State Space Research Articles

A new diagonalization based method for parallel-in-time solution of linear-quadratic optimal control problems

A new diagonalization technique for the parallel-in-time solution of linear-quadratic optimal control problems with time-invariant system matrices is introduced. The target problems are often derived from a semi-discretization of a Partial Differential Equation (PDE)-constrained optimization problem. The solution of large-scale time dependent optimal control problems is computationally challenging as the states, controls, and adjoints are coupled to each other throughout the whole time domain. This computational difficulty motivates the use of parallel-in-time methods. For time-periodic problems our diagonalization efficiently transforms the discretized optimality system into K (=number of time steps) decoupled complex valued 2n y by 2n y systems, where n y is the dimension of the state space. These systems resemble optimality systems corresponding to a steady-state version of the optimal control problem and they can be solved in parallel across the time steps, but are complex valued. For optimal control problems with initial value state equations a direct solution via diagonalization is not possible, but an efficient preconditioner can be constructed from the corresponding time periodic optimal control problem. The preconditioner can be efficiently applied parallel-in-time using the diagonalization technique. The observed number of preconditioned GMRES iterations is small and insensitive to the size of the problem discretization.

Exploring fracture of H-BN and graphene by neural network force fields

Extreme mechanical processes such as strong lattice distortion and bond breakage during fracture often lead to catastrophic failure of materials and structures. Understanding the nucleation and growth of cracks is challenged by their multiscale characteristics spanning from atomic-level structures at the crack tip to the structural features where the load is applied. Atomistic simulations offer ‘first-principles’ tools to resolve the progressive microstructural changes at crack fronts and are widely used to explore the underlying processes of mechanical energy dissipation, crack path selection, and dynamic instabilities (e.g. kinking, branching). Empirical force fields developed based on atomic-level structural descriptors based on atomic positions and the bond orders do not yield satisfying predictions of fracture, especially for the nonlinear, anisotropic stress–strain relations and the energy densities of edges. High-fidelity force fields thus should include the tensorial nature of strain and the energetics of bond-breaking and (re)formation events during fracture, which, unfortunately, have not been taken into account in either the state-of-the-art empirical or machine-learning force fields. Based on data generated by density functional theory calculations, we report a neural network-based force field for fracture (NN-F3) constructed by using the end-to-end symmetry preserving framework of deep potential—smooth edition (DeepPot-SE). The workflow combines pre-sampling of the space of strain states and active-learning techniques to explore the transition states at critical bonding distances. The capability of NN-F3 is demonstrated by studying the rupture of hexagonal boron nitride (h-BN) and twisted bilayer graphene as model problems. The simulation results elucidate the roughening physics of fracture defined by the lattice asymmetry in h-BN, explaining recent experimental findings, and predict the interaction between cross-layer cracks in twisted graphene bilayers, which leads to a toughening effect.

Method for Collaborative Layout Optimization of Ship Equipment and Pipe Based on Improved Multi-Agent Reinforcement Learning and Artificial Fish Swarm Algorithm

