Computational Diagnostics of Jacobi Unstable Dynamical Systems with the Use of Hybrid Algorithms of Global Optimization

2021 ◽  
pp. 40-56
Author(s):  
P.M. Shkapov ◽  
A.V. Sulimov ◽  
V.D. Sulimov
Keyword(s):  
Inverse Problem ◽  
Dynamical Systems ◽  
Global Solutions ◽  
Hybrid Algorithms ◽  
Optimization Approach ◽  
Learning Mechanisms ◽  
Practical Applications ◽  
Scanning Procedure ◽  
Criterion Functions ◽  
Computational Diagnostics

The study focuses on the problems of restoration and analysis of free parameters of dynamical systems from indirect, approximately given information. In the context of the Kosambi --- Cartan --- Chern theory, a geometric description of the time-evolution of the system is introduced. Five geometric invariants are determined for the system under study. The eigenvalues of the second invariant estimate the Jacobi stability of the system. Such a study is of interest in practical applications, where it is required to identify the regions in which both Lyapunov stability and Jacobi stability occur simultaneously. The inverse problem of computational diagnostics of the system is formulated for approximately given eigenvalues of the second invariant. The solution to the regularized inverse problem is determined using an optimization approach. Scalar criterion functions are assumed to be continuous, multidimensional, locally Lipschitzian, and not necessarily everywhere differentiable. When searching for global solutions, we used new hybrid algorithms that integrate stochastic algorithms for scanning the space of variables and a deterministic local minimization procedure. The numerical scanning procedure is implemented with the use of two modified versions: quasi-opposition-based and rotation-based learning mechanisms. In the phase of local search, two-parameter smoothing approximations of criterion functions are introduced. Examples of solving problems of computational diagnostics of Jacobi unstable dynamical systems are given: the Lorentz system and a controllable elliptical pendulum

Shape and parameter reconstruction for the Robin transmission inverse problem

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Antoine Laurain ◽  
Houcine Meftahi
Keyword(s):  
Inverse Problem ◽  
Shape Optimization ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Optimization Approach ◽  
Reconstruction Method ◽  
Piecewise Constant ◽  
Piecewise Constant Conductivity ◽  
Level Set Approach ◽  
Parameter Reconstruction

AbstractIn this paper we consider the inverse problem of simultaneously reconstructing the interface where the jump of the conductivity occurs and the Robin parameter for a transmission problem with piecewise constant conductivity and Robin-type transmission conditions on the interface. We propose a reconstruction method based on a shape optimization approach and compare the results obtained using two different types of shape functionals. The reformulation of the shape optimization problem as a suitable saddle point problem allows us to obtain the optimality conditions by using differentiability properties of the min-sup combined with a function space parameterization technique. The reconstruction is then performed by means of an iterative algorithm based on a conjugate shape gradient method combined with a level set approach. To conclude we give and discuss several numerical examples.

scholarly journals A LEXICOGRAPHIC OPTIMIZATION APPROACH FOR BERTH SCHEDULE RECOVERY PROBLEM IN CONTAINER TERMINALS

Transport ◽  
2016 ◽  
Vol 31 (1) ◽  
pp. 76-83 ◽  
Author(s):  
Qian Zhang ◽  
Qingcheng Zeng ◽  
Hualong Yang
Keyword(s):  
Container Terminals ◽  
Optimization Approach ◽  
Technical Problems ◽  
Trade Off ◽  
Practical Applications ◽  
Lexicographic Optimization ◽  
Multi Stage ◽  
Schedule Recovery ◽  
Equipment Failures ◽  
Recovery Problem

In container terminals, the planned berth schedules often have to be revised because of disruptions caused by severe weather, equipment failures, technical problems and other unforeseen events. In this paper, the problem of berth schedule recovery is addressed to reduce the influences caused by disruptions. A multi-objective, multi-stage model is developed considering the characteristics of different customers and the trade-off of all parties involved. An approach based on the lexicographic optimization is designed to solve the model. Numerical experiments are provided to illustrate the validity of the proposed Model A and algorithms. Results indicate that the designed Model A and algorithm can tackle the berth plan recovery problem efficiently because the beneficial trade-off among all parties involved are considered. In addition, it is more flexible and feasible with the aspect of practical applications considering that the objective order can be adjusted by decision makers.

