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Journal articles on the topic 'Mixed Logical Dynamical Systems'

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Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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1

Frick, Damian, Alexander Domahidi, and Manfred Morari. "Embedded optimization for mixed logical dynamical systems." Computers & Chemical Engineering 72 (January 2015): 21–33. http://dx.doi.org/10.1016/j.compchemeng.2014.06.005.

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2

Bernardo, C., and F. Vasca. "A Mixed Logical Dynamical Model of the Hegselmann–Krause Opinion Dynamics." IFAC-PapersOnLine 53, no. 2 (2020): 2826–31. http://dx.doi.org/10.1016/j.ifacol.2020.12.952.

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3

Misik, Stefan, Jakub Arm, and Zdenek Bradac. "Formulation and Simulation of Receding Horizon Control over Mixed Logical Dynamical System." IFAC-PapersOnLine 51, no. 6 (2018): 390–95. http://dx.doi.org/10.1016/j.ifacol.2018.07.185.

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4

Araújo Elias, Tiago, Paulo Renato Costa Mendes, and Júlio Elias Normey‐Rico. "Mixed Logical Dynamical Nonlinear Model Predictive Controller for Large‐Scale Solar Fields." Asian Journal of Control 21, no. 4 (January 17, 2019): 1881–91. http://dx.doi.org/10.1002/asjc.1967.

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5

Bemporad, A. "Efficient Conversion of Mixed Logical Dynamical Systems Into an Equivalent Piecewise Affine Form." IEEE Transactions on Automatic Control 49, no. 5 (May 2004): 832–38. http://dx.doi.org/10.1109/tac.2004.828315.

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6

Zanma, Tadanao, Keizo Fuke, Shang Chang Ma, and Muneaki Ishida. "Simultaneous identification of piecewise affine systems and number of subsystems using mixed logical dynamical systems theory." Electronics and Communications in Japan 91, no. 5 (May 2008): 1–10. http://dx.doi.org/10.1002/ecj.10109.

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7

NAKAO, Shogo, and Toshimitsu USHIO. "Self-Triggered Predictive Control with Time-Dependent Activation Costs of Mixed Logical Dynamical Systems." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E97.A, no. 2 (2014): 476–83. http://dx.doi.org/10.1587/transfun.e97.a.476.

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8

Zanma, Tadanao, Keizo Fuke, Shang Chang Ma, and Muneaki Ishida. "Simultaneous Identification of PieceWise Affine Systems and Number of Subsystems Using Mixed Logical Dynamical System Theory." IEEJ Transactions on Electronics, Information and Systems 127, no. 8 (2007): 1251–58. http://dx.doi.org/10.1541/ieejeiss.127.1251.

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9

Zanma, Tadanao, Shinya Akiba, Koki Hoshikawa, and Kang-Zhi Liu. "Cruise Control for a Two-Wheeled Mobile Vehicle Using Its Mixed Logical Dynamical System Model." IEEE Transactions on Industrial Informatics 16, no. 5 (May 2020): 3145–56. http://dx.doi.org/10.1109/tii.2019.2910280.

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10

Ma, H., S. Wei, L. Li, T. Lin, and S. Chen. "Mixed logical dynamical model of the pulsed gas tungsten arc welding process with varied gap." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 225, no. 2 (March 2011): 270–80. http://dx.doi.org/10.1243/09596518jsce1016.

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11

Olama, Alireza, Mokhtar Shasadeghi, Amin Ramezani, Mostafa Khorramizadeh, and Paulo R. C. Mendes. "Ellipsoidal Lyapunov-based hybrid model predictive control for mixed logical dynamical systems with a recursive feasibility guarantee." Transactions of the Institute of Measurement and Control 41, no. 9 (October 11, 2018): 2475–87. http://dx.doi.org/10.1177/0142331218801126.