The engine room is the core area of a ship, critical to its operation, safety, and efficiency. Currently, many researchers merely address the ship engine room layout design (SERLD) problem using optimization algorithms and independent layout strategies. However, the engine room environment is complex, involving two significantly different challenges: equipment layout and pipe layout. Traditional methods fail to achieve optimal collaborative layout objectives. To address this research gap, this paper proposes a collaborative layout method that combines improved reinforcement learning and heuristic algorithms. For equipment layout, the engine room space is first discretized into a grid, and a Markov decision process (MDP) framework suitable for equipment layout is proposed, including state space, action space, and reward mechanisms suitable for equipment layout. An improved adaptive guided multi-agent Q-learning (AGMAQL) algorithm is employed to train the layout model in a centralized manner, with enhancements made to the agent’s exploration state, exploration action, and learning strategy. For pipe layout, this paper proposes an improved adaptive trajectory artificial fish swarm algorithm (ATAFSA). This algorithm incorporates a hybrid encoding method, adaptive strategy, scouting strategy, and parallel optimization strategy, resulting in enhanced stability, accuracy, and problem adaptability. Subsequently, by comprehensively considering layout objectives and engine room attributes, a collaborative layout method incorporating hierarchical and adaptive weight strategies is proposed. This method optimizes in phases according to the layout objectives and priorities of different stages, achieving multi-level optimal layouts and providing designers with various reference schemes with different focuses. Finally, based on a typical real-world engine room engineering case, various leading algorithms and strategies are tested and compared. The results show that the proposed AGMAQL-ATAFSA (AGMAQL-ATA) exhibits robustness, efficiency, and engineering practicality. Compared to previous research methods and algorithms, the final layout quality improved overall: equipment layout effectiveness increased by over 4.0%, pipe optimization efficiency improved by over 40.4%, and collaborative layout effectiveness enhanced by over 2.2%.

Chaotic edge regimes in magnetohydrodynamic channel flow: An alternative path towards the tipping point

The effect of an imposed magnetic field on the flow of an electrically conducting fluid in a channel geometry is investigated numerically using high-performance temporal simulations. For the strongest spanwise magnetic fields considered, the turbulent state appears metastable, which makes the determination of the associated tipping point arduous. As an alternative, edge states, i.e., unstable states located on the state space boundary between the laminar and the turbulent basin of attraction, are investigated in detail. Their continuation smoothly leads to the tipping point where they are expected to collide with the turbulent dynamics. As the magnetic field intensity is raised, edge states become, on average, more energetic and more unstable, while their fluctuations become more chaotic, less predictable, and less symmetric. Nevertheless, their continuation allows one to accurately determine the value of the tipping point beyond which the laminar state becomes the only attractor. Published by the American Physical Society 2024

Prevalence of Diseases Among Working-age Men of Altai Region Living Near the Rocket and Space Activity Zone

Part of the population of the Altai Region is exposed to rocket and space activities. In order to identify possible medical consequences of such exposure, within the framework of the state space program in the region, since 1999, medical examinations of residents of territories adjacent to the fall areas of the second stages of launch vehicles launched from the Baikonur cosmodrome have been conducted. This paper presents the results of a dynamic analysis of the prevalence of diseases in men of working age in Krasnoshchekovsky district in 2003, 2008, 2013 and 2018. The most significant diseases, levels of indicators for the most widespread diseases and trends in the dynamics of indicators have been identified. The dynamics of the overall prevalence of diseases in men of working age and the prevalence of certain classes of diseases and nosologies is not unambiguous.

Simulation-based Inference on Virtual Brain Models of Disorders

Abstract Connectome-based models, also known as Virtual Brain Models (VBMs), have been well established in network neuroscience to investigate pathophysiological causes underlying a large range of brain diseases. The integration of an individual's brain imaging data in VBMs has improved patient-specific predictivity, although Bayesian estimation of spatially distributed parameters remains challenging even with state-of-the-art Monte Carlo sampling. VBMs imply latent nonlinear state space models driven by noise and network input, necessitating advanced probabilistic machine learning techniques for widely applicable Bayesian estimation. Here we present Simulation-based Inference on Virtual Brain Models (SBI-VBMs), and demonstrate that training deep neural networks on both spatio-temporal and functional features allows for accurate estimation of generative parameters in brain disorders. The systematic use of brain stimulation provides an effective remedy for the non-identifiability issue in estimating the degradation limited to smaller subset of connections. By prioritizing model structure over data, we show that the hierarchical structure in SBI-VBMs renders the inference more effective, precise and biologically plausible. This approach could broadly advance precision medicine by enabling fast and reliable prediction of patient-specific brain disorders.

