Distributed Optimization by Network Flows With Spatio-Temporal Compression

: The Commanding General, Marine Corps Combat Development Command (MCCDC) asked the Center for Naval Analyses to assess the general applicability of the new science to land warfare. New Sciences is a catch-all phrase that refers to the tools and methodologies used in nonlinear dynamics and complex systems theory to study physical dynamical systems exhibiting a complicated dynamics. This report concludes that the concepts, ideas, theories, tools and general methodologies of nonlinear dynamics and complex systems theory show enormous, almost unlimited, potential for not just providing better solutions for certain existing problems of land combat, but for fundamentally altering our general understanding of the basic processes of war, at all levels. Indeed, the new sciences' greatest legacy may, in the end, prove to be not just a set of creative answers to old questions but and entirely new set of questions to be asked of what really happens on the battlefield The central thesis of this paper is that land combat is a complex adaptive system. That is to say, that land combat is essentially a nonlinear dynamical system composed of many interacting semi-autonomous and hierarchically organized agents continuously adapting to a changing environment.

In today’s competitive business environment, organizations are being challenged to improve performance by improving processes, minimizing costs, and increasing output. Such changes can only be made by looking beyond traditional management systems. Continuous improvement (CI) and total quality management (TQM) have been the focus of recent quality improvement initiatives. However, in many ways, the results have not been as dramatic as desired. Business process reengineering (BPR) focuses on innovation and creativity in redesigning processes in an effort to meet customers’ needs and expectations. Experience using nonlinear systems theory in applied health care settings has revealed that nonlinear science does offer a practical new frame of reference for BPR initiatives. This article describes why radically different approaches are necessary to sustain continued quality improvement, provides the key practical insights offered by nonlinear systems theory, and provides a clinical example of multidimensional thinking as applied in an acute care setting.

Wireless Sensor Networks (WSN) are often deployed to sample the desired environmental attributes and deliver the acquired samples to the sink for processing, analysis or simulations as per the application needs. Many applications stipulate high granularity and data accuracy that results in high data volumes. Sensor nodes are battery powered and sending the requested large amount of data rapidly depletes their energy. Fortunately, the environmental attributes (e.g., temperature, pressure) often exhibit spatial and temporal correlations. Moreover, a large class of applications such as scientific measurement and forensics tolerate high latencies for sensor data collection. Accordingly, we develop a fully distributed adaptive technique for spatial and temporal in-network data compression with accuracy guarantees. We exploit the spatio-temporal correlation of sensor readings while benefiting from possible data delivery latency tolerance to further minimize the amount of data to be transported to the sink. Using real data, we demonstrate that our proposed scheme can provide significant communication/energy savings without sacrificing the accuracy of collected data. In our simulations, we achieved data compression of up to 95% on the raw data requiring around 5% of the original data to be transported to the sink.

In nonlinear systems theory, the flatness property refers to the ability for dynamical systems of being exactly linearized via endogenous feedback. A system satisfying the flatness property is called a differentially flat system. The main attribute of flat systems is that the state and input variables can be directly expressed without integrating any differential equation, in terms of one particular set of variables called a flat output and a finite number of its derivatives. Through the d’Alembert method, the differential flatness property of the drilling system described by a pair of wave equations subject to Newton-like nonlinear boundary conditions is proved in this chapter. It is worthy of mention that the flatness property of a nonlinear dynamical system is useful to deal with trajectory tracking problems. Based on the idea that the elimination of drilling vibrations requires the angular and axial velocities of the drilling bit to follow a constant reference path, a pair of controllers aimed at tackling the steering problem is designed. Simulation results show that the flatness-based feedback controllers, allowing an exponential convergence of the system trajectories, accurately eliminate the stick-slip and bit-bounce drilling vibrations.KeywordsDifferential flatnessTrajectory tracking problemDrilling system flatness propertyFlatness-based drilling vibration control.

