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STOCHASTIC MODELS
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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY
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Enhancing rheological muscle models with stochastic processes
PublicationPurpose: Biological musculoskeletal systems operate under variable conditions. Muscle stiffness, activation signals, and loads change during each movement. The presence of noise and different harmonic components in force production significantly influences the behaviour of the muscular system. Therefore, it is essential to consider these factors in numerical simulations. Methods: This study aims to develop a rheological mathematical...
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Application of a stochastic compartmental model to approach the spread of environmental events with climatic bias
PublicationWildfires have significant impacts on both environment and economy, so understanding their behaviour is crucial for the planning and allocation of firefighting resources. Since forest fire management is of great concern, there has been an increasing demand for computationally efficient and accurate prediction models. In order to address this challenge, this work proposes applying a parameterised stochastic model to study the propagation...
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Testing the impact of simplifications adopted in models describing wave loads on ship
PublicationThe wave-ship system in naval architecture is generally assumed to be a linear one. This allows for the computation of a transfer function of ship response to waves including wave loads on ship. The transfer function and the wave spectral density function enable the development of the stochastic process of wave loads on ship, corresponding to the irregular wave generating that loads. If the mathematical models of wave load transfer...
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Testing the impact of simplifications adopted in models describing wave loads on ship
PublicationThe wave-ship system in naval architecture is generally assumed to be a linear one. This allows for the computation of a transfer function of ship response to waves including wave loads on ship. The transfer function and the wave spectral density function enable the development of the stochastic process of wave loads on ship, corresponding to the irregular wave generating that loads. If the mathematical models of wave load transfer...
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Application of Pierson-Moskowitz wave spectrum to solution differential equations of multihull vessel
PublicationMotion of a dynamic system can be generated by different external or internal factors. At mathematical modelling external excitation factors of the most significant effect on the system, are selected. Such external factors are usually called excitations. Response of the system to given excitations is mathematically characterized by a definite transformation called operator of a system. For a broad class of dynamic systems the...
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Deterministic versus stochastic modelling of unsaturated flow in a sandy field soil based on dual tracer breakthrough data
PublicationThe 216 km2 Neuenhagen Millcreeck catchment can be characterized as a drought sensitive landscape in NE Germany. It is therefore a fundamental human interest to understand how water that fell as precipitation moves through the unsaturated soils and recharges groundwater. Additionally, a better knowledge of nutrient transport from soil to groundwater is important also, especially in landscapes with light sandy soils. For a better...
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Hierarchical random models in road transport safety
PublicationIn this paper multilevel approach to the issue of road safety level on the road network of European regions, classified as NUTS 2 in statistical databases of the EU, has been presented. The risk calculated as the number of death casualties in road accidents per 100,000 inhabitants of a given region has Poisson distribution. Therefore, generalized Poisson model has been assumed in the modelling process. Multilevel stochastic analysis...
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Investigations of the Methods of Time Delay Measurement of Stochastic Signals Using Cross-correlation with the Hilbert Transform
PublicationThe article presents the results of simulation studies of four methods of estimating time delay for random signals using cross-correlation with the Hilbert Transform. Selected models of mutually delayed stochastic signals were used in the simulations, corresponding to the signals obtained from scintillation detectors in radioisotope measurements of liquid-gas two-phase flow. Standard deviations of the values of the individual functions...
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Investigation of long-range dependencies in the stochastic part of daily GPS solutions
PublicationThe long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series...
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Non-linear FEM analysis of pounding-involved response of buildings under non-uniform earthquake excitation
PublicationThe aim of the paper is to show the results of the study investigating the influence of non-uniform earthquake excitation, due to spatial seismic effects connected with the propagation of seismic wave, on the pounding-involved response of two buildings. The three-dimensional non-linear FEM analysis has been conducted using the detailed models of colliding structures. Acceleration records for different structural supports have been...
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A multiparameter simulation-driven analysis of ship response when turning concerning a required number of irregular wave realizations
PublicationThe growing implementation of Decision Support Systems on modern ships, digital-twin technology, and the introduction of autonomous vessels cause the marine industry to seek accurate modeling of vessel response. Despite the contemporary 6DOF models can be used to predict ship motions in irregular waves, the impact of their stochastic realization is usually neglected and remains under-investigated. Especially in the case of turning, differences...