The African Penguin Spheniscus demersus should be considered Critically Endangered

The African Penguin Spheniscus demersus has been considered a threatened species since 1984 and, aside from a short period around 2000, its population has been in constant decline since at least the 1950s. By combining counts of the numbers of breeding pairs made at 26 colonies in South Africa and Namibia between 1979 and 2023 with Bayesian state–space models we reassess the species’ conservation status. The breeding population has declined by 77.8% (95% credible intervals: 71.8–84.6%) over the last 30 years (3 generations), from ∼44 300 breeding pairs in 1993 to ∼9 900 pairs in 2023. This falls just below the threshold for a global IUCN Red List status of Critically Endangered (CR) under criterion A2. However, the decline in Namibia exceeds that threshold at the national level (30-year decline = 82.4%, 78.2–86.2%) following the loss of ∼3 600 breeding pairs there in the last 5 years. In South Africa, the Western Cape population is now declining at <1.5% per annum, but the annual rate of decline in the Eastern Cape has worsened substantially, reaching 13% over the last 10 years. Overall, the global population has more than halved in the last decade and has fallen below 10 000 pairs for the first time. Moreover, “moving window reductions” over 3 generations using observed and projected population trajectories (up to the year 2033) indicate that the decline of the African Penguin population will exceed the 80% CR threshold (under criterion A4ab) with a high probability by 2028. Accordingly, we propose that the African Penguin should be transferred to the IUCN Red List category Critically Endangered.

Continuous variation operator configuration for decomposition-based evolutionary multi-objective optimization

There are various multi-objective evolutionary algorithms (MOEAs) for solving multi-objective optimization problems (MOPs), and the significant difference between them lies in the way they generate offspring, which are the so-called variation operators. Since different variation operators have their own characteristics, it is often tedious to select a suitable EA for a given MOP. Even if the optimal operator is assigned, the fixed operator and hyper-parameters make it difficult to balance exploration and exploitation during the evolutionary process. It is imperative to configure variation operators and hyper-parameters automatically during the evolutionary process, which can improve the efficiency of algorithm search. However, numerous configurations only consider operators or discretize hyper-parameters, making it difficult to achieve satisfactory results. In this paper, we formulate the operator configuration as a continuous Markov Decision Process (MDP) and use a suitable Reinforcement Learning (RL) paradigm to realize the online configuration of EAs. To simplify the deployment of MDP, we adopt a decomposition-based framework and use a one-dimensional vector with a combination of weights and objectives as state spaces. In addition, we take the selection of crossover and mutation operators and the fine-tuning of their hyper-parameters as joint action spaces. With an RL technique, we expect to achieve maximum improvement in the performance of offspring on each preference by selecting an action in a given state. We further explore the effectiveness of the proposed methodology on different characteristic MOPs. Experimental results show that our method is more competitive than other configurations and state-of-the-art EAs.

Quantum optimization algorithm based on multistep quantum computation

Abstract We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation, and apply the algorithm for solving optimization problems with continuous variables. We construct the state space of the problem by discretizing the variables of the problem, and divide the state space according to the function values of the vectors of the state space. By comparing the function values of the vectors with a series of threshold values in decreasing order, we construct a sequence of Hamiltonians where the search space of a Hamiltonian is nested in that of the previous one. By applying a multistep quantum computation process for&amp;#xD;finding the ground state of the last Hamiltonian, the optimal vector of the state space of the problem is located in a small search space and can be determined efficiently. One of the most difficult problems in optimization algorithms is that a trial vector is trapped in a deep local minimum while the global minimum is missed, this problem can be alleviated in our algorithm and the run time is proportional to the number of the steps of the algorithm, provided that the reduction rate of the search spaces is polynomial large. We discuss the implementation of the algorithm and test the algorithm for some test functions.

