute the correlation. The extensive experiments show that the proposed topology preserving relaxation algorithm significantly improves the matching performance compared to other state-of-the-art point matching algorithms.

Fast alignment using rotation vector and adaptive Kalman filter

A fast and convenient alignment method is proposed. To improve the speed of convergence, we used rotation vectors instead of traditional Euler angles. Furthermore, we developed an algorithm to automatically tune the measurement noise covariance matrix using adaptive Kalman filtering. Finally, the developed algorithms were applied to an aerial imaging system to automatically geo-locate the centers of the images.

Cumulants and Risk-Sensitive Control: A Cost Mean and Variance Theory with Application to Seismic Protection of Structures

The risk-sensitive optimal stochastic control problem is interpreted in terms of managing the value of linear combinations of the cumulants of a traditional performance index. The coefficients in these linear combinations are fixed, explicit functions of the risk parameter. This paper demonstrates the possibility of controlling linear combinations of index cumulants with broader opportunities to choose the coefficients. In view of the considerable interest given to cumulants in the theories of signal processing, detection, and estimation over the last decade, such an interpretation offers the possibility of new insights into the broad modern convergence of the concepts of robust control in general. Considered in detail are the foundations for a full-state-feedback solution to the problem of controlling the second cumulant of a cost function, given modest constraints on the first cumulant. The formulation is carried out for a class of nonlinear stochastic differential equations, associated with an appropriate class of nonquadratic performance indices. A Hamilton-Jacobi framework is adopted; and the defining equations for solving the linear, quadratic case are determined. The method is then applied to a situation in which a building is to be protected from earthquakes. Densities of the cost function are computed, so as to give insight into the question of how the first and second cumulants affect a cost considered as a random variable.

High-Resolution Tactile Imaging Sensor Using Total Internal Reflection and Nonrigid Pattern Matching Algorithm

A novel tactile imaging sensor, that is capable of measuring the elasticity of the touched object, is designed, implemented, and tested. In the proposed sensor, a multilayer Polydimethylsiloxane optical waveguide has been fabricated as the sensing probe. The light is illuminated at the critical angle to totally reflect within the flexible and transparent waveguide. When a waveguide is compressed by an object, the contact area of the waveguide deforms and causes the light to scatter. The scattered light is captured by a high-resolution camera. To find the elastic modulus of a touched object, multiple tactile images are taken from slightly different loading force values. The applied force has been estimated using the integrated pixel values of the tactile image. The strain has been estimated by matching the series of tactile images using the proposed nonrigid pattern matching algorithm. The measurement method was validated by the commercial soft polymer samples with the known elastic modulus. The experimental results showed that the tactile imaging sensor can measure the elastic modulus with the error less than 5.38%.

Regional navigation system using geosynchronous satellites and stratospheric airships

A methodology is proposed to design a regional navigation system using geosynchronous satellites and stratospheric airships. One important factor in designing a navigation system is dilution of precision (DOP). We design a regional navigation system based on the simulations of the systems DOP. The system would consist of geosynchronous orbit satellites (GSO) and stratospheric airships for the urban areas. In the beginning stage, the system would augment the existing GPS constellation, and in the later stage with sufficient satellites and airships, we could achieve an independent alternative navigation system.

Nonlinear n-th Cost Cumulant Control and Hamilton-Jacobi-Bellman Equations for Markov Diffusion Process

A general nonlinear stochastic system with non-quadratic cost function is considered for cost cumulant control of a Markov diffusion problem. The Hamilton-Jacobi-Bellman equation for the n-th cost moment case is derived as a necessary condition for optimality. The n-th cost cumulant Hamilton-Jacobi-Bellman equation derivation procedure is given. Second, third, and fourth cost cumulant Hamilton-Jacobi-Bellman equations are derived using the proposed procedure. The solutions of the nonlinear cost cumulant control problem is discussed using the state dependent Riccati equation method.

Fuel- or Time-Optimal Transfers Between Coplanar, Coaxial Ellipses Using Lambert' s Theorem

Undoubtedly, minimum-fuel and minimum-time orbit transfer are the two major goals of the optimal orbit maneuver. This paper considers two coplanar elliptic orbits when the apsidal lines coincide. We analytically e nd the conditions for the two-impulse minimum-time transfer orbit using Lambert’ s theorem. In the minimum-time transfer the transfer time is a decreasing function of a variable related to the transfer orbit’ s semimajor axis. Consequently there exists no unique minimum-time solution. Thus for the minimum-time case, there is a limiting solution only; however, there exists a unique solution in the case of minimum-fuel transfer, for which we e nd the necessary and sufe cient conditions. Furthermore, as a special case, we consider when the transfer angle is 180 deg. In thiscaseweshowthat weobtainthefuel-optimal Hohmann transfer orbit.Wealso derivetheHohmann transfer time and delta-velocity equations from more general equations, which are also obtained using Lambert’ s theorem. There is a tradeoff between minimum-time and minimum-fuel transfer. Finally, we propose an optimal coplanar orbit maneuver algorithm for trading off the minimum-time goal against the minimum-fuel goal.

Cumulants in risk-sensitive control: the full-state-feedback cost variance case

The risk-sensitive optimal stochastic control problem has an interpretation in terms of managing the value of a denumerable linear combination of the cumulants of a traditional performance index. This paper considers in detail the foundations for a full-state-feedback solution to the problem of controlling the second cumulant of a cost function, given modest constraints on the first cumulant. The formulation is carried out for a class of nonlinear stochastic differential equations, associated with an appropriate class of non-quadratic performance indices. A Hamilton-Jacobi framework is adopted, and the defining equations for solving the linear, quadratic case are determined. The method is then applied to a situation in which a building is to be protected from earthquakes.