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A hybrid approach to optimization of radial inflow turbine with principal component analysis
PublicationEnergy conversion efficiency is one of the most important features of power systems as it greatly influences the economic balance. The efficiency can be increased in many ways. One of them is to optimize individual components of the power plant. In most Organic Rankine Cycle (ORC) systems the power is created in the turbine and these systems can benefit from effective turbine optimization. The paper presents the use of two kinds...
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Limitations of WSSUS modeling of stationary underwater acoustic communication channel
PublicationPerformances of underwater acoustic communication (UAC) systems are strongly related to specific propagation conditions of the underwater channel. Due to their large variability, there is a need for adaptive matching of the UAC systems signaling to the transmission properties of the channel. This requires a knowledge of instantaneous channel characteristics, in terms of the specific parameters of stochastic models. The wide-sense...
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Computing methods for fast and precise body surface area estimation of selected body parts
PublicationCurrently used body surface area (BSA) formulas give satisfactory results only for individuals with typical physique, while for elderly, obese or anorectic people accurate results cannot be expected. Particularly noteworthy are the results for individuals with severe obesity (body-mass index greater than 35 kg/m2), for which BSA estimation errors reached 80%. The main goal of our study is the development of precise BSA models for...
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Michał Bernard Pietrzak dr hab.
PeopleMichal Pietrzak is head of the Department of Statistics and Econometrics at the Faculty of Economics and Management, Gdańsk University of Technology, and Deputy Editor-in-Chief for Statistical Reviewing of the journals: Oeconomia Copernicana and Equilibrium. Quarterly Journal of Economics and Economic Policy. Until October 2021, he worked as an associate professor at the Faculty of Economic Sciences and Management, Nicolaus...
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Time Delay Estimation in Two-Phase Flow Investigation Using the γ-Ray Attenuation Technique.
PublicationTime delay estimation is an important research question having many applications in a range of technologies. Measurement of a two-phase flow in a pipeline or an open channel using radioisotopes is an example of such application. For instance, the determination of velocity of dispersed phase in that case is based on estimation of the time delay between two stochastic signals provided by scintillation probes. The proper analysis...
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Detecting type of hearing loss with different AI classification methods: a performance review
PublicationHearing is one of the most crucial senses for all humans. It allows people to hear and connect with the environment, the people they can meet and the knowledge they need to live their lives to the fullest. Hearing loss can have a detrimental impact on a person's quality of life in a variety of ways, ranging from fewer educational and job opportunities due to impaired communication to social withdrawal in severe situations. Early...
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Multi-fidelity robust aerodynamic design optimization under mixed uncertainty
PublicationThe objective of this paper is to present a robust optimization algorithm for computationally efficient airfoil design under mixed (inherent and epistemic) uncertainty using a multi-fidelity approach. This algorithm exploits stochastic expansions derived from the Non-Intrusive Polynomial Chaos (NIPC) technique to create surrogate models utilized in the optimization process. A combined NIPC expansion approach is used, where both...
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A multiparameter simulation-driven analysis of ship turning trajectory concerning a required number of irregular wave realizations
PublicationIn times of progressive automation of the marine industry, accurate modeling of ship maneuvers is of utmost importance to all parties involved in maritime transportation. Despite the existence of modern collisionavoidance algorithms using 6DOF motion models to predict ship trajectories in waves, the impact of stochastic realization of irregular waves is usually neglected and remains under-investigated. Therefore, herein, this phenomenon...
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Decoupled Kalman filter based identification of time-varying FIR systems
PublicationWhen system parameters vary at a fast rate, identification schemes based on model-free local estimation approaches do not yield satisfactory results. In cases like this, more sophisticated parameter tracking procedures must be used, based on explicit models of parameter variation (often referred to as hypermodels), either deterministic or stochastic. Kalman filter trackers, which belong to the second category, are seldom used in...
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Low-Cost and Highly-Accurate Behavioral Modeling of Antenna Structures by Means of Knowledge-Based Domain-Constrained Deep Learning Surrogates
PublicationThe awareness and practical benefits of behavioral modeling methods have been steadily growing in the antenna engineering community over the last decade or so. Undoubtedly, the most important advantage thereof is a possibility of a dramatic reduction of computational expenses associated with computer-aided design procedures, especially those relying on full-wave electromagnetic (EM) simulations. In particular, the employment of...
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Automatic Identification System (AIS) Dynamic Data Integrity Monitoring and Trajectory Tracking Based on the Simultaneous Localization and Mapping (SLAM) Process Model
PublicationTo enhance the safety of marine navigation, one needs to consider the involvement of the automatic identification system (AIS), an existing system designed for ship-to-ship and shipto- shore communication. Previous research on the quality of AIS parameters revealed problems that the system experiences with sensor data exchange. In coastal areas, littoral AIS does not meet the expectations of operational continuity and system availability,...