Network flow control under capacity constraints: A case study

Simulated annealing (SA) is a generic optimization method that is quite popular because of its ease of implementation and its global convergence properties. However, SA is widely reported to converge very slowly, and it is common practice to allow extra freedom in its design at the expense of losing global convergence guarantees. A natural way to increase the flexibility of SA is to allow the objective function and the communication mechanism to be temperature-dependent, the idea being to gradually reveal the complexity of the optimization problem and to increase the mixing rate at low temperatures. We call this general class of annealing processes stochastic continuation (SC). In the first part of this paper, we introduce SC starting from SA, and we derive simple sufficient conditions for the global convergence of SC. Our main result is interesting in two respects: first, the conditions for global convergence are surprisingly weak--in particular, they do not involve the variations of the objective function with temperature--and second, exponential cooling makes it possible to be arbitrarily close to the best possible convergence speed exponent of SA. The second part is devoted to the application of SC to the problem of producing aesthetically pleasing drawings of undirected graphs. We consider the objective function defined by Kamada and Kawai (Inf Process Lett 31(1):7---15, 1989), which measures the quality of a drawing as a weighted sum of squared differences between Euclidean and graph-theoretic inter-vertex distances. Our experiments show that SC outperforms SA with optimal communication setting both in terms of minimizing the objective function and in terms of standard aesthetic criteria.

Continuous flow synthesis and applications of carbon dots: a mini-review

Theory of nonlinear systems

Exact linearization is a traditional method for nonlinear system in the nonlinear system theory, the basic idea of which is to linearize the whole or parts of a nonlinear system using nonlinear coordinate transformation and nonlinear state feedback method. The input-output relationship of the nonlinear system can be represented by a linearized model which can be built using linear system design method. In order to enhance the robustness of an established system which has been linearized via feedback method, the robust control strategy should be adopted. As a result, the control law is composed of feedback linearization control and robust control. Sliding mode variable structure control is a robust control method which is proposed in this paper as a robust control strategy for the exact linearization system.

Analysis of heart rate (HR) variability has become an important widely used method for assessing cardiac autonomic regulation. Conventionally, HR variability has been analyzed with time and frequency domain methods. Analysis of HR dynamics by methods based on nonlinear systems theory has opened a novel approach for studying the abnormalities in HR behavior. Recent studies have shown that these measures, particularly scaling analysis methods of HR dynamics, are altered among various patients populations with cardiovascular diseases, and they provide prognostic information. Altered long-term scaling properties of HR dynamics and more random short-term HR fluctuation has been observed, e.g., among patients with previous myocardial infarction, and these alterations have been shown to be associated with increased mortality rate. A relatively large body of data indicate that altered scaling properties of R-R intervals are physiologically deleterious. These findings support the notion that some nonlinear methods, such as scaling and complexity measures, give clinically valuable information for risk stratification among various patient populations. This article provides a review of our current knowledge of the usefulness of dynamical measures of HR fluctuation.

The term “linear quadratic problem” refers to the problems of dynamics where linear controlled systems are associated with a certain quadratic functional of performance. “Linear” approaches are the approaches that are usually applied to linear systems, e.g. the methods of the integral transforms (Laplace, Fourier), the linear functional analysis and the frequency domain methods. The paper considers some cases where these approaches are applied to nonlinear systems.

Efficient eigenvalue assignments for general linear MIMO systems

A power system is a dynamic system that includes several kinds of nonlinear elements. According to nonlinear analyses using the Hopf bifurcation theory, it is detected that a limit cycle exists around an operating point, which may affect the stability of the power system significantly. This paper presents a numerical method to analyze the nonlinear characteristics in power systems by observing the power swing after some perturbation where the coefficients of nonlinear terms are determined by the least mean square method. The effectiveness of the proposed method is confirmed through some numerical analyses. The method is used to evaluate the transient stability. The result shows that the region of stability is occasionally narrower than the region evaluated by the classical method. © 2000 Scripta Technica, Electr Eng Jpn, 134(3): 16–25, 2001

138 Stability of Fuzzy control systems by using nonlinear system theory

In this paper, the problem of controlling the relative pose between a robot camera and a rigid object of interest is solved using nonlinear system theory. The camera-object visual interaction model is derived in the state space form in terms of image points. Then it is shown that the image-based visual system is completely controllable. Moreover, as a consequence of nonlinear controllability, global uniform asymptotic stability of the image reference set-point is formally proved using Lyapunov's direct method. Active contours are used to track the 2-D projection of the visible object's surface in the image plane, and 3-D estimation procedure based on prediction errors is used to cope with the unknown depth of the object. Experimental results with a 6-DOF robot manipulator endowed with a camera on its wrist validate the framework.