Computing large deviation prefactors of stochastic dynamical systems based on machine learning

We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.

Dynamic Constraint-Driven Event-Triggered Control of Strict-Feedback Systems Without Max/Min Values on Irregular Constraints

This work proposes an event-triggered adaptive control approach for a class of uncertain nonlinear systems under irregular constraints.Unlike the constraints considered in most existing papers,here the external irregular constraints are considered and a constraints switching mechanism(CSM)is introduced to circumvent the difficulties arising from irregular output constraints.Based on the CSM,a new class of generalized barrier functions are constructed,which allows the control results to be independent of the maximum and minimum values(MMVs)of constraints and thus extends the existing results.Finally,we proposed a novel dynamic constraint-driven event-triggered strategy(DCDETS),under which the stress on signal transmission is reduced greatly and no constraints are violated by making a dynamic trade-off among system state,external constraints,and inter-execution intervals.It is proved that the system output is driven to close to the reference trajectory and the semi-global stability is guaranteed under the proposed control scheme,regardless of the external irregular output constraints.Simulation also verifies the effectiveness and benefits of the proposed method.

Dynamic Interaction Analysis of Coupled Axial-Torsional-Lateral Mechanical Vibrations in Rotary Drilling Systems

Maintaining the integrity and longevity of structures is essential in many industries,such as aerospace,nuclear,and petroleum.To achieve the cost-effectiveness of large-scale systems in petroleum drilling,a strong emphasis on structural durability and monitoring is required.This study focuses on the mechanical vibrations that occur in rotary drilling systems,which have a substantial impact on the structural integrity of drilling equipment.The study specifically investigates axial,torsional,and lateral vibrations,which might lead to negative consequences such as bit-bounce,chaotic whirling,and high-frequency stick-slip.These events not only hinder the efficiency of drilling but also lead to exhaustion and harm to the system’s components since they are difficult to be detected and controlled in real time.The study investigates the dynamic interactions of these vibrations,specifically in their high-frequency modes,usingfield data obtained from measurement while drilling.Thefindings have demonstrated the effect of strong coupling between the high-frequency modes of these vibrations on drilling sys-tem performance.The obtained results highlight the importance of considering the interconnected impacts of these vibrations when designing and implementing robust control systems.Therefore,integrating these compo-nents can increase the durability of drill bits and drill strings,as well as improve the ability to monitor and detect damage.Moreover,by exploiting thesefindings,the assessment of structural resilience in rotary drilling systems can be enhanced.Furthermore,the study demonstrates the capacity of structural health monitoring to improve the quality,dependability,and efficiency of rotary drilling systems in the petroleum industry.

Foundations and Applications of Information Systems Dynamics

Although numerous advances have been made in information technology in the past decades,there is still a lack of progress in information systems dynamics(ISD),owing to the lack of a mathematical foundation needed to describe information and the lack of an analytical framework to evaluate information systems.The value of ISD lies in its ability to guide the design,development,application,and evaluation of largescale information system-of-systems(So Ss),just as mechanical dynamics theories guide mechanical systems engineering.This paper reports on a breakthrough in these fundamental challenges by proposing a framework for information space,improving a mathematical theory for information measurement,and proposing a dynamic configuration model for information systems.In this way,it establishes a basic theoretical framework for ISD.The proposed theoretical methodologies have been successfully applied and verified in the Smart Court So Ss Engineering Project of China and have achieved significant improvements in the quality and efficiency of Chinese court informatization.The proposed ISD provides an innovative paradigm for the analysis,design,development,and evaluation of large-scale complex information systems,such as electronic government and smart cities.

THE EQUATIONS OF EXTERNAL IMPACTED DYNAMICS BETWEEN MULTI-RIGIDBODY SYSTEMS

This paper discusses the problem of impact dynamics between two multi-rigidbody systems, and presents the mathematical model of this kind of impact problem. In this model the impact impulses at collision points are not coupled with the increments of the velocities, and they are also suitable for computer coding. So the model obtained in this paper is of practical value.