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Stateczność i niezawodność pełnomorskich platform wiertniczych
PublicationW pracy przedstawiono wieloletnie doświadczenia Autora w zakresie wybranych aspektów numerycznej analizy pełnomorskich platform wiertniczych, w szczególności stacjonarnych platform stalowych poddanych działaniu fal wiatrowych i wiatru. W opisie zachowania się platform uwzględniono współoddziaływanie trzech ośrodków: materiału konstrukcji, morskich fal wiatrowych i podłoża gruntowego. Przyjęcie do opisu stochastycznych właściwości...
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Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform
PublicationBirth–and–death models are now a common mathematical tool to describe branching patterns observed in real–world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth–and–death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the...
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Ekonometryczna analiza konsumpcji w Polsce w latach 1995-2018- statyczne modele wydatków konsumpcyjnych w wartościach nominalnych
PublicationW artykule przeprowadzono badania makroekonomicznych związków pomiędzy konsumpcją globalną (C) a produktem krajowym brutto (PKB). W części teoretycznej artykułu: • zdefiniowano postacie analityczne przyczynowo-skutkowych makromodeli konsumpcji, • sformułowano interpretację mierników opisujących badane zależności, • sformułowano założenia stochastyczne dla rozważanych makromodeli konsumpcji, W części empirycznej artykułu:...
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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
PublicationThis paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.
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Historical carpentry corner log joints—Numerical analysis within stochastic framework
PublicationThe paper presents the results of numerical analysis performed on historical, traditional carpentry corner logjoints of two basic topologies: the short-corner dovetail connection and the saddle notch connection. These types of carpentry joints are commonly used in currently preserved objects of wooden architecture. All connections have been modelled in pinewood, which has been defined in the Finite Element software MSC.Marc/Mentat...
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On mixing in the class of quadratic stochastic operators
PublicationWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Stochastic resonance in measurements
PublicationNoise is usually associated with the negative phenomenon, hampering the measurements data and their analysis. This view has been broken in the '80s when the phenomenon of stochastic resonance (Stochastic Resonance - SR) was discovered. It is a phenomenon that occurs in nonlinear dynamic measurement systems when the selected input noise can optimize system performance. SR became a way to improve efficiency of weak signals detection....
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Damage-involved response of two colliding buildings under non-uniform earthquake loading
PublicationPounding between insufficiently separated buildings, which may result in considerable damage or may even lead to the total collapse of colliding structures, has been repeatedly observed during earthquakes. Earthquake-induced collisions of buildings has been intensively studied applying various structural models. It was assumed in the analyses, however, that the seismic excitation is identical for all structural supports; whereas,...
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Mathematical model to assess energy consumption using water inflow-drainage system of iron-ore mines in terms of a stochastic process
PublicationPurpose is to develop a unified mathematical model to assess energy efficiency of a water inflow-drainage process as the real variant of stochastic method for water pumping from underground workings of iron-ore mines. Methods. The research process was based upon the methods of probability theory as well as stochastic modelling methods. The stochastic function integration has been reduced to summation of its ordinates and further...
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublicationQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait
PublicationQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently. In the present work we discuss biological interpretations that can be attributed to them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.
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On DoA estimation for rotating arrays using stochastic maximum likelihood approach
PublicationThe flexibility needed to construct DoA estimators that can be used with rotating arrays subject to rapid variations of the signal frequency is offered by the stochastic maximum likelihood approach. Using a combination of analytic methods and Monte Carlo simulations, we show that for low and moderate source correlations the stochastic maximum likelihood estimator that assumes noncorrelated sources has accuracy comparable to the...
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Wiktoria Wojnicz dr hab. inż.
PeopleDSc in Mechanics (in the field of Biomechanics) - Lodz Univeristy of Technology, 2019 PhD in Mechanics (in the field of Biomechanics) - Lodz Univeristy of Technology, 2009 (with distinction) List of papers (2009 - ) Wojnicz W., Wittbrodt E., Analysis of muscles' behaviour. Part I. The computational model of muscle. Acta of Bioengineering and Biomechanics, Vol. 11, No.4, 2009, s. 15-21 Wojnicz W., Wittbrodt E., Analysis of...
