Trajectories Of System Research Articles

A mechanical model for polar curves

Abstract In this work, we discuss the feasibility of the well-known classical polar curves (limacons, roses, and logarithmic spirals), studied in calculus courses, to emerge naturally as trajectories of a mass-spring system, limited to moving along a passing axis that rotates in a uniform circular motion with controlled angular velocity. Simulations using the free software Modellus visually show how the appearance of polar curves is closely related to the initial conditions of the problem. A discussion about the physical reality of more general orbits, with multiple return points, is presented considering the attractive and repulsive character of the central force field promoted by the elastic force present in the system considered.

Correction to: selection and evaluation of FOPID criteria for the X-15 adaptive flight control system (AFCS) via Lyapunov candidates: Optimizing trade-offs and critical values using optimization algorithms

Recently, there has been a growing interest among academics worldwide in studying flight control systems. The advancement of tracking technologies, such as the X-15 adaptive flight control system developed at NASA (National Aeronautics and Space Administration), has sparked significant exploration efforts by scientists. The vast availability of aerial resources further contributes to the importance of studying adaptive flight control systems (AFCS). The successful operation of AFCS relies on effectively managing the three fundamental motions: pitch, roll, and yaw. Therefore, scientists have been diligently working on developing optimization algorithms and models to assist AFCS in achieving optimal gains during motion. However, in real-world scenarios, each motion requires its own set of criteria, which presents several challenges. Firstly, there are multiple criteria available for selecting appropriate optimization values for each motion. Secondly, the relative importance of these criteria influences the selection process. Thirdly, there is a trade-off between the performance of the criteria within a single optimization case and across different cases. Lastly, determining the critical value of the criteria poses another obstacle. Consequently, evaluating and selecting optimum methods for AFCS trajectory controls becomes a complex operation. To address the need for optimizing AFCS for various maneuvers, this study proposes a new selection process. The suggested approach involves utilizing black hole optimization (BHO), Jaya optimization algorithm (JOA), and sunflower optimization (SFO) as methods for detecting and correcting trajectories in adaptive flight control systems. These methods aim to determine the best launch of missiles from the AFCS based on the coordinate location for both long and short distances. Additionally, the methods determine the optimal gains for the FOPID (fractional order proportional integral derivative) controller and enhance protection against enemy attacks. The research framework consists of two parts. The first part focuses on improving the FOPID motion gains by employing optimization algorithms (BHO, JOA, and SFO) that are evaluated based on the FOPID criteria. Lower significant weighting values of the optimization algorithms demonstrate the best missile launching in a cosine wave trajectory within AFCS, while higher significant values indicate the best missile launching in a sine wave trajectory within AFCS. The FOPID controller criteria, including Kp_pitch, Ki_roll, Kd_yaw, λ_pitch, and µ_yaw, are considered in all situations. Furthermore, the study reports the best weights obtained for the "Kp_pitch" criterion across the motions as follows: (0.8147, 66.7190, and 54.4716). For the "Ki_roll" criterion, the best weights are (0.0975, 64.4938, and 64.7311), and for "Kd_yaw" the weights are (0.1576, 35.2811, and 54.3886). The results of the selection process by the BHO, JOA, and SFO algorithms also include λ_pitch (0.1419, 40.0791, and 72.1047) and µ_yaw (0.6557, 13.5752, and 52.2495). To ensure the validity of the proposed research framework, a systematic evaluation and precise analysis were conducted.

Experiments with Combining LiDAR and Camera Data Acquired by UAS and Smartphone to Support Mapping