Quantum optimization algorithm based on multistep quantum computation

Abstract We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation, and apply the algorithm for solving optimization problems with continuous variables. We construct the state space of the problem by discretizing the variables of the problem, and divide the state space according to the function values of the vectors of the state space. By comparing the function values of the vectors with a series of threshold values in decreasing order, we construct a sequence of Hamiltonians where the search space of a Hamiltonian is nested in that of the previous one. By applying a multistep quantum computation process for&amp;#xD;finding the ground state of the last Hamiltonian, the optimal vector of the state space of the problem is located in a small search space and can be determined efficiently. One of the most difficult problems in optimization algorithms is that a trial vector is trapped in a deep local minimum while the global minimum is missed, this problem can be alleviated in our algorithm and the run time is proportional to the number of the steps of the algorithm, provided that the reduction rate of the search spaces is polynomial large. We discuss the implementation of the algorithm and test the algorithm for some test functions.

Moral and formal model-based control strategy for autonomous vehicles at traffic-light-free intersections

Making an effective traffic strategy is a challenging problem that involves efficiency and safety, where traffic lights play an important role. Especially in cases without traffic lights, creating traffic strategies benefits significantly more complex and challenging. This complexity underscores the importance of research on autonomous vehicles, which has been trained widespread attention in recent years. In order to avoid these potential crises, the designed traffic strategy at traffic light-free intersections must be effective and reliable, ensuring the basic processes work properly. In this paper, we propose a novel method to formally model the traffic strategy for vehicles to make sure they safely and orderly pass through traffic light-free intersections. We use the state space analysis method to analyze the vehicle traffic model to ensure the decision made at each step is correct. By using Petri net, our proposed model achieves excellent analytical capabilities for asynchronous or highly concurrent systems than simpler Unified Modeling Language (UML) systems, as well as the ability to dynamically analyze system security and reliability.

Visual State Space Model for Image Deraining with Symmetrical Scanning

Image deraining aims to mitigate the adverse effects of rain streaks on image quality. Recently, the advent of convolutional neural networks (CNNs) and Vision Transformers (ViTs) has catalyzed substantial advancements in this field. However, these methods fail to effectively balance model efficiency and image deraining performance. In this paper, we propose an effective, locally enhanced visual state space model for image deraining, called DerainMamba. Specifically, we introduce a global-aware state space model to better capture long-range dependencies with linear complexity. In contrast to existing methods that utilize fixed unidirectional scan mechanisms, we propose a direction-aware symmetrical scanning module to enhance the feature capture of rain streak direction. Furthermore, we integrate a local-aware mixture of experts into our framework to mitigate local pixel forgetting, thereby enhancing the overall quality of high-resolution image reconstruction. Experimental results validate that the proposed method surpasses state-of-the-art approaches on six benchmark datasets.

Reliability analysis of a three-phase interleaved step-up DC-DC converter for electric vehicle

Increasing the amount of direct current (DC) loads in applications such as airplanes, spacecraft, electric vehicles (EV), and other similar applications DC-DC converters are commonly used. Hence, a three-phase interleaved step-up DC-DC converter (ISC) has been designed, and implemented, which is more appropriate for high-power applications. The modes of operation are explained in detail, and voltage gain calculations are performed. The state space matrix is derived from the voltage equation and the bode diagram is plotted using MATLAB code to investigate the stability study, which makes for a thorough frequency response analysis for the proposed converter. The military handbook (MIL-HDBK-217F) data have been used to perform the calculations to determine each and every component's reliability. The proposed ISC design is implemented into a hardware prototype that produces peak-to-peak output voltage of 139 V, rated voltage of 120 V and the testing outcomes are presented in great depth.