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This paper proposes an ellipsoidal hybrid model predictive control approach to solve the robust stability problem of uncertain hybrid dynamical systems modelled by the mixed logical dynamical framework. In this approach, the traditional terminal equality constraint is replaced by an ellipsoid that results in a maximal positive invariant set for the closed-loop system. Then, a Lyapunov decreasing condition along with the robustness criterion is introduced to the optimization problem to achieve the robust stability of the closed-loop system. As the main advantages, the ellipsoidal terminal set proposed in this paper attains a larger domain of attraction along with the recursive feasibility guarantee. Moreover, the stability and robustness constraints are achieved by a lower prediction horizon, which leads to a smaller dimension optimization problem. In addition, to reduce the computational complexity of the corresponding optimization problem, a suboptimal version of the proposed algorithm is introduced. Finally, numerical and car suspension system examples show the capabilities of the proposed method.

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12

Hejri, Mohammad, Alessandro Giua, and Hossein Mokhtari. "On the complexity and dynamical properties of mixed logical dynamical systems via an automaton-based realization of discrete-time hybrid automaton." International Journal of Robust and Nonlinear Control 28, no. 16 (August 2, 2018): 4713–46. http://dx.doi.org/10.1002/rnc.4278.

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13

Hirana, K., T. Suzuki, and S. Okuma. "Formulation of Peg-in-Hole Motion Based on Mixed Logical Dynamical System and Optimal Planning." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2002 (2002): 31. http://dx.doi.org/10.1299/jsmermd.2002.31_1.

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14

Hammi, Yosra, Nadia Zanzouri, and Mekki Ksouri. "Passive Fault Tolerant Control of Motorboat System." International Journal of Energy 15 (November 21, 2021): 110–15. http://dx.doi.org/10.46300/91010.2021.15.17.

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A hybrid passive control strategy is developed for a class of hybrid systems modeled by Mixed Logical Dynamical (MLD) approach. It allows to model different operating modes of the system and constraints. We proposed using the MPC for control system .The passive controller is used to take in account the actuator failure and the optimization problem is transformed into a mixed-integer quadratic programming problem (MIQP). The considering fault-tolerance capabilities are developed and discussed. The proposed method is illustrated by a motorboat system.

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15

Moness, Mohammed, and Ahmed Mahmoud Moustafa. "Hybrid modelling and predictive control of utility-scale variable-speed variable-pitch wind turbines." Transactions of the Institute of Measurement and Control 42, no. 9 (January 15, 2020): 1724–39. http://dx.doi.org/10.1177/0142331219895117.

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Wind energy has proven to be the highest reliable source of renewables due to the maturity of the technology. Wind turbine (WT) systems are complex systems with undergoing development process that requires innovative methods of design and control. In this paper, WTs are studied through hybrid systems framework. Hybrid models of WT are extracted with representable dynamics from nonlinear complex design code. The WT model is formulated into a mixed-logical dynamical model (MLD) and a piecewise affine (PWA) model. Then, a receding horizon control strategy is applied to WT hybrid model resulting in a hybrid model predictive control (HMPC) with mixed-integer programming (MIP) problem. The performance of the proposed controller is compared against the baseline controller within a simulation environment for the National Renewable Energy Laboratory (NREL) 5MW benchmark WT as a case study. The analysis and investigation of HMPC highlight its capability as a potential tool for exploiting the control objectives of WT systems.

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16

Hirana, Kazuaki, Tatsuya Suzuki, and Shigeru Okuma. "Formulation and motion planning of the peg-in-hole task with mixed logical dynamical system theory." Advanced Robotics 18, no. 3 (January 2004): 315–30. http://dx.doi.org/10.1163/156855304322972468.

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17

Zhang, Yan, Xiaoli Chu, Yang Liu, and Yongqiang Liu. "A Modelling and Control Approach for a Type of Mixed Logical Dynamical System Using in Chilled Water System of Refrigeration System." Mathematical Problems in Engineering 2019 (March 20, 2019): 1–12. http://dx.doi.org/10.1155/2019/7131380.