Abstract. Aerial mapping using Unmanned Aerial Systems (UAS), such as the DJI Mavic 3 Enterprise, has revolutionized photogrammetry, enabling efficient data capture for small-scale projects. The typical nadir perspective of UAS mapping, however, imposes limitations on capturing critical details of features due to its predominantly vertical viewpoint. Overcoming this challenge often requires manual, low-altitude flights by experienced UAS pilots to achieve high-angle oblique perspectives, unless gimbled camera mount is used. This study explores the integration of high oblique angle perspectives using the iPhone 15 Pro, which boasts advanced camera capabilities and an integrated LiDAR sensor, to complement UAS imagery. The iPhone 15 Pro's camera sensors provide a Ground Sampled Distance (GSD) comparable to UAS cameras, while its LiDAR sensor, with about five meters of range, enhances mapping capabilities by delivering accurate depth measurements in close range. By utilizing various georeferencing options for the imagery and LiDAR data from the iPhone 15 Pro with UAS nadir imagery, we can achieve a more comprehensive object space reconstruction, significantly improving the accuracy of geospatial mapping. Both the Mavic 3 Enterprise and the iPhone 15 Pro, though operating independently on their respective platforms, support Real-Time Kinematic (RTK) corrections, facilitating precise positioning for the entire system trajectory. Strategic placement and utilization of Ground Control Points (GCPs) aid in the georeferencing of the complete dataset, enhancing its overall accuracy. To validate the accuracy of the acquired data, checkpoints are established on-site. The positions derived from the integrated UAS and iPhone 15 Pro data are compared against these checkpoints to quantify the accuracy and reliability of the data. Additionally, Post-Processed Kinematic (PPK) techniques are employed to validate the trajectories of all data collection systems, ensuring the reliability of the acquired data, especially in instances where RTK corrections may be lacking. In summary, this research showcases comprehensive, multi-dimensional geospatial datasets by conducting validation studies that assess the accuracy and reliability of georeferenced datasets against known ground truth checkpoints. Such validation studies are crucial for identifying gaps in current methodologies and suggesting areas for improvement, thereby aiming to enhance the quality and accuracy of geospatial mapping applications. Through the integration of UAS and smartphone mapping, complemented by rigorous validation efforts, we aspire to achieve improved geospatial mapping accuracy.

Learning the effective order of a hypergraph dynamical system.

Dynamical systems on hypergraphs can display a rich set of behaviors not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much of this hypergraph structure is actually necessary to faithfully replicate the observed dynamical behavior. To answer this question, we propose a method to determine the minimum order of a hypergraph necessary to approximate the corresponding dynamics accurately. Specifically, we develop a mathematical framework that allows us to determine this order when the type of dynamics is known. We use these ideas in conjunction with a hypergraph neural network to directly learn the dynamics itself and the resulting order of the hypergraph from both synthetic and real datasets consisting of observed system trajectories.

Analysis of the evolution path of new energy system under polymorphic uncertainty—A case study of China

The exploration and promotion of new energy constitute a significant initiative for numerous countries in their pursuit of sustainable development and efforts to alleviate climate change. However, the influence of a multitude of uncertain factors on the evolutionary path of new energy is currently poorly studied. By establishing a dynamic evolution model for new energy under polymorphic uncertainty, this paper analyses the complex interaction between new energy, economic growth, and carbon trading over the period 2020–2060, using China as a case study. We employ numerical simulation and sensitivity analysis to investigate the evolutionary trajectories of the new energy system under various parameter value scenarios. We show that the evolutionary trajectories will undergo substantial fluctuations before 2030, subsequently stabilizing from 2030 onwards. The study highlights that an excessively rapid pace of new energy development is detrimental to new energy systems, whereas energy storage system deployment has the opposite effect. There exists a significant risk of the system collapsing as a result of slow new energy development, over-building energy storage facilities, or over-intervening in carbon trading. We also find that overdevelopment of energy storage system may have greater negative impacts on the economic system than underdevelopment.

A realist interpretation of unitarity in quantum gravity

Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalisability and the problem of time. We take a realist approach based on pilot-wave theory to address this issue in the Ashtekar formulation of the Wheeler–DeWitt equation. We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system recently discussed in Alexander et al (2022 Phys. Rev. D 106 106012), by parameterising a variation of a Weyl-spinor that depends on the Kodama state. The total Hamiltonian constraint yields a time-dependent Schrodinger equation, without semi-classical approximations, which we use to derive a local continuity equation over the configuration space. We implement the reality conditions at the level of the guidance equation, and obtain a real spin-connection, extrinsic curvature and triad along the system trajectory. We obtain quantum corrections to deSitter spacetime from the guidance equation. The non-normalisable Kodama state is naturally factored out of the full quantum state in the conserved current density, opening the possibility for quantum-mechanical unitarity. We also give a pilot-wave generalisation of the notion of unitarity applicable to non-normalisable states, and show the existence of equilibrium density for our system. Lastly, we find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.

