Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

Robust filtering and smoothing with gaussian processes

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of system identification is more robust than finding point estimates of a parametric function representation. Our principled filtering/smoothing approach for GP dynamic systems is based on analytic moment matching in the context of the forward-backward algorithm. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail. © 2011 IEEE.

Path-following steering control for articulated vehicles

Passive steering systems have been used for some years to control the steering of trailer axles on articulated vehicles. These normally use a 'command steer' control strategy, which is designed to work well in steady-state circles at low speeds, but which generates inappropriate steer angles during transient low-speed maneuvers and at high speeds. In this paper, 'active' steering control strategies are developed for articulated heavy goods vehicles. These aim to achieve accurate path following for tractor and trailer, for all paths and all normal vehicle speeds, in the presence of external disturbances. Controllers are designed to implement the path-following strategies at low and high speeds, whilst taking into account the complexities and practicalities of articulated vehicles. At low speeds, the articulation and steer angles on articulated heavy goods vehicles are large and small-angle approximations are not appropriate. Hence, nonlinear controllers based on kinematics are required. But at high-speeds, the dynamic stability of control system is compromised if the kinematics-based controllers remain active. This is because a key state of the system, the side-slip characteristics of the trailer, exhibits a sign-change with increasing speeds. The low and high speed controllers are blended together using a speed-dependent gain, in the intermediate speed range. Simulations are conducted to compare the performance of the new steering controllers with conventional vehicles (with unsteered drive and trailer axles) and with vehicles with command steer controllers on their trailer axles. The simulations show that active steering has the potential to improve significantly the directional performance of articulated vehicles for a wide range of conditions, throughout the speed range. © VC 2013 by ASME.

Minimum maneuver time calculation using convex optimization

The problem of calculating the minimum lap or maneuver time of a nonlinear vehicle, which is linearized at each time step, is formulated as a convex optimization problem. The formulation provides an alternative to previously used quasi-steady-state analysis or nonlinear optimization. Key steps are: the use of model predictive control; expressing the minimum time problem as one of maximizing distance traveled along the track centerline; and linearizing the track and vehicle trajectories by expressing them as small displacements from a fixed reference. A consequence of linearizing the vehicle dynamics is that nonoptimal steering control action can be generated, but attention to the constraints and the cost function minimizes the effect. Optimal control actions and vehicle responses for a 90 deg bend are presented and compared to the nonconvex nonlinear programming solution. Copyright © 2013 by ASME.

An adaptive controller for a class of nonlinear system using direction basis function

For a class of nonlinear dynamical systems, the adaptive controllers are investigated using direction basis function (DBF) in this paper. Based on the criterion of Lyapunov' stability, DBF is designed which guarantees that the output of the controlled system asymptotically tracks the reference signals. Finally, the simulation shows the good tracking effectiveness of the adaptive controller.

Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

This paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.

Control of Vibration in Mechanical Systems Using Shaped Reference Inputs

Dynamic systems which undergo rapid motion can excite natural frequencies that lead to residual vibration at the end of motion. This work presents a method to shape force profiles that reduce excitation energy at the natural frequencies in order to reduce residual vibration for fast moves. Such profiles are developed using a ramped sinusoid function and its harmonics, choosing coefficients to reduce spectral energy at the natural frequencies of the system. To improve robustness with respect to parameter uncertainty, spectral energy is reduced for a range of frequencies surrounding the nominal natural frequency. An additional set of versine profiles are also constructed to permit motion at constant speed for velocity-limited systems. These shaped force profiles are incorporated into a simple closed-loop system with position and velocity feedback. The force input is doubly integrated to generate a shaped position reference for the controller to follow. This control scheme is evaluated on the MIT Cartesian Robot. The shaped inputs generate motions with minimum residual vibration when actuator saturation is avoided. Feedback control compensates for the effect of friction Using only a knowledge of the natural frequencies of the system to shape the force inputs, vibration can also be attenuated in modes which vibrate in directions other than the motion direction. When moving several axes, the use of shaped inputs allows minimum residual vibration even when the natural frequencies are dynamically changing by a limited amount.