Modelling of internal ballistics of gun systems:A review

A deep understanding of the internal ballistic process and the factors affecting it is of primary importance to efficiently design a gun system and ensure its safe management. One of the main goals of internal ballistics is to estimate the gas pressure into the combustion chamber and the projectile muzzle velocity in order to use the propellant to its higher efficiency while avoiding over-pressure phenomena. Dealing with the internal ballistic problem is a complex undertaking since it requires handling the interaction between different constituents during a transient time lapse with very steep rise of pressure and temperature. Several approaches have been proposed in the literature, based on different assumptions and techniques. Generally, depending on the used mathematical framework, they can be classified into two categories: computational fluid dynamics-based models and lumped-parameter ones. By focusing on gun systems, this paper offers a review of the main contributions in the field by mentioning their advantages and drawbacks. An insight into the limitations of the currently available modelling strategies is provided,as well as some considerations on the choice of one model over another. Lumped-parameter models, for example, are a good candidate for performing parametric analysis and optimisation processes of gun systems, given their minimum requirements of computer resources. Conversely, CFD-based models have a better capacity to address more sophisticated phenomena like pressure waves and turbulent flow effects. The performed review also reveals that too little attention has been given to small calibre guns since the majority of currently available models are conceived for medium and large calibre gun systems.Similarly, aspects like wear phenomena, bore deformations or projectile-barrel interactions still need to be adequately addressed and our suggestion is to dedicate more effort on it.

A Dynamical System-Based Framework for Dimension Reduction

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap.

Dynamics of Plate Equations with Memory Driven by Multiplicative Noise on Bounded Domains

This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback attractors on the tails estimates, and the asymptotic compactness of the random dynamical system is proved by decomposition method, and then we obtain the existence of a random attractor.

THE VARIATIONAL PRINCIPLE FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.

Distributed dynamic event-based finite-time dissipative synchronization control for semi-Markov switched fuzzy cyber-physical systems against random packet losses

This paper is concerned with the finite-time dissipative synchronization control problem of semi-Markov switched cyber-physical systems in the presence of packet losses, which is constructed by the Takagi–Sugeno fuzzy model. To save the network communication burden, a distributed dynamic event-triggered mechanism is developed to restrain the information update. Besides, random packet dropouts following the Bernoulli distribution are assumed to occur in sensor to controller channels, where the triggered control input is analyzed via an equivalent method containing a new stochastic variable. By establishing the mode-dependent Lyapunov–Krasovskii functional with augmented terms, the finite-time boundness of the error system limited to strict dissipativity is studied. As a result of the help of an extended reciprocally convex matrix inequality technique, less conservative criteria in terms of linear matrix inequalities are deduced to calculate the desired control gains. Finally, two examples in regard to practical systems are provided to display the effectiveness of the proposed theory.

Resistor-Capacitor Circuit as a Dynamic System

The paper considers the response to the accumulated energy in the resistor (R)-capacitor (C) circuit. In the (RC) circuit, the capacitor C is initially charged with the “capacitive” voltage U0. At that moment t=0, the P circuit switch turns on. By using Kirchhoff’s laws on the elements, a homogeneous differential equation of the first order with constant coefficients is obtained with the initial condition UC(0)=U0. The solution of the differential equation is presented in exponential form UC(t)=U0⋅e−t/τ. Qualitative analysis RC of the circuit gives a phase portrait on the line. From the phase portrait on the line, it can be seen that the charge UC(t)→UC∗=0when t→∞stabilizes, regardless of the initial conditions. It is shown that from UC(t)=U0⋅e−t/τa dynamic system defined by the function φ(t,UC)=UC⋅e−t/τcan be formed from. It has also been shown that, from the formed dynamic system, an autonomous system (circuit equation RC) can be found whose solution describes the formed dynamic system. It is also shown that the dynamic system φ(t,UC)=UC⋅e−t/τhas one attractive fixed point UC=0.

Einstein-Podolsky-Rosen Steering and Nonlocality in Open Quantum Systems

We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.