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublicationIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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Model studies to identify input parameters of an algorithm controlling electric supply/consumption process by underground iron ore enterprises
PublicationPurpose is the development of the research format of a mathematical model to select and assess input parameters of an algorithm controlling distribution of electric energy flows in the monitoring structure of electricity supply/ consumption by using equipment of mining enterprises engaged in underground iron ore raw materials extraction. Methods. The analytical research involved a theory of random processes adapted to the real...
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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators
PublicationWe study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L1(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure...
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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublicationThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...
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FE analysis of a coupled energetic-statistical size effect in plain concrete beams with varying material properties.
PublicationThe numerical FE investigations of a coupled energetic-statistical size effect in unnotched concrete beams of similar geometry under quasi-static three point bending were performed within elasto-plasticity with non-local softening. The stochastic FE analyses were carried out with three different beam sizes. Deterministic calculations were performed with the uniform distribution of a uniaxial tensile strength. In statistical calculations...
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Locally Adaptive Cooperative Kalman Smoothing and Its Application to Identification of Nonstationary Stochastic Systems
PublicationOne of the central problems of the stochastic approximation theory is the proper adjustment of the smoothing algorithm to the unknown, and possibly time-varying, rate and mode of variation of the estimated signals/parameters. In this paper we propose a novel locally adaptive parallel estimation scheme which can be used to solve the problem of fixed-interval Kalman smoothing in the presence of model uncertainty. The proposed solution...
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Structural Reliability Assessment Of Corroded Tanker Ship Based On Experimentally Estimated Ultimate Strength
PublicationThis work deals with the reliability assessment of a tanker ship hull structure subjected to a vertical bending moment and corrosion degradation. The progressive collapse and ultimate load carrying capacity are estimated based on experimentally tested scaled box-shaped-specimens. The translation of the strength estimate of the scaled specimen to the real tanker ship hull structure is performed based on the dimensional theory developing...
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Assessment of Wide-Sense Stationarity of an Underwater Acoustic Channel Based on a Pseudo-Random Binary Sequence Probe Signal
PublicationThe performances of Underwater Acoustic Communication (UAC) systems are strongly related to the specific propagation conditions of the underwater channel. Designing the physical layer of a reliable data transmission system requires a knowledge of channel characteristics in terms of the specific parameters of the stochastic model. The Wide-Sense Stationary Uncorrelated Scattering (WSSUS) assumption simplifies the stochastic description...
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DESIGN OF THE DUAL CONSTELLATION GPS/GALILEO MOBILE DEVICE FOR IMPROVING NAVIGATION OF THE VISUALLY IMPAIRED IN AN URBAN AREA, POLISH MARITIME RESEARCH
PublicationThe article discusses damages of essential tribological associations in crankshaft and piston systems of large power two-stroke engines used as main engines, which take place during transport tasks performed by those ships. Difficulties are named which make preventing those damages impossible, despite the fact that the technical state of engines of this type is identified with the aid of complex diagnostic systems making use of...
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IDENTIFICATION OF DAMAGES OF TRIBOLOGICAL ASSOCIATIONS IN CRANKSHAFT AND PISTON SYSTEMS OF TWO-STROKE INTERNAL COMBUSTION ENGINES USED AS MAIN PROPULSION IN SEA-GOING VESSELS AND PROPOSAL OF PROBABILISTIC DESCRIPTION OF LOADS AS CAUSES OF THESE DAMAGES
PublicationThe article discusses damages of essential tribological associations in crankshaft and piston systems of large power two-stroke engines used as main engines, which take place during transport tasks performed by those ships. Difficulties are named which make preventing those damages impossible, despite the fact that the technical state of engines of this type is identified with the aid of complex diagnostic systems making use of...
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Robust-adaptive dynamic programming-based time-delay control of autonomous ships under stochastic disturbances using an actor-critic learning algorithm
PublicationThis paper proposes a hybrid robust-adaptive learning-based control scheme based on Approximate Dynamic Programming (ADP) for the tracking control of autonomous ship maneuvering. We adopt a Time-Delay Control (TDC) approach, which is known as a simple, practical, model free and roughly robust strategy, combined with an Actor-Critic Approximate Dynamic Programming (ACADP) algorithm as an adaptive part in the proposed hybrid control...
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Quadratic stochastic operators on Banach lattices
PublicationWe study the convergence of iterates of quadratic stochastic operators that are mean monotonic. They are defined on the convex set of probability measures concentrated on a weakly compact order interval S = [0, f] of a fixed Banach lattice F. We study their regularity and identify the limits of trajectories either as the “infimum” or “supremum” of the support of initial distributions.