Towards a situation-awareness-driven design of operational business intelligence & analytics systems

With the swamping and timeliness of data in the organizational context, the decision maker’s choice of an appropriate decision alternative in a given situation is defied. In particular, operational actors are facing the challenge to meet business-critical decisions in a short time and at high frequency. The construct of Situation Awareness (SA) has been established in cognitive psychology as a valid basis for understanding the behavior and decision making of human beings in complex and dynamic systems. SA gives decision makers the possibility to make informed, time-critical decisions and thereby improve the performance of the respective business process. This research paper leverages SA as starting point for a design science project for Operational Business Intelligence and Analytics systems and suggests a first version of design principles.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

A Fractional Perspective to the Bond Graph Modelling of World Economies

Inspired in dynamic systems theory and Brewer’s contributions to apply it to economics, this paper establishes a bond graph model. Two main variables, a set of inter-connectivities based on nodes and links (bonds) and a fractional order dynamical perspective, prove to be a good macro-economic representation of countries’ potential performance in nowadays globalization. The estimations based on time series for 50 countries throughout the last 50 decades confirm the accuracy of the model and the importance of scale for economic performance.

Estimating Nonlinear DSGE Models by the Simulated Method of Moments

This paper studies the application of the simulated method of moments (SMM) for the estimation of nonlinear dynamic stochastic general equilibrium (DSGE) models. Monte Carlo analysis is employed to examine the small-sample properties of SMM in specifications with different curvature. Results show that SMM is computationally efficient and delivers accurate estimates, even when the simulated series are relatively short. However, asymptotic standard errors tend to overstate the actual variability of the estimates and, consequently, statistical inference is conservative. A simple strategy to incorporate priors in a method of moments context is proposed. An empirical application to the macroeconomic effects of rare events indicates that negatively skewed productivity shocks induce agents to accumulate additional capital and can endogenously generate asymmetric business cycles.

Nonlinear Dynamics of Semiconductor LasersControl and Synchronization of Chaos:

Nonlinear dynamics of laser systems has become an interesting area of research in recent times. Lasers are good examples of nonlinear dissipative systems showing many kinds of nonlinear phenomena such as chaos, multistability and quasiperiodicity. The study of these phenomena in lasers has fundamental scientific importance since the investigations on these effects reveal many interesting features of nonlinear effects in practical systems. Further, the understanding of the instabilities in lasers is helpful in detecting and controlling such effects. Chaos is one of the most interesting phenomena shown by nonlinear deterministic systems. It is found that, like many nonlinear dissipative systems, lasers also show chaos for certain ranges of parameters. Many investigations on laser chaos have been done in the last two decades. The earlier studies in this field were concentrated on the dynamical aspects of laser chaos. However, recent developments in this area mainly belong to the control and synchronization of chaos. A number of attempts have been reported in controlling or suppressing chaos in lasers since lasers are the practical systems aimed to operated in stable or periodic mode. On the other hand, laser chaos has been found to be applicable in high speed secure communication based on synchronization of chaos. Thus, chaos in laser systems has technological importance also. Semiconductor lasers are most applicable in the fields of optical communications among various kinds of laser due to many reasons such as their compactness, reliability modest cost and the opportunity of direct current modulation. They show chaos and other instabilities under various physical conditions such as direct modulation and optical or optoelectronic feedback. It is desirable for semiconductor lasers to have stable and regular operation. Thus, the understanding of chaos and other instabilities in semiconductor lasers and their xi control is highly important in photonics. We address the problem of controlling chaos produced by direct modulation of laser diodes. We consider the delay feedback control methods for this purpose and study their performance using numerical simulation. Besides the control of chaos, control of other nonlinear effects such as quasiperiodicity and bistability using delay feedback methods are also investigated. A number of secure communication schemes based on synchronization of chaos semiconductor lasers have been successfully demonstrated theoretically and experimentally. The current investigations in these field include the study of practical issues on the implementations of such encryption schemes. We theoretically study the issues such as channel delay, phase mismatch and frequency detuning on the synchronization of chaos in directly modulated laser diodes. It would be helpful for designing and implementing chaotic encryption schemes using synchronization of chaos in modulated semiconductor laser

Robust fault detection using consistency techniques for uncertainty handling

Often practical performance of analytical redundancy for fault detection and diagnosis is decreased by uncertainties prevailing not only in the system model, but also in the measurements. In this paper, the problem of fault detection is stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem can be solved using modal interval analysis and consistency techniques. Consistency techniques are then shown to be particularly efficient to check the consistency of the analytical redundancy relations (ARRs), dealing with uncertain measurements and parameters. Through the work presented in this paper, it can be observed that consistency techniques can be used to increase the performance of a robust fault detection tool, which is based on interval arithmetic. The proposed method is illustrated using a nonlinear dynamic model of a hydraulic system