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The chilled water system of central air conditioning is a typical hybrid system. The dynamic adjustment of cooling capacity based on hybrid system can achieve accurate temperature control and real-time energy saving. Mixed logical dynamical (MLD) systems have advantage for solving constrained optimization problems of this type of case by numerical methods. This paper proposes a novel modified type of MLD system, which enhances the model applicability and improves the switching flexibility and control effect for the framework. In order to meet the needs of cooling capacity and energy saving, the optimal control problem is transformed as MIQP problem by defined performance index. As a numeral example of application, the model and control method is used in pumps group control for variable water volume in chilled water system of central air conditioning. At last, the dynamic and energy-saving effects of the system are simulated, which shows the ideal control results.

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18

Huang, Liangyu, and Yimin Lu. "Hybrid Modeling Method and Bifurcation Characteristics Analysis for Buck Converter with Constant Power Load." Mathematical Problems in Engineering 2019 (March 6, 2019): 1–10. http://dx.doi.org/10.1155/2019/9342064.

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We establish a novel hybrid model of a continuous conduction mode buck converter with a constant power load based on the mixed logical dynamical modeling method. Based on the proposed model, the influence of the constant power load’s negative impedance (RCPL) on the dynamics of the buck converter with a constant power load is studied by computing bifurcation diagrams and the spectrum of the largest Lyapunov exponents with the variation of the absolute value of RCPL. Numerical results show that the system’s bifurcations exhibit two different types of behavior, namely, Hopf bifurcations and state jumping. Moreover, the accuracy and effectiveness of the established mathematical model are verified via simulation and experimental results. Because of including different discrete mappings of the system exhibited in different working modes in a unified model, the proposed hybrid model solves the problem of choosing different discrete mappings according to different working models. That is, the hybrid model in this paper provides a new unified model for future research on the dynamic properties and design of controllers for such systems.

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19

Zhu, Xinjian, Chunyue Song, Jun Zhao, and Zuhua Xu. "A Semi-Continuous PWA Model Based Optimal Control Method for Nonlinear Systems." Processes 8, no. 2 (February 4, 2020): 170. http://dx.doi.org/10.3390/pr8020170.

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To alleviate the mode mismatch of multiple model methods for nonlinear systems when completely discrete dynamical equations are adopted, a semi-continuous piecewise affine (SCPWA) model based optimal control method is proposed. Firstly, a SCPWA model is constructed where modes evolve in continuous time and continuous states evolve in discrete time. Thanks to this model, a piecewise affine (PWA) system can switch at any time instant whereas mode switching only occurs at sample instants when a completely discrete PWA model is adopted, which improves the prediction accuracy of multi-models. Secondly, the switching condition is relaxed such that operating subspaces have overlaps and switching condition parameters are introduced. As a consequence, an optimal control problem with fixed mode switching sequence is established. Finally, a SCPWA model based model predictive control (MPC) policy is designed for nonlinear systems. The convergence of the MPC algorithm is proved. Compared with widely used mixed logical dynamic (MLD) model based methods, the proposed method not only alleviates mode mismatch, but also lightens the computing burden, hence improves the control performance and reduces the computation time. Some numerical examples are provided as well to show the efficiency of the method.

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20

Wei, Tao, and Liu Zhiqiang. "Damping Multimode Switching Control of Semiactive Suspension for Vibration Reduction in a Wheel Loader." Shock and Vibration 2019 (March 21, 2019): 1–11. http://dx.doi.org/10.1155/2019/4535072.

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The aim of this work is the control design and analysis of a semiactive axle suspension system for vibration reduction in a wheel loader. Unlike a traditional semiactive suspension system with continuously adjustable shock absorber, in this work, a novel axle suspension with multiple damping modes is proposed for the wheel loader. The multimode switching damping characteristics are achieved by just changing the discrete statuses of two high-speed switch electromagnetic valves, which makes the damping adjustment simpler and more reliable. However, because of the existence of discrete events, i.e., the on-off statuses of switch electromagnetic valves, the axle suspension proposed for the wheel loader poses a challenging hybrid control problem. To solve this problem, the mixed logical dynamical (MLD) modeling approach for hybrid systems is applied to model the dynamic characteristics of the system damping control procedure. Using this model, a hybrid model predictive control (HMPC) strategy is further designed, which can determine the optimal switching sequences of the discrete damping modes according to the axle suspension performance indices. Finally, to verify the effectiveness of the proposed semiactive axle suspension with multiple damping modes and its control approach, simulation analyses are conducted.