Tracking 4 years in the life of a female whale shark shows consistent migrations in the Gulf of Mexico and Caribbean

Context Satellite telemetry has revolutionised the study of animal movement, particularly for mobile marine animals, whose movements and habitat make consistent, long-term observation difficult. Aims Summarise the movements of Rio Lady, a mature female whale shark (Rhincodon typus), to characterise these movements, and to predict expected behaviour throughout the Gulf of Mexico (GOM). Methods Rio Lady was tracked using satellite telemetry for over 1600 days, generating over 1400 locations and travelling over 40,000 km. State–space and move persistence modelling enabled characterisation of behaviour, and machine learning (ML) enabled the development of habitat-suitability models to predict habitat utilisation, on the basis of location transmissions and their environmental covariates. Key results Rio Lady exhibited annually consistent patterns of movements among three regions within the GOM. Final ML models produced seasonally dynamic predictions of habitat use throughout the GOM. Conclusions The application of these methods to long-term location data exemplifies how long-term movement patterns and core areas can be discovered and predicted for marine animals. Implications Despite our limited dataset, our integrative approach advances methods to summarise and predict behaviour of mobile species and improve understanding of their ecology.

Novel Dynamic Defense Strategies in Networked Control Systems under Stochastic Jamming Attacks

In contemporary networked control systems (NCSs), ensuring robust and adaptive security measures against dynamic threats like jamming attacks is crucial. These attacks can disrupt the control signals, leading to degraded performance or even catastrophic failures. This paper introduces a novel approach to enhance NCS security by applying stochastic game theory to model and resolve interactions between a defender and a jammer. We develop a two-player zero-sum game where the defender employs mixed strategies to minimize the expected cost of maintaining system stability and control effectiveness in the face of potential jamming. Our model discretizes the state space and employs backward induction to dynamically update the value functions associated with various system states, reflecting the ongoing adjustment of strategies in response to the adversary’s actions. Utilizing linear programming in MATLAB, we optimize the defender’s mixed strategies to systematically mitigate the impact of jamming. The results from extensive simulations demonstrate the efficacy of our proposed strategies in attack scenarios, indicating a substantial enhancement in the resilience and performance of NCSs against jamming attacks. Specifically, the proposed method improved network state stability by 75%, reducing the fluctuation range by over 50% compared with systems without defense mechanisms. This study not only advances the theoretical framework for security in NCSs but also provides practical insights for the design of resilient control systems under uncertainty.

Novel Dynamic Defense Strategies in Networked Control Systems under Stochastic Jamming Attacks

In contemporary networked control systems (NCSs), ensuring robust and adaptive security measures against dynamic threats like jamming attacks is crucial. These attacks can disrupt the control signals, leading to degraded performance or even catastrophic failures. This paper introduces a novel approach to enhance NCS security by applying stochastic game theory to model and resolve interactions between a defender and a jammer. We develop a two-player zero-sum game where the defender employs mixed strategies to minimize the expected cost of maintaining system stability and control effectiveness in the face of potential jamming. Our model discretizes the state space and employs backward induction to dynamically update the value functions associated with various system states, reflecting the ongoing adjustment of strategies in response to the adversary’s actions. Utilizing linear programming in MATLAB, we optimize the defender’s mixed strategies to systematically mitigate the impact of jamming. The results from extensive simulations demonstrate the efficacy of our proposed strategies in attack scenarios, indicating a substantial enhancement in the resilience and performance of NCSs against jamming attacks. Specifically, the proposed method improved network state stability by 75%, reducing the fluctuation range by over 50% compared with systems without defense mechanisms. This study not only advances the theoretical framework for security in NCSs but also provides practical insights for the design of resilient control systems under uncertainty.

The fundamental role of character coding in Bayesian morphological phylogenetics.

Phylogenetic trees establish a historical context for the study of organismal form and function. Most phylogenetic trees are estimated using a model of evolution. For molecular data, modeling evolution is often based on biochemical observations about changes between character states. For example, there are four nucleotides, and we can make assumptions about the probability of transitions between them. By contrast, for morphological characters, we may not know a priori how many characters states there are per character, as both extant sampling and the fossil record may be highly incomplete, which leads to an observer bias. For a given character, the state space may be larger than what has been observed in the sample of taxa collected by the researcher. In this case, how many evolutionary rates are needed to even describe transitions between morphological character states may not be clear, potentially leading to model misspecification. To explore the impact of this model misspecification, we simulated character data with varying numbers of character states per character. We then used the data to estimate phylogenetic trees using models of evolution with the correct number of character states and an incorrect number of character states. The results of this study indicate that this observer bias may lead to phylogenetic error, particularly in the branch lengths of trees. If the state space is wrongly assumed to be too large, then we underestimate the branch lengths, and the opposite occurs when the state space is wrongly assumed to be too small.