Optimal control problem with state constraints via penalty functions

In this paper, we derive necessary conditions of optimality for problems with state constraints using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., de Pinho et al., 2022). Our aim is to provide a proof of the Maximum Principle that can be easily followed by those with basic knowledge of classical optimal control and elementary functional analysis. We intentionally consider a smooth case and the simplest boundary conditions; we consider global minimum and assume that the set of trajectories of the control system is compact.

Finite and fixed‐time stabilization of discrete‐time systems using passivity‐based control

AbstractIn this paper, we propose a new passivity‐based controller design technique for discrete‐time fully actuated systems. The controller establishes finite‐time and fixed‐time convergence of dynamical system trajectories to an equilibrium state. A new form of a dissipation function, selected a priori, is introduced to design a feedback control rule to achieve such convergence properties. An energy shaping and damping injection methodology is extended to achieve non‐asymptotic stabilization. A numerical example to validate the proposed methods is provided.

Tectonic influence on the evolutionary dynamics of deep-water channel systems along the active accretionary prism margin in the Rakhine Basin, Myanmar: A high-resolution 3d seismic analysis

This study reveals the morphological transformations of a deep-water channel system within the Rakhine Basin in the northeastern Bay of Bengal through a comprehensive analysis of high-resolution 3D seismic data integrated with drilling logs. Employing the “source-channel-sink” paradigm, this investigation examined the impact of various factors, including tectonic transformations, sediment influx, slope dynamics, climatic changes, and relative sea-level fluctuations, on the evolutionary trajectory of these channel systems. Applying precise time-slicing techniques integrating root-mean-square amplitude attributes, coherent amplitude attributes, and horizontal amplitudes on seismic profiles, this investigation recognized three distinct stages in the evolution of channel-levee complexes (CLCs): the Middle Miocene erosional deep-water channel-levee complex (CLC-1), the Pliocene erosional-depositional deep-water channel-levee complex (CLC-2), and the Pleistocene depositional deep-water channel-levee complex (CLC-3). Comparative analysis revealed that the CLC-3 exhibits unique characteristics, including shallower channel depth (D), wider channel width (WC), extensive U-shaped cross-sectional area (S), broader natural levee width (WL) and height (H), and the highest tortuosity coefficient (LC/LS) when contrasted with the other two CLCs. Furthermore, this study substantiated how tectonic processes, primarily the collision between the Indo-Eurasian plates, resulting in the Himalayan and Indo-Burma Range orogenies, have shaped the region's geological and climatic framework, thereby influencing monsoon circulation and precipitation patterns, which in turn augmented detrital material influx into the basin. Moreover, this tectonic collision has led to gradual changes in the slope gradient of the Rakhine Basin and its deep-water areas, impacting internal flow velocities and channel curvature, thus governing deep-water channel systems' development and spatial distribution. Also, episodic sea level fluctuations were identified as significant contributors to sediment transport from shelves to deep-water regions and sediment deposit reworking. Overall, this study underscores the role of tectonic changes after the Eocene in driving the evolutionary dynamics of the deep-water channel system within the Rakhine Basin, Myanmar.

Integral sliding mode control and stability for Markov jump systems with structured perturbations and time-varying delay driven by fractional Brownian motion

The issues of stability and sliding mode control (SMC) for time-varying delay Markov jump systems (MJSs) with structured perturbations constrained by fractional Brownian motion (fBm) are explored. First, constructing a novel Lyapunov-Krasovskii functional (LKF) with exponential terms that contain the double-integral term, the pth moment exponential stability conditions are derived by utilizing the generalized fractional Itoˆ formula and conditional mathematical expectation. Subsequently, by designing the innovative integral sliding mode surface (SMS) associated with time-varying delay and the SMC law, the state trajectories of the dynamic systems can reach the designed SMS within a finite time. Ultimately, the numerical experiment is executed to confirm and ensure the accuracy and reliability of the obtained results.

