915 research outputs found

    Asynchronous switching control for fuzzy Markov jump systems with periodically varying delay and its application to electronic circuits

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    This article focuses on addressing the issue of asynchronous H∞ control for Takagi-Sugeno (T-S) fuzzy Markov jump systems with generally incomplete transition probabilities (TPs). The delay is assumed to vary periodically, resulting in one monotonically increasing interval and one monotonically decreasing interval during each period. Meanwhile, a new Lyapunov-Krasovskii functional (LKF) is devised, which depends on membership functions (MFs) and two looped functions formulated for the monotonic intervals. Since the modes and TPs of the original system are assumed to be unavailable, an asynchronous switching fuzzy controller on the basis of hidden Markov model is proposed to stabilize the fuzzy Markov jump systems (FMJSs) with generally incomplete TPs. Consequently, a stability criterion with improved practicality and reduced conservatism is derived, ensuring the stochastic stability and H∞ performance of the closed-loop system. Finally, this technique is employed to the tunnel diode circuit system, and a comparison example is given, which verifies the practicality and superiority of the method

    Weight Try-Once-Discard Protocol-Based L_2 L_infinity State Estimation for Markovian Jumping Neural Networks with Partially Known Transition Probabilities

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    It was the L_2 L_infinity performance index that for the first time is initiated into the discussion on state estimation of delayed MJNNs with with partially known transition probabilities, which provides a more general promotion for the estimation error.The WTOD protocol is adopted to dispatch the sensor nodes so as to effectively alleviate the updating frequency of output signals. The hybrid effects of the time delays, Markov chain, and protocol parameters are apparently reflected in the co-designed estimator which can be solved by a combination of comprehensive matrix inequalities

    Reconstructing Dynamical Systems From Stochastic Differential Equations to Machine Learning

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    Die Modellierung komplexer Systeme mit einer großen Anzahl von Freiheitsgraden ist in den letzten Jahrzehnten zu einer großen Herausforderung geworden. In der Regel werden nur einige wenige Variablen komplexer Systeme in Form von gemessenen Zeitreihen beobachtet, während die meisten von ihnen - die möglicherweise mit den beobachteten Variablen interagieren - verborgen bleiben. In dieser Arbeit befassen wir uns mit dem Problem der Rekonstruktion und Vorhersage der zugrunde liegenden Dynamik komplexer Systeme mit Hilfe verschiedener datengestützter Ansätze. Im ersten Teil befassen wir uns mit dem umgekehrten Problem der Ableitung einer unbekannten Netzwerkstruktur komplexer Systeme, die Ausbreitungsphänomene widerspiegelt, aus beobachteten Ereignisreihen. Wir untersuchen die paarweise statistische Ähnlichkeit zwischen den Sequenzen von Ereigniszeitpunkten an allen Knotenpunkten durch Ereignissynchronisation (ES) und Ereignis-Koinzidenz-Analyse (ECA), wobei wir uns auf die Idee stützen, dass funktionale Konnektivität als Stellvertreter für strukturelle Konnektivität dienen kann. Im zweiten Teil konzentrieren wir uns auf die Rekonstruktion der zugrunde liegenden Dynamik komplexer Systeme anhand ihrer dominanten makroskopischen Variablen unter Verwendung verschiedener stochastischer Differentialgleichungen (SDEs). In dieser Arbeit untersuchen wir die Leistung von drei verschiedenen SDEs - der Langevin-Gleichung (LE), der verallgemeinerten Langevin-Gleichung (GLE) und dem Ansatz der empirischen Modellreduktion (EMR). Unsere Ergebnisse zeigen, dass die LE bessere Ergebnisse für Systeme mit schwachem Gedächtnis zeigt, während sie die zugrunde liegende Dynamik von Systemen mit Gedächtniseffekten und farbigem Rauschen nicht rekonstruieren kann. In diesen Situationen sind GLE und EMR besser geeignet, da die Wechselwirkungen zwischen beobachteten und unbeobachteten Variablen in Form von Speichereffekten berücksichtigt werden. Im letzten Teil dieser Arbeit entwickeln wir ein Modell, das auf dem Echo State Network (ESN) basiert und mit der PNF-Methode (Past Noise Forecasting) kombiniert wird, um komplexe Systeme in der realen Welt vorherzusagen. Unsere Ergebnisse zeigen, dass das vorgeschlagene Modell die entscheidenden Merkmale der zugrunde liegenden Dynamik der Klimavariabilität erfasst.Modeling complex systems with large numbers of degrees of freedom have become a grand challenge over the past decades. Typically, only a few variables of complex systems are observed in terms of measured time series, while the majority of them – which potentially interact with the observed ones - remain hidden. Throughout this thesis, we tackle the problem of reconstructing and predicting the underlying dynamics of complex systems using different data-driven approaches. In the first part, we address the inverse problem of inferring an unknown network structure of complex systems, reflecting spreading phenomena, from observed event series. We study the pairwise statistical similarity between the sequences of event timings at all nodes through event synchronization (ES) and event coincidence analysis (ECA), relying on the idea that functional connectivity can serve as a proxy for structural connectivity. In the second part, we focus on reconstructing the underlying dynamics of complex systems from their dominant macroscopic variables using different Stochastic Differential Equations (SDEs). We investigate the performance of three different SDEs – the Langevin Equation (LE), Generalized Langevin Equation (GLE), and the Empirical Model Reduction (EMR) approach in this thesis. Our results reveal that LE demonstrates better results for systems with weak memory while it fails to reconstruct underlying dynamics of systems with memory effects and colored-noise forcing. In these situations, the GLE and EMR are more suitable candidates since the interactions between observed and unobserved variables are considered in terms of memory effects. In the last part of this thesis, we develop a model based on the Echo State Network (ESN), combined with the past noise forecasting (PNF) method, to predict real-world complex systems. Our results show that the proposed model captures the crucial features of the underlying dynamics of climate variability