Deep reinforcement learning driven cost minimization for batch order scheduling in robotic mobile fulfillment systems

Robotic Mobile Fulfillment Systems (RMFS) are extensively employed in modern warehouses. In the era of booming e-commerce, this parts-to-picker model significantly reduces warehouse costs and enhances operational efficiency. The primary focus of this article is on the scheduling of batch orders, which involves the simultaneous allocation of mobile robots and picking stations to orders to meet their requirements, with the aim of minimizing processing costs. While the optimization of RMFS has been extensively investigated by scholars in recent years., research on categorized storage remains limited. Furthermore, combinatorial optimization in scenarios with large orders, numerous picking stations, and multiple mobile robots presents an ongoing and significant challenge. To overcome these challenges, we introduce the Enhanced Deep Reinforcement Learning Method for Batch Order Scheduling (EDRL-OBOS), designed to minimize operational costs in RMFS. Our proposed algorithm, EDRL-OBOS, features a uniquely designed state space that encompasses the allocation of all orders, with the variable portion of the state space diminishing as the algorithm evolves. Moreover, we substitute traditional actions with heuristic rules, significantly enhancing the efficiency of the algorithm. Additionally, we establish a reward function based on a greedy algorithm, ensuring that our method surpasses conventional algorithms. As the number of episodes progresses, the EDRL-OBOS algorithm assigns picking stations and sequences of mobile robots to each order until all orders within the state space are fulfilled, subsequently determining the reward. Subsequently, all states are reset to their initial conditions, and the order allocation scheme is optimized through the learning experience from the previous episode, until convergence is reached. Ultimately, we conduct simulation experiments by varying the number of orders, picking stations, and mobile robots. The results indicate that the EDRL-OBOS algorithm achieves a maximum cost reduction of 22.89%, a minimum of 19.66%, and an average of 21.57%, across various scenarios. At the same time, the computation of our algorithms is superior to that of traditional algorithms.

Frequency regulation feasible region assessment and optimization of wind farm based on data-driven model predictive control

With the integration of large-scale wind turbines (WTs) into grids via electronic interfaces, power system operators have necessitated frequency support from wind farms. Due to the large number of WTs and their complex dynamic characteristics, it is necessary to assess the primary frequency regulation (PFR) capability and construct feasible region of wind farms. In order to cope with the problems of incomplete parameters, analytical solving complexity and the coupling influence of power system regulation characteristics, this paper develops a data-driven state space mapping linear model predictive control (MPC) to assess the maximum PFR capability of wind farms and reasonably distribute coefficients to WTs. Besides, a coordinated iteration framework between dispatching center and wind farms is proposed to further optimize the wind farm regulation feasible region. The simulation results verify that the proposed method has the advantages of independence from physical parameters, fast analytical solution, and lower requirements of training samples on limited scenarios.

Extraction of nonlinearity in neural networks with Koopman operator

Nonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode decomposition, and the tensor-train format. The Koopman operator approach has been recently developed in physics and nonlinear sciences; the Koopman operator deals with the time evolution in the observable space instead of the state space. Since we can replace the nonlinearity in the state space with the linearity in the observable space, it is a hopeful candidate for understanding complex behavior in nonlinear systems. Here, we analyze learned neural networks for the classification problems. As a result, the replacement of the nonlinear middle layers with the Koopman matrix yields enough accuracy in numerical experiments. In addition, we confirm that the pruning of the Koopman matrix gives sufficient accuracy even at high compression ratios. These results indicate the possibility of extracting some features in the neural networks with the Koopman operator approach.