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21

Wiegand, C., C. Hedayat, and U. Hilleringmann. "Non-linear behaviour of charge-pump phase-locked loops." Advances in Radio Science 8 (October 1, 2010): 161–66. http://dx.doi.org/10.5194/ars-8-161-2010.

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Abstract. The analysis of the mixed analogue and digital structure of charge-pump phase-locked loops (CP-PLL) is a challenge in modelling and simulation. In most cases the system is designed and characterized using its continuous linear model or its discrete linear model neglecting its non-linear switching behaviour. I.e., the time-varying model is approximated by a time-invariant representation using its average dynamics. Depending on what kind of phase detector is used, the scopes of validity of these approximations are different. Here, a preeminent characterization and simulation technique based on the systems event-driven feature is presented, merging the logical and analogue inherent characteristics of the system. In particular, the high-grade non-linear locking process and the dead-zone are analyzed.

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22

Sarwary, Mohammad, Mirza AmirkhaniT, and Hassan Malistani. "An Attempt for Construction of Carbonate Platform Geometry from Devonian Hajigak Formation, Central Afghanistan, with the Help of Facies Analysis and Petrography." Academic Journal of Research and Scientific Publishing 3, no. 31 (November 2021): 49–73. http://dx.doi.org/10.52132/ajrsp.e.2021.31.4.

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The subject of sedimentology fundamentally remained subdivided into two sectors viz. siliciclastic and carbonate with the understanding that these two systems are mutually dissociative in terms of their genesis. Even in the highly referred textbooks, siliciclastics and carbonates are always discussed in separate sections. Presumably, the limited occurrences of mixed siliciclastic-carbonate sediments in nature are because of constraining effects that siliciclastics have on carbonate-secreting organisms; the two sediments rarely found mutually associated in nature. Although the mixed carbonate-siliciclastic sediments are subordinate in occurrence, their presence in some instances proved that they do not represent any geological oddity. Rather, their sediment logical history may tell us a great deal about the dynamics and interactions of facies, paleoecologies of many carbonate-secreting organisms, and tectonic histories of depositional basins. Keeping this in mind, the present study attempted to recognize and draw the paleoenvironmental conditions and processes of the Devonian Hajigak Formation, Afghanistan by means of detailed facies analysis and petrographical signatures. An attempt has also been made to characterize sandstone wedges that punctuate the carbonate succession and some variable deposits of shales and marls.

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23

Niklas, Karl J. "Modeling fossil plant form-function relationships: A critique." Paleobiology 26, S4 (2000): 289–304. http://dx.doi.org/10.1017/s009483730002697x.

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Attempts to model form-function relationships for fossil plants rely on the facts that the physiological and structural requirements for plant growth, survival, and reproductive success are remarkably similar for the majority of extant and extinct species regardless of phyletic affiliation and that most of these requirements can be quantified by means of comparatively simple mathematical expressions drawn directly from the physical and engineering sciences. Owing in part to the advent and rapid expansion of computer technologies, the number of fossil plant form-function models has burgeoned in the last two decades and encompasses every level of biological organization ranging from molecular self-assembly to ecological and evolutionary dynamics. This recent and expansive interest in modeling fossil plant form-function relationships is discussed in the context of the general philosophy of modeling past biological systems and how the reliability of models can be examined (i.e., direct experimental manipulation or observation of the system being modeled). This philosophy is illustrated and methods of validating models are critiqued in terms of four models drawn from the author's work (the quantification of wind-induced stem bending stresses, wind pollination efficiency of early Paleozoic ovulate reproductive structures, population dynamics and species extinction in monotypic and “mixed” communities, and the adaptive radiation of early vascular land plants). The assumptions and logical (mathematical) consequences (predictions) of each model are broadly outlined, and, in each case, the model is shown to be overly simplistic despite its ability to predict the general or particular behavior or operation of the system modeled. Nonetheless, these four models, which illustrate some of pros and cons of modeling fossil form-function relationships, are argued to be pedagogically useful because, like all models, they expose the internal logical consistency of our basic assumptions about how organic form and function interrelate.

