There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The simultaneous localization and map building (SLAM) problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle location. Starting from estimation-theoretic foundations of this problem, the paper proves that a solution to the SLAM problem is indeed possible. The underlying structure of the SLAM problem is first elucidated. A proof that the estimated map converges monotonically to a relative map with zero uncertainty is then developed. It is then shown that the absolute accuracy of the map and the vehicle location reach a lower bound defined only by the initial vehicle uncertainty. Together, these results show that it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and, using relative observations only, incrementally build a perfect map of the world and to compute simultaneously a bounded estimate of vehicle location. The paper also describes a substantial implementation of the SLAM algorithm on a vehicle operating in an outdoor environment using millimeter-wave radar to provide relative map observations. This implementation is used to demonstrate how some key issues such as map management and data association can be handled in a practical environment. The results obtained are cross-compared with absolute locations of the map landmarks obtained by surveying. In conclusion, the paper discusses a number of key issues raised by the solution to the SLAM problem including suboptimal map-building algorithms and map management.

/pdf/a-solution-to-the-simultaneous-localization-and-map-building-2pp3i7uhdj.pdf

A solution to the simultaneous localization and map building (SLAM) problem

Evaluation of hybrid Bayesian networks using analytical density representations

In this paper, we consider infinite-horizon networked LQG control over multipurpose networks that do not provide acknowledgments (UDP-like networks). The information communicated over the network experiences transmission delays and losses that are modeled as stochastic processes. In oder to mitigate the delays and losses in the controller-actuator channel, the controller transmits sequences of predicted control inputs in addition to the current control input. To be able to reduce the impact of delays and losses in the feedback channel, the estimator computes the estimate using the M last measurements. In this scenario, the separation principle does not hold and the optimal control law is in general nonlinear. However, we show that by restricting the controller and the estimator to linear systems with constant gains, we can find the optimal solution. The presented control law is demonstrated in a numerical example.

Infinite-horizon sequence-based networked control without acknowledgments

Model identification and measurement acquisition is always to some degree uncertain. Therefore, a framework for nonlinear model predictive control (NMPC) is proposed that explicitly considers the noise influence on nonlinear dynamic systems with continuous state spaces and a finite set of control inputs in order to significantly increase the control quality. Integral parts of NMPC are the prediction of system states over a finite horizon as well as the problem specific modeling of reward functions. For achieving an efficient and also accurate state prediction, the introduced framework uses transition densities approximated by means of axis-aligned Gaussian mixtures. The representation power of Gaussian mixtures is also used to model versatile reward functions. Thus, together with the prediction technique a closed-form calculation of the optimization problems arising from NMPC is possible. Additionally, an efficient algorithm for calculating an approximate value function of the corresponding optimal control problem employing dynamic programming is presented. Thus, the value function can be calculated off-line, which reduces the on-line computational burden significantly and also permits the use of long optimization horizons. The capabilities of the framework and especially the benefits that can be gained by incorporating the noise in the controller are illustrated by the example of a two-wheeled differential-drive mobile robot following a given path.

/pdf/efficient-control-of-nonlinear-noise-corrupted-systems-using-1s36gon0rp.pdf

Efficient Control of Nonlinear Noise-Corrupted Systems Using a Novel Model Predictive Control Framework

Extended range telepresence allows a human user to intuitively teleoperate a mobile robot through arbitrarily large remote environments by natural walking. In order to give the user the possibility to navigate the robot through an arbitrarily large remote environments, while his own environment is of limited size, Motion Compression is used. The Motion Compression framework provides a nonlinear transformation between the user's path and the robot's path, which preserves path length and turning angles. There is, however, a difference in path curvature, which is minimized in order to guarantee a high degree of immersion. A major drawback of the current system is its inability to deal with non-convex time-variant environments or environments shared by multiple users. This paper presents a systematic approach to extending Motion Compression to non-convex environments. This solution will then be used to cover the multi-user case.

/pdf/simultaneous-motion-compression-for-multi-user-extended-5bzlgvddy0.pdf

Simultaneous Motion Compression for Multi-User Extended Range Telepresence

In this paper, an approach to the finite-horizon optimal state-feedback control problem of nonlinear, stochastic. discrete-time systems is presented. Starting from the dynamic programming equation, the value function will be approximated by means of Taylor series expansion up to second-order derivatives. Moreover, the problem will be reformulated, such that a minimum principle can be applied to the stochastic problem. Employing this minimum principle, the optimal control problem can be rewritten as a two-point boundary-value problem to be solved at each time step of a shrinking horizon. To avoid numerical problems, the two-point boundary-value problem will be solved by means of a continuation method. Thus, the curse of dimensionality of dynamic programming is avoided, and good candidates for the optimal state-feedback controls are obtained. The proposed approach will be evaluated by means of a scalar example system.

/pdf/finite-horizon-optimal-state-feedback-control-of-nonlinear-3m0i3vh86z.pdf

Uwe D. Hanebeck

Papers

Evaluation of hybrid Bayesian networks using analytical density representations

Infinite-horizon sequence-based networked control without acknowledgments

Efficient Control of Nonlinear Noise-Corrupted Systems Using a Novel Model Predictive Control Framework

Simultaneous Motion Compression for Multi-User Extended Range Telepresence

Finite-Horizon Optimal State-Feedback Control of Nonlinear Stochastic Systems Based on a Minimum Principle