This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear syst...This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.展开更多
1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved....1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).展开更多
Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are co...Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.展开更多
The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory...The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory of oscillatory matrix, the signoscillatory property of stiffness matrices of this system was proved, and the necessary and sufficient condition for the system to be positive was obtained completely.展开更多
Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive a...Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.展开更多
In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov fu...In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.展开更多
Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic ...Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear （2 ＋ 1） dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.展开更多
The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active be...The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.展开更多
This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an e...This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.展开更多
This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equiv...This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.展开更多
This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system wi...This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium.Through phase portrait,bifurcation diagrams,and largest Lyapunov exponents,it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors.Also,different tests are used to confirm the existence of chaos,such as 0-1 test and C0 complexity.In addition,the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique.Furthermore,based on the fractional linearization method,a one-dimensional controller to stabilize the new system is proposed.Numerical results are presented to validate the findings of the paper.展开更多
This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetit...This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetitive processes is used to develop formulas for gain matrices design, together with convergent conditions in terms of linear matrix inequalities. An extension to deal with model uncertainty of the polytopic or norm bounded form is also developed and an illustrative example is given.展开更多
In this paper, H ∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a ...In this paper, H ∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H ∞ performance indices is induced, and then a strategy for H ∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H ∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach. Keywords Multi-time-delay - discrete time system - LMI - delay-dependent - H ∞ control Bai-Da Qu received B. S. degree in electrical automation from Fuxin Mining Institute, China in 1982, M. Eng. degree from Hefei University of Polytechnology in 1990, and Ph.D from Northerneastern University in 1999. He was an electro-mechanical engineer at Erdaohezi Mine, Heilongjiang, China from 1982 to 1990, a Lecturer, Senior Engineer, Associate Professor and Professor in Shenyang Institue of Technology from 1990 to 2002. He is currently a professor in Communication and Control Engineering School, Southern Yangtze University. His research interests include control theory and applications (robust control, H ∞ control, time-delay systems, complex systems), system engineering (modeling, analysis and simulation, MIS,CMIS), power-electronics and electrical driving, signal detecting and process, industrial automation.展开更多
In this paper, we study the nonlinear discrete systems and obtain several lyapunov inequalities for them. Then we give the application for lyapunov inequality.
A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular mo...A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular model, called Forna- sini-Marchesini (FM) second model was proposed by Fornasini and Marchesini in 1978. The aim of this paper is to present a survey of the existing literature on the stability of FM second model.展开更多
This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New line...This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.展开更多
A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This ...A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This equation presents arbitrarily nearest-neighbor nonlinearities. We analyze the properties of such model both in connection to their modulational stability, as well as in regard to the generation of intrinsic localized modes. We present a generalized discrete Lange-Newell criterion. Numerical simulations are performed and we show that discrete breathers are generated through modulational instability.展开更多
The flexible satellite batch production line is a complex discrete production system with multiple cross-disciplinary fields and mixed serial parallel tasks.As the source of the satellite batch production line process...The flexible satellite batch production line is a complex discrete production system with multiple cross-disciplinary fields and mixed serial parallel tasks.As the source of the satellite batch production line process,the warehousing system has urgent needs such as uncertain production scale and rapid iteration and optimization of business processes.Therefore,the requirements and architecture of complex discrete warehousing systems such as flexible satellite batch production lines are studied.The physical system of intelligent equipment is abstracted as a digital model to form the underlying module,and a digital fusion framework of“business domain+middleware platform+intelligent equipment information model”is constructed.The granularity of microservice splitting is calculated based on the dynamic correlation relationship between user access instances and database table structures.The general warehousing functions of the platform are divided to achieve module customization,addition,and configuration.An open discrete warehousing system based on microservices is designed.Software architecture and design develop complex discrete warehousing systems based on the SpringCloud framework.This architecture achieves the decoupling of business logic and physical hardware,enhances the maintainability and scalability of the system,and greatly improves the system’s adaptability to different complex discrete warehousing business scenarios.展开更多
This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density...This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density of prey species with interval parameters.The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature.The equilibria of the model are obtained,and the dynamic behaviours of the proposed system are examined.Simulations of the model are performed for different parameters of the model.Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.Our study,through analytical derivation and numerical example,presents the effect of refuge on population dynamics under imprecise biological parameters.展开更多
With the development of cyber-physical systems,system security faces more risks from cyber-attacks.In this work,we study the problem that an external attacker implements covert sensor and actuator attacks with resourc...With the development of cyber-physical systems,system security faces more risks from cyber-attacks.In this work,we study the problem that an external attacker implements covert sensor and actuator attacks with resource constraints(the total resource consumption of the attacks is not greater than a given initial resource of the attacker)to mislead a discrete event system under supervisory control to reach unsafe states.We consider that the attacker can implement two types of attacks:One by modifying the sensor readings observed by a supervisor and the other by enabling the actuator commands disabled by the supervisor.Each attack has its corresponding resource consumption and remains covert.To solve this problem,we first introduce a notion of combined-attackability to determine whether a closedloop system may reach an unsafe state after receiving attacks with resource constraints.We develop an algorithm to construct a corrupted supervisor under attacks,provide a verification method for combined-attackability in polynomial time based on a plant,a corrupted supervisor,and an attacker's initial resource,and propose a corresponding attack synthesis algorithm.The effectiveness of the proposed method is illustrated by an example.展开更多
基金supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Research on model order reduction methods based on the discrete orthogonal polynomials”(2023D01C163)The Tianchi Talent Introduction Plan Project of Xinjiang Uygur Autonomous