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24

Ebrahimzadeh, Abolfazl. "Logical entropy of quantum dynamical systems." Open Physics 14, no. 1 (January 1, 2016): 1–5. http://dx.doi.org/10.1515/phys-2015-0058.

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AbstractThis paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.

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25

Markechová, Dagmar, and Beloslav Riečan. "Logical Entropy of Fuzzy Dynamical Systems." Entropy 18, no. 4 (April 23, 2016): 157. http://dx.doi.org/10.3390/e18040157.

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26

Frischat, S. D., and E. Doron. "Dynamical tunneling in mixed systems." Physical Review E 57, no. 2 (February 1, 1998): 1421–43. http://dx.doi.org/10.1103/physreve.57.1421.

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27

Ebrahimzadeh, Abolfazl, Zahra Giski, and Dagmar Markechová. "Logical Entropy of Dynamical Systems—A General Model." Mathematics 5, no. 1 (January 6, 2017): 4. http://dx.doi.org/10.3390/math5010004.

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28

Bortakovskii, A. S. "Necessary optimality conditions for control of logical-dynamical systems." Journal of Computer and Systems Sciences International 46, no. 6 (December 2007): 854–71. http://dx.doi.org/10.1134/s1064230707060020.

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29

Peters, Karsten, and Ulrich Parlitz. "Hybrid Systems Forming Strange Billiards." International Journal of Bifurcation and Chaos 13, no. 09 (September 2003): 2575–88. http://dx.doi.org/10.1142/s0218127403008090.

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Hybrid dynamical systems consist of piecewise defined continuous time evolution processes interfaced with some logical or decision making process. These switches between different evolutions are triggered if the continuous state of the system reaches thresholds in state space. In the present work we investigate hybrid systems forming a special type of dynamical systems, so-called strange billiards. They show a rich variety of dynamical behavior including some unusual bifurcations and chaos, even if the continuous part of the system evolution is just linear. By means of Poincaré map techniques we discuss different dynamical behaviors. Applications to the simulation of manufacturing systems and consequences for their dynamical behavior are outlined.

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30

Bin-Mohsin, Bandar, Muhammad Aslam Noor, Khalida Inayat Noor, and Rafia Latif. "Resolvent dynamical systems and mixed variational inequalities." Journal of Nonlinear Sciences and Applications 10, no. 06 (June 7, 2017): 2925–33. http://dx.doi.org/10.22436/jnsa.010.06.07.

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31

Noor, Muhammad Aslam. "Resolvent dynamical systems for mixed variational inequalities." Korean Journal of Computational & Applied Mathematics 9, no. 1 (January 2002): 15–26. http://dx.doi.org/10.1007/bf03012337.

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32

Wang, Gang. "Automatical Knowledge Representation of Logical Relations by Dynamical Neural Network." Journal of Intelligent Systems 26, no. 4 (September 26, 2017): 625–39. http://dx.doi.org/10.1515/jisys-2016-0101.

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AbstractCurrently, most artificial neural networks (ANNs) represent relations, such as back-propagation neural network, in the manner of functional approximation. This kind of ANN is good at representing the numeric relations or ratios between things. However, for representing logical relations, these ANNs have disadvantages because their representation is in the form of ratio. Therefore, to represent logical relations directly, we propose a novel ANN model called probabilistic logical dynamical neural network (PLDNN). Inhibitory links are introduced to connect exciting links rather than neurons so as to inhibit the connected exciting links conditionally to make them represent logical relations correctly. The probabilities are assigned to the weights of links to indicate the belief degree in logical relations under uncertain situations. Moreover, the network structure of PLDNN is less limited in topology than traditional ANNs, and it is dynamically built completely according to the data to make it adaptive. PLDNN uses both the weights of links and the interconnection structure to memorize more information. The model could be applied to represent logical relations as the complement to numeric ANNs.