A mass assembly of associative mechanisms: A dynamical systems account of natural social interaction

2014 ◽  
Vol 37 (2) ◽  
pp. 198-198
Author(s):  
Nicholas D. Duran ◽  
Rick Dale ◽  
Daniel C. Richardson
Keyword(s):  
Social Interaction ◽  
Dynamical Systems ◽  
Associative Learning ◽  
Learning Mechanisms ◽  
Target Article ◽  
Mass Assembly

AbstractThe target article offers a negative, eliminativist thesis, dissolving the specialness of mirroring processes into a solution of associative mechanisms. We support the authors' project enthusiastically. What they are currently missing, we argue, is a positive, generative thesis about associative learning mechanisms and how they might give way to the complex, multimodal coordination that naturally arises in social interaction.

scholarly journals Toward optimal mapping of human dual-arm motion to humanoid motion for tasks involving contact with the environment

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141875737 ◽  
Author(s):  
Marija Tomić ◽  
Kosta Jovanović ◽  
Christine Chevallereau ◽  
Veljko Potkonjak ◽  
Aleksandar Rodić
Keyword(s):  
Humanoid Robots ◽  
Joint Space ◽  
Human Motion ◽  
Inverse Optimization ◽  
Optimal Combination ◽  
Optimization Approach ◽  
Control Approach ◽  
Criterion Functions ◽  
Dual Arm ◽  
Weight Coefficients

In this article, we explore human motion skills in the dual-arm manipulation tasks that include contact with equipment with the final aim to generate human-like humanoid motion. Human motion is analyzed using the optimization approaches starting with the assumption that human motion is optimal. A combination of commonly used optimization criteria in the joint space with the weight coefficients is considered: minimization of kinetic energy, minimization of joint velocities, minimization of the distance between the current and ergonomic positions, and maximization of manipulability. The contribution of each criterion for seven different dual-arm manipulation tasks to provide the most accurate imitation of the human motion is given via suggested inverse optimization approach calculating values of weight coefficients. The effects on actors’ body characteristics and the characteristics of the environment (involved equipment) on the choice of criterion functions are additionally analyzed. The optimal combination of weight coefficients calculated by the inverse optimization approach is used in our inverse kinematics algorithm to transfer human motion skills to the motion of the humanoid robots. The results show that the optimal combination of weight coefficients is able to generate human-like humanoid motions rather than individual one of the considered criterion functions. The recorded human motion and the motion of the humanoid robot ROMEO, obtained with the strategy used by human and defined by our inverse optimal control approach, for the tasks “opening/closing a drawer” are assessed visually and quantitatively.

scholarly journals Optimizing Excitation Coil Currents for Advanced Magnetorelaxometry Imaging

2019 ◽  
Vol 62 (2) ◽  
pp. 238-252 ◽  
Author(s):  
Peter Schier ◽  
Maik Liebl ◽  
Uwe Steinhoff ◽  
Michael Handler ◽  
Frank Wiekhorst ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Magnetic Fields ◽  
Measurement Data ◽  
Quantitative Detection ◽  
Optimization Approach ◽  
Problem Solution ◽  
Reconstruction Algorithms ◽  
System Matrix ◽  
Imaging Quality ◽  
Excitation Coil

AbstractMagnetorelaxometry imaging is a highly sensitive technique enabling noninvasive, quantitative detection of magnetic nanoparticles. Electromagnetic coils are sequentially energized, aligning the nanoparticles’ magnetic moments. Relaxation signals are recorded after turning off the coils. The forward model describing this measurement process is reformulated into a severely ill-posed inverse problem that is solved for estimating the particle distribution. Typically, many activation sequences employing different magnetic fields are required to obtain reasonable imaging quality. We seek to improve the imaging quality and accelerate the imaging process using fewer activation sequences by optimizing the applied magnetic fields. Minimizing the Frobenius condition number of the system matrix, we stabilize the inverse problem solution toward model uncertainties and measurement noise. Furthermore, our sensitivity-weighted reconstruction algorithms improve imaging quality in lowly sensitive areas. The optimization approach is employed to real measurement data and yields improved reconstructions with fewer activation sequences compared to non-optimized measurements.

Design of Compliant Structural Mechanisms Using B-Spline Elements

2011 ◽  
Author(s):  
Ashok V. Kumar ◽  
Anand Parthasarathy
Keyword(s):  
Inverse Problem ◽  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Spline Approximation ◽  
Structural Response ◽  
Field Application ◽  
Optimization Approach ◽  
Objective Functions ◽  
B Spline ◽  
Spline Basis

Structural design is an inverse problem where the geometry that fits a specific design objective is found iteratively through repeated analysis or forward problem solving. In the case of compliant structures, the goal is to design the structure for a particular desired structural response that mimics traditional mechanisms and linkages. It is possible to state the inverse problem in many different ways depending on the choice of objective functions used and the method used to represent the shape. In this paper, some of the objective functions that have been used in the past, for the topology optimization approach to designing compliant mechanisms are compared and discussed. Topology optimization using traditional finite elements often do not yield well-defined smooth boundaries. The computed optimal material distributions have shape irregularities unless special techniques are used to suppress them. In this paper, shape is represented as the contours or level sets of a characteristic function that is defined using B-spline approximation to ensure that the contours, which represent the boundaries, are smooth. The analysis is also performed using B-spline elements which use B-spline basis functions to represent the displacement field. Application of this approach to design a few simple mechanisms is presented.