    Decentralised sliding mode control for nonlinear interconnected systems with uncertainties

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    With the advances in science and technology, nonlinear large-scale interconnected systems have widely appeared in the real life. Traditional centralised control methods have inevitable disadvantages when they are used to deal with complex nonlinear interconnected systems with uncertainties. In connection with this, people desire to develop the novel control strategy which can be applied to complex interconnected systems. Therefore, decentralised sliding mode control (SMC) for interconnected systems has attracted great attention in related fields due to its advantages, for instance, simple structure, low cost of calculation, fast response, reduced-order sliding mode dynamics and insensitivity to matched variation of parameters and disturbances in systems. This thesis focuses on the development of decentralised SMC for nonlinear interconnected systems with uncertainties under certain assumptions. Several methods and different techniques have been considered in design of the controller to improve the robustness. The main contributions of this thesis include: • The state feedback decentralised SMC is developed for nonlinear interconnected systems with matched uncertainty and mismatched unknown interconnections. A state feedback decentralised SMC strategy, under the assumption that all system states are accessible, is proposed to attenuate the impact of the uncertainties by using bounds on uncertainties and interconnections. The bounds used in the design are fully nonlinear which provide higher applicability for different complex interconnected systems. Especially, for this fully nonlinear system, the proposed method does not need to use the technique of linearisation, which is widely used in existing work to deal with nonlinear interconnected systems with uncertainties. • The dynamic observer is applied to complex nonlinear interconnected systems with matched and mismatched uncertainties. This dynamic observer can estimate the system states which can not be achieved during the controller design. The proposed method has great identification ability with small estimated errors for the states of nonlinear interconnected systems with matched and mismatched uncertainties. It should be pointed out that the considered uncertainties of nonlinear interconnected systems have general forms, which means that the proposed method can be effectively used in more generalised nonlinear interconnected systems. • A variable structure observer-based decentralised SMC is proposed to control a class of nonlinear interconnected systems with matched and mismatched uncertainties. Based on the designed dynamic observer, a dynamic decentralised output feedback SMC using outputs and estimated states is presented to control the interconnected systems with matched and mismatched uncertainties. The nonlinear interconnections are employed in the control design to reduce the conservatism of the developed results. The bounds of the uncertainties are relaxed which are nonlinear and take more general forms. Moreover, the limitation for the interconnected system is reduced when compared with the existing results in which the proposed strategies adopt the full-order observer. Besides that, the presented method improves the robustness of nonlinear interconnected systems to be against the effects of uncertainties. This thesis also provides several numerical and practical simulations to demonstrate the effectiveness of the proposed decentralised SMC for nonlinear interconnected systems with matched uncertainty, mismatched uncertainty and nonlinear interconnections

    Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities

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    The issue of extended dissipative analysis for neural networks (NNs) with additive time-varying delays (ATVDs) is examined in this research. Some less conservative sufficient conditions are obtained to ensure the NNs are asymptotically stable and extended dissipative by building the agumented Lyapunov-Krasovskii functional, which is achieved by utilizing some mathematical techniques with improved integral inequalities like auxiliary function-based integral inequalities (gives a tighter upper bound). The present study aims to solve the H,L2L H_{\infty}, L_2-L_{\infty} , passivity and (Q,S,R) (Q, S, R) -γ \gamma -dissipativity performance in a unified framework based on the extended dissipativity concept. Following this, the condition for the solvability of the designed NNs with ATVDs is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach were demonstrated through four numerical examples

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Extended Dissipative Filter for Delayed T-S Fuzzy Network of Stochastic System with Packet Loss

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    This research investigates a time-varying delay-based adaptive event-triggered dissipative filtering problem for the interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy networked stochastic system. The concept of extended dissipativity is used to solve the ,  and dissipative performances for (IT-2) T-S fuzzy stochastic systems in a unified manner. Data packet failures and latency difficulties are taken into account while designing fuzzy filters. An adaptive event-triggered mechanism is presented to efficiently control network resources and minimise excessive continuous monitoring while assuring the system’s efficiency with extended dissipativity. A new adaptive event triggering scheme is proposed which depends on the dynamic error rather than pre-determined constant threshold. A new fuzzy stochastic Lyapunov-Krasovskii Functional (LKF) using fuzzy matrices with higher order integrals is built based on the Lyapunov stability principle for mode-dependent filters. Solvability of such LKF leads to the formation of appropriate conditions in the form of linear matrix inequalities, ensuring that the resulting error mechanism is stable. In order to highlight the utility and perfection of the proposed technique, an example is presented

    Ghost In the Grid: Challenges for Reinforcement Learning in Grid World Environments

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    The current state-of-the-art deep reinforcement learning techniques require agents to gather large amounts of diverse experiences to train effective and general models. In addition, there are also many other factors that have to be taken into consideration: for example, how the agent interacts with its environment; parameter optimization techniques; environment exploration methods; and finally the diversity of environments that is provided to an agent. In this thesis, we investigate several of these factors. Firstly we introduce Griddly, a high-performance grid-world game engine that provides a state-of-the-art combination of high performance and flexibility. We demonstrate that grid worlds provide a principled and expressive substrate for fundamental research questions in reinforcement learning, whilst filtering out noise inherent in physical systems. We show that although grid-worlds are constructed with simple rules-based mechanics, they can be used to construct complex open-ended, and procedurally generated environments. We improve upon Griddly with GriddlyJS, a web-based tool for designing and testing grid-world environments for reinforcement learning research. GriddlyJS provides a rich suite of features that assist researchers in a multitude of different learning approaches. To highlight the features of GriddlyJS we present a dataset of 100 complex escape-room puzzle levels. In addition to these complex puzzle levels, we provide human-generated trajectories and a baseline policy that can be run in a web browser. We show that this tooling enables significantly faster research iteration in many sub-fields. We then explore several areas of RL research that are made accessible by the features introduced by Griddly: Firstly, we explore learning grid-world game mechanics using deep neural networks. The {\em neural game engine} is introduced which has competitive performance in terms of sample efficiency and predicting states accurately over long time horizons. Secondly, {\em conditional action trees} are introduced which describe a method for compactly expressing complex hierarchical action spaces. Expressing hierarchical action spaces as trees leads to action spaces that are additive rather than multiplicative over the factors of the action space. It is shown that these compressed action spaces reduce the required output size of neural networks without compromising performance. This makes the interfaces to complex environments significantly simpler to implement. Finally, we explore the inherent symmetry in common observation spaces, using the concept of {\em geometric deep learning}. We show that certain geometric data augmentation methods do not conform to the underlying assumptions in several training algorithms. We provide solutions to these problems in the form of novel regularization functions and demonstrate that these methods fix the underlying assumptions

    Nonlinear Systems

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    Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

    Operational Research: methods and applications

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    This is the final version. Available on open access from Taylor & Francis via the DOI in this recordThroughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes
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