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33

Phani, Vinod, Cyril Joseph, and Satya Narayan Agarwal. "Modeling of Mixed Logical Dynamical (MLD) Model to Hybrid Three Tank System." IJIREEICE 3, no. 5 (May 15, 2015): 211–12. http://dx.doi.org/10.17148/ijireeice.2015.3551.

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34

Asano, Nobuhiro, Tadanao Zanma, and Muneaki Ishida. "Optimal Control of DC-DC Converter using Mixed Logical Dynamical System Model." IEEJ Transactions on Industry Applications 127, no. 3 (2007): 339–46. http://dx.doi.org/10.1541/ieejias.127.339.

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35

Vrbanc, Filip, Filip Rukavina, Vinko Lešić, and Mario Vašak. "Mixed Logical Dynamical Modelling of a Stratified Storage with Phase-Change Material." IFAC-PapersOnLine 55, no. 20 (2022): 145–50. http://dx.doi.org/10.1016/j.ifacol.2022.09.086.

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36

Huang, Kun, Yongchao Zhang, and Fan Yu. "Predictive controller design for electromagnetic suspension based on mixed logical dynamical model." Journal of Vibration and Control 18, no. 8 (September 23, 2011): 1165–76. http://dx.doi.org/10.1177/1077546311409609.

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37

Lemmon, Michael, and Panos J. Antsaklis. "Inductively inferring valid logical models of continuous-state dynamical systems." Theoretical Computer Science 138, no. 1 (February 1995): 201–10. http://dx.doi.org/10.1016/0304-3975(94)00148-c.

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38

Rudenko, E. A. "Optimal recurrent logical-dynamical finite memory filter." Journal of Computer and Systems Sciences International 56, no. 4 (July 2017): 607–15. http://dx.doi.org/10.1134/s106423071704013x.

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39

Markechová, Dagmar. "Tsallis Entropy of Fuzzy Dynamical Systems." Mathematics 6, no. 11 (November 18, 2018): 264. http://dx.doi.org/10.3390/math6110264.

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This article deals with the mathematical modeling of Tsallis entropy in fuzzy dynamical systems. At first, the concepts of Tsallis entropy and Tsallis conditional entropy of order where is a positive real number not equal to 1, of fuzzy partitions are introduced and their mathematical behavior is described. As an important result, we showed that the Tsallis entropy of fuzzy partitions of order satisfies the property of sub-additivity. This property permits the definition of the Tsallis entropy of order of a fuzzy dynamical system. It was shown that Tsallis entropy is an invariant under isomorphisms of fuzzy dynamical systems; thus, we acquired a tool for distinguishing some non-isomorphic fuzzy dynamical systems. Finally, we formulated a version of the Kolmogorov–Sinai theorem on generators for the case of the Tsallis entropy of a fuzzy dynamical system. The obtained results extend the results provided by Markechová and Riečan in Entropy, 2016, 18, 157, which are particularized to the case of logical entropy.

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40

Rahman, Aminur, Ian Jordan, and Denis Blackmore. "Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2209 (January 2018): 20170111. http://dx.doi.org/10.1098/rspa.2017.0111.

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It has been observed through experiments and SPICE simulations that logical circuits based upon Chua’s circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.

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41

Chu, Tianguang, and Lin Huang. "Mixed monotone decomposition of dynamical systems with application." Chinese Science Bulletin 43, no. 14 (July 1998): 1171–75. http://dx.doi.org/10.1007/bf02883218.

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42

Sirmatel, Isik Ilber, and Nikolas Geroliminis. "Mixed logical dynamical modeling and hybrid model predictive control of public transport operations." Transportation Research Part B: Methodological 114 (August 2018): 325–45. http://dx.doi.org/10.1016/j.trb.2018.06.009.