Joint Trajectory and Resource Allocation Design for RIS-Assisted UAV-Enabled ISAC Systems

Joint Trajectory and Resource Allocation Design for RIS-Assisted UAV-Enabled ISAC Systems

An integrated tube robust iterative learning model predictive control strategy based on dynamic partial least squares algorithm for batch processes

AbstractIn this paper, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

On the extension of singular linear infinite-dimensional Hamiltonian flows

We study the phenomenon of phase trajectories of a Hamiltonian system going to infinity in a finite time, the phase space of which is a separable Hilbert space. It is shown that if the Hamiltonian is a densely defined quadratic form on the phase space, which is not majorized either from below or from above by the quadratic form of the Hilbert norm, then the phase trajectories allow going to infinity in a finite time. To describe the phase flow of such Hamiltonian systems, an extended phase space is introduced, which is a locally convex space to which the Hamiltonian function, trajectories of the Hamiltonian system, and the symplectic form defined on the original Hilbert space can be extended. Flowinvariant measures on extended space are also studied. The properties of the Koopman unitary representation of the extended phase flow in the Hilbert space of functions that are quadratically integrable with respect to an invariant measure are investigated.

Passivity-based control of underactuated mechanical systems with Coulomb friction: Application to earthquake prevention

Passivity property gives a sense of energy balance. The classical definitions and theorems of passivity in dynamical systems require time invariance and locally Lipschitz functions. However, these conditions are not met in many systems. Characteristic examples are nonautonomous and discontinuous systems due to the presence of Coulomb friction. This paper presents an extended result for the negative feedback connection of two passive nonautonomous systems with set-valued right-hand side based on an invariance-like principle. Such extension is the base of a structural passivity-based control synthesis for underactuated mechanical systems with Coulomb friction. The first step consists of designing the control able to restore the passivity in the considered friction law, achieving stabilization of the system trajectories to a domain with zero velocities. Then, an integral action is included to improve the latter result and perform a tracking over a constant reference (regulation). Finally, the control is designed considering dynamics in the actuation. These control objectives are obtained using fewer control inputs than degrees of freedom, as a result of the underactuated nature of the plant. The presented control strategy is implemented in an earthquake prevention scenario, where a mature seismogenic fault represents the considered frictional underactuated mechanical system. Simulations are performed to show how the seismic energy can be slowly dissipated by tracking a slow reference, thanks to fluid injection far from the fault, accounting also for the slow dynamics of the fluid’s diffusion.

Green’s matching: an efficient approach to parameter estimation in complex dynamic systems

Abstract Parameters of differential equations are essential to characterize intrinsic behaviours of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green’s matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate trajectories in dynamic systems but not their derivatives due to the inverse of differential operators by Green’s function. This yields a statistically optimal guarantee for parameter estimation in general-order equations, a feature not shared by existing methods, and provides an efficient framework for broad statistical inferences in complex dynamic systems.

Trajectories of socio-ecological systems: A case study in the tropical Andes.

Scenario and policy assessments in socioeconomic and environmental studies face significant challenges in socio-ecological systems (SES). There are a limited number of studies that have looked at the impact of different scenarios within integrated approaches, and many have used a static approach with a single driver of change. The present work analyzes the SES dynamics for a strategic basin in the Colombian Andes when implementing and analyzing scenarios and policies related to land cover and land use change using a system dynamics simulation model. The model includes natural, ecosystem services, sociocultural, and economic components. Scenarios and policy options are analyzed both individually and jointly to identify synergies or trade-off effects between the different SES components. The results showed the different trajectories of the socio-ecological system according to the cases studied, and its impact on different variables in the analyzed components. Some counterintuitive effects were also identified, such as the importance of intrinsic motivations in decision-making processes, and determinants in land management and policy design.

Complexity of sustainable trajectories of a socioecological system. An application of the wayfinder guide in the tropical andes (Colombia)

Socioecological systems (SES) are complex and adaptive systems with variables and relationships that interact at different temporal and spatial scales. Identifying and analyzing these variables and interactions, as well as understanding the main leverage points and critical thresholds of the SES, are important to define the strategies and policies aimed at finding a sustainable SES. The Wayfinder Guide is a sustainability analysis and adaptive management planning tool to guide decision-making. The research question addressed in this study was regarding the challenges and opportunities of using the Wayfinder Guide to elucidate the complexity of sustainability trajectories and guide territorial planning in the challenging environmental conditions of the Global South, particularly the strategic mountain SES in the tropical Andes in Colombia. Using the Wayfinder Guide to begin an SES analysis may require a large number of resources and an extended period (years) to consolidate the effective implementation thereof, especially for the first phases of the guide. In this study, we propose methodological changes to apply the guidelines in the context of scarce SES information.