Q-factor inversion using reconstructed source spectral consistency

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R699-R710 ◽  
Author(s):  
Matan Shustak ◽  
Ariel Lellouch
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Seismic Waves ◽  
Velocity Model ◽  
Physical Principle ◽  
Optimization Approach ◽  
Full Spectrum ◽  
Viscoelastic Wave Propagation ◽  
Attenuation Models ◽  
Basic Physical Principle

Seismic waves propagating in an anelastic medium undergo phase and amplitude distortions. Although these effects may be compensated for during imaging processes, a background [Formula: see text]-model is generally required for their successful application. We have developed a new approach to the [Formula: see text]-estimation problem, which is fundamentally related to the basic physical principle of time reversal. It is based on back-propagating recorded traces to their known source location using the reverse tomographic equation. This equation is a ray approximation of viscoelastic wave propagation. It is applied assuming a known and correct velocity model. We subsequently measure consistency between spectral shapes of traces that were back-propagated using the tomographic equation. We formulate an inverse problem using this consistency as an objective function. In conventional inversion, on the contrary, the discrepancy between modeled and recorded data, or some data characteristics, is minimized. The inverse problem is solved by ant-colony optimization, a global optimization approach, to avoid local minima present in the objective function. This method does not require knowledge of the source function and uses the full spectrum rather than its parametric reduction. Through synthetic and field cross-hole examples, we illustrate its accuracy and sensitivity in inverting for complex attenuation models. In the synthetic case, we also compare reconstructed source consistency with the conventional centroid frequency shift objective function. The latter displays poor resolution when recovering complex [Formula: see text] structures. We determine that the reconstructed source-consistency approach should be used as a part of an iterative workflow, possibly yielding initial models for a joint velocity and [Formula: see text] inversion.

Dynamics of G-processes

2020 ◽  
Vol 20 (01) ◽  
pp. 2050037
Author(s):  
W. Jung ◽  
K. Lee ◽  
C.A. Morales
Keyword(s):  
Dynamical Systems ◽  
Group Structure ◽  
Global Solutions ◽  
Topological Stability ◽  
Natural Group ◽  
Shadowing Property ◽  
Infinite Dimensional ◽  
Mathematical Sciences ◽  
The Relationship

A G-process is briefly a process ([A. N. Carvalho, J. A. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Applied Mathematical Sciences, Vol. 182 (Springer, 2013)], [C. M. Dafermos, An invariance principle for compact processes, J. Differential Equations 9 (1971) 239–252], [P. E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, Mathematical Surveys and Monographs, Vol. 176 (Amer. Math. Soc., 2011)]) for which the role of evolution parameter is played by a general topological group [Formula: see text]. These processes are broad enough to include the [Formula: see text]-actions (characterized as autonomous [Formula: see text]-processes) and the two-parameter flows (where [Formula: see text]). We endow the space of [Formula: see text]-processes with a natural group structure. We introduce the notions of orbit, pseudo-orbit and shadowing property for [Formula: see text]-processes and analyze the relationship with the [Formula: see text]-processes group structure. We study the equicontinuous [Formula: see text]-processes and use it to construct nonautonomous [Formula: see text]-processes with the shadowing property. We study the global solutions of the [Formula: see text]-processes and the corresponding global shadowing property. We study the expansivity (global and pullback) of the [Formula: see text]-processes. We prove that there are nonautonomous expansive [Formula: see text]-processes and characterize the existence of expansive equicontinuous [Formula: see text]-processes. We define the topological stability for [Formula: see text]-processes and prove that every expansive [Formula: see text]-process with the shadowing property is topologically stable. Examples of nonautonomous topologically stable [Formula: see text]-processes are given.

scholarly journals Dynamic ICSP Graph Optimization Approach for Car-Like Robot Localization in Outdoor Environments

Computers ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 63
Author(s):  
Zhan Wang ◽  
Alain Lambert ◽  
Xun Zhang
Keyword(s):  
Particle Filtering ◽  
Constraint Satisfaction Problem ◽  
Real Data ◽  
Constraint Propagation ◽  
Optimization Approach ◽  
Robot Localization ◽  
Data Set ◽  
Practical Applications ◽  
Outdoor Environments ◽  
Interval Constraint

Localization has been regarded as one of the most fundamental problems to enable a mobile robot with autonomous capabilities. Probabilistic techniques such as Kalman or Particle filtering have long been used to solve robotic localization and mapping problem. Despite their good performance in practical applications, they could suffer inconsistency problems. This paper presents an Interval Constraint Satisfaction Problem (ICSP) graph based methodology for consistent car-like robot localization in outdoor environments. The localization problem is cast into a two-stage framework: visual teach and repeat. During a teaching phase, the interval map is built when a robot navigates around the environment with GPS-support. The map is then used for real-time ego-localization as the robot repeats the path autonomously. By dynamically solving the ICSP graph via Interval Constraint Propagation (ICP) techniques, a consistent and improved localization result is obtained. Both numerical simulation results and real data set experiments are presented, showing the soundness of the proposed method in achieving consistent localization.

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