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43

Kong, Xiangshan, Qilong Sun, and Haitao Li. "Survey on Mathematical Models and Methods of Complex Logical Dynamical Systems." Mathematics 10, no. 20 (October 11, 2022): 3722. http://dx.doi.org/10.3390/math10203722.

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Logical dynamical systems (LDSs) have wide applications in gene regulation, game theory, digital circuits, and so on. In LDSs, phenomena such as impulsive effect, time delays, and asynchronous behavior are not negligible, which generate complex LDSs. This paper presents a detailed survey on models and methods of investigating LDSs. Firstly, some preliminary results on LDSs and semi-tensor product (STP) method are presented. Secondly, some new developments on modeling complex LDSs are summarized, including switched LDSs, probabilistic LDSs, delayed LDSs, LDSs with impulsive effects, asynchronous LDSs, constrained LDSs, and implicit LDSs. Finally, the control design techniques of LDSs are reviewed, including reachable set approach, sampled-data control, event-triggered control, and control Lyapunov function method.

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44

Wu, Yuhu, and Tielong Shen. "Policy Iteration Algorithm for Optimal Control of Stochastic Logical Dynamical Systems." IEEE Transactions on Neural Networks and Learning Systems 29, no. 5 (May 2018): 2031–36. http://dx.doi.org/10.1109/tnnls.2017.2661863.

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45

Rudenko, E. A. "An optimal discrete nonlinear logical-dynamical filter-predictor." Journal of Computer and Systems Sciences International 52, no. 3 (May 2013): 354–64. http://dx.doi.org/10.1134/s1064230713030131.

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46

Chu, Moody T. "Linear algebra algorithms as dynamical systems." Acta Numerica 17 (April 25, 2008): 1–86. http://dx.doi.org/10.1017/s0962492906340019.

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Any logical procedure that is used to reason or to infer either deductively or inductively, so as to draw conclusions or make decisions, can be called, in a broad sense, a realization process. A realization process usually assumes the recursive form that one state develops into another state by following a certain specific rule. Such an action is generally formalized as a dynamical system. In mathematics, especially for existence questions, a realization process often appears in the form of an iterative procedure or a differential equation. For years researchers have taken great effort to describe, analyse, and modify realization processes for various applications.The thrust in this exposition is to exploit the notion of dynamical systems as a special realization process for problems arising from the field of linear algebra. Several differential equations whose solutions evolve in submanifolds of matrices are cast in fairly general frameworks, of which special cases have been found to afford unified and fundamental insights into the structure and behaviour of existing discrete methods and, now and then, suggest new and improved numerical methods. In some cases, there are remarkable connections between smooth flows and discrete numerical algorithms. In other cases, the flow approach seems advantageous in tackling very difficult open problems. Various aspects of the recent development and application in this direction are discussed in this paper.

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CHEN, Gan, Toshiharu SUGIE, Toru FUJINAKA, and Hiroshi SHIBATA. "Mixed-^|^mu; Analysis for Dynamical Systems using Descriptor Form." Transactions of the Society of Instrument and Control Engineers 36, no. 5 (2000): 402–8. http://dx.doi.org/10.9746/sicetr1965.36.402.

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Pokrovskii, A. V., A. J. Kent, and J. G. McInerney. "Mixed moments of random mappings and chaotic dynamical systems." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 456, no. 2002 (October 8, 2000): 2465–87. http://dx.doi.org/10.1098/rspa.2000.0621.

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Khan, Mohammad Ali. "Mixed Synchronization Scheme for Coupled Different Dimensional Dynamical Systems." International Journal of Applied and Computational Mathematics 3, no. 3 (June 24, 2016): 2687–94. http://dx.doi.org/10.1007/s40819-016-0197-0.

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Sun, XiaoQiang, Long Chen, ShaoHua Wang, and Xing Xu. "Vehicle height control of electronic air suspension system based on mixed logical dynamical modelling." Science China Technological Sciences 58, no. 11 (June 16, 2015): 1894–904. http://dx.doi.org/10.1007/s11431-015-5861-9.

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