Hidden attractors and nonlocal oscillations in gene networks models

Abstract We study periodic trajectories of nonlinear dynamical systems considered as models of the simplest molecular repressilator. In the phase portraits of these systems, we find hidden attractors and nonlocal oscillations. The cases of nonuniqueness of cycles in these portraits are described as well.

Design of three-dimensional encryption algorithm for image based on improved 6th-order cellular neural network

The chaotic trajectory of the traditional natural chaotic system and the single chaotic system is relatively simple, and the keyspace is small, resulting in low security, low complexity, and poor resistance to attacks based on traditional chaotic design encryption algorithms. This article first constructed a 6th-order cellular neural network hyperchaotic system based on the theory of a 6th-order cellular neural network. Then the Chaotic Sequence Enhancer (CSE) is constructed by using infinite folding mapping. We use CSE to improve our cellular neural network. Compared with the old system, the new system has a larger Lyapunov exponent, higher PE complexity values, and 0–1 test results. Then based on the new chaotic system, a three-dimensional encryption algorithm was designed. The algorithm rearranges the pixels of the image into cubes and performs scrambling and diffusion operations based on the cubes. While making the encryption effect better, the information entropy of the ciphertext image is also above 7.99, and the correlation between adjacent pixels is less than 0.1. At the same time, the encryption algorithm can better resist various corrosion attacks, and the original image can still be better decrypted even when the ciphertext image has received a 25% loss. The result of the NPCR and UACI test is close to the expected values of 99.61% and 33.46%. The ciphertext image produced by the algorithm can pass the NIST SP800-22 statistical tests. The results of various tests and experiments show that our proposed encryption algorithm has high initial value sensitivity, resistance to differential attacks, and resistance to cropping attacks, and has good application prospects in the field of image security.

Beyond Automation: Exploring the Synergy of Cloud, AI, Machine Learning, and IoT for Intelligent Systems

In the rapidly evolving landscape of Industry 4.0 and beyond, the amalgamation of Cloud Computing, Artificial Intelligence (AI), Machine Learning (ML), and the Internet of Things (IoT) has emerged as a transformative force capable of elevating traditional automation to intelligent systems. This research paper delves into the profound potential of synergizing these advanced technologies, aiming to surpass the limitations of rule-based automation and foster a new era of adaptability, efficiency, and innovation.
 The study begins by articulating the escalating demand for intelligent systems that can dynamically respond to complex and ever-changing environments. The integration of Cloud, AI, ML, and IoT is posited as a solution to the constraints of conventional automation, offering the ability to process vast datasets, make informed decisions, and continuously learn from interactions.
 A comprehensive review of existing approaches and related works forms the foundation of this research. The analysis encompasses diverse applications, ranging from smart manufacturing to healthcare, showcasing the ways in which individual technologies have been leveraged. By scrutinizing these approaches, the study aims to distill the strengths and weaknesses, paving the way for a novel methodology that harnesses their collective power.
 Identifying the limitations of current approaches, such as scalability challenges, real-time processing bottlenecks, and interoperability issues, serves as a critical precursor to the proposed methodology. The paper presents a holistic strategy that intricately weaves together Cloud, AI, ML, and IoT into a unified framework. The architectural design, data flow, and interaction mechanisms are elucidated to demonstrate how this synergy can overcome existing challenges, providing adaptability and innovation in diverse domains.
 Empirical results derived from the implementation of the proposed methodology are presented and rigorously analyzed in the Results and Discussion section. Performance metrics, efficiency gains, and the impact on decision-making processes are thoroughly examined. Real-world case studies exemplify the effectiveness of the integrated approach, offering tangible evidence of its potential applications.
 Concluding remarks encapsulate the key findings, emphasizing the significance of the research in shaping the trajectory of intelligent systems. The broader implications of the proposed methodology across various industries are discussed, and avenues for future work are suggested. As technologies continue to evolve, the proposed methodology serves as a foundation for ongoing exploration, adaptation, and integration with emerging technologies.
 In essence, this research paper offers a detailed exploration into the synergy of Cloud, AI, ML, and IoT, paving the way for a new era of intelligent systems that transcend the limitations of traditional automation, fostering adaptability, efficiency, and innovation in an ever-changing technological landscape.