Time/Space and Inertial System Reconsidered Based on the Adaptive Dynamical View

We have succeeded in 2-slit interference simulation by assuming that a travelling particle interacts with its environment, getting information on the environmental condition according to the adaptive dynamics by Ohya, thus proposed the possibility that the entanglement comes from the interaction with the environment (Ando et al., 2023). This concept means that there should be no isolated or inertial system other than our unique universe space. Taking this message into account and assuming that the signal velocity is constant against our unique universe space, we reconsidered the inertial system and relativity theory by Galilei and Einstein and found several misunderstandings and errors. Time delay and Lorentz shrinkage were derived similarly to the prediction by special relativity theory, but Lorentz transformation and 4-dimensional time/space view were not. They must have implicitly and unconsciously assumed that any signals transfer information without giving any influences to any systems different from our adaptive dynamical view. We propose that their relativity theories should be reinterpreted in view of adaptive dynamics.

Implementation of configuration dependent stiffness proportional damping for the dynamics of rigid multi-block systems

The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.

Robust Output Feedback Control for a Class of Nonlinear Systems with Input Unmodeled Dynamics

The robust global stabilization problem of a class of uncertain nonlinear systems with input unmodeled dynamics is considered using output feedback, where the uncertain nonlinear terms satisfy a far more relaxed condition than the existing triangulartype condition. Under the assumption that the input unmodeled dynamics is minimum-phase and of relative degree zero, a dynamic output compensator is explicitly constructed based on the nonseparation principle. An example illustrates the usefulness of the proposed method.

Towards a Modeling of the Impacts of Road Verge Management on the Pollination Service Using System Dynamics: A Case Study in France

Several research studies have proven that eliciting and predicting the impact of human activity on ecosystem services will be crucial to support stakeholders’ awareness and to decide how to interact with the environment in a more sustainable manner. In this sense, the ecosystems known as road verges are particularly important because of their length and surface at an international scale, and their role in mitigating the damage done by roads. Plant pollination by insects is one of the most important ecosystem services. Because of its nature and the fact that they extend across a variety of landscapes, roadside can contribute to the maintenance of healthy ecosystems, under the condition of adapted management practices. This research is the first attempt to develop a System Dynamics-based aiming to estimate the ecological and economic impact of maintenance on the road verge pollination service in France. Maintenance strategies of road verges are simulated to compare their performance. The results show that there are ways to improve current maintenance strategies in terms of pollination value, but also that the model needs to consider other ecosystem services and synergistic effects that could further affect pollination to obtain more accurate estimations.

Novel sensitivity analysis method and dynamics optimization for multiple launch rocket systems

This study establishes the launch dynamics method,sensitivity analysis method,and multiobjective dynamic optimization method for the dynamic simulation analysis of the multiple launch rocket system(MLRS)based on the Riccati transfer matrix method for multibody systems(RMSTMM),direct differentiation method(DDM),and genetic algorithm(GA),respectively.Results show that simulation results of the dynamic response agree well with test results.The sensitivity analysis method is highly programming,the matrix order is low,and the calculation time is much shorter than that of the Lagrange method.With the increase of system complexity,the advantage of a high computing speed becomes more evident.Structural parameters that have the greatest influence on the dynamic response include the connection stiffness between the pitching body and the rotating body,the connection stiffness between the rotating body and the vehicle body,and the connection stiffnesses among 14^(#),16^(#),and 17^(#)wheels and the ground,which are the optimization design variables.After optimization,angular velocity variances of the pitching body in the revolving and pitching directions are reduced by 97.84%and 95.22%,respectively.

Advances in dynamics and control of tethered satellite systems

The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.

State feedback stabilization for high-order stochastic nonlinear systems with zero dynamics

In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.

SIMULATING REGIONAL SYSTEMS: A SYSTEM DYNAMICS APPROACH

System dynamics is a rigorous method for qualitative description,exploration and analysis of complex systems in terms of their processes, information flows, orgaruzational boundaries and strategies, which facilitates quantitative modelling and analysis for design of system structure and the improvement of system behaviour. It can be applied to the study of a wide range of systems, and its ability to describe socio-economic characteristics and behaviour makes it suitable for the analysis of the regional development process. Three examples of System Dynamics models are reviewd to demonstrate the suitability of the method for regional analysis, and on the basis of this review the potential use of system dynamics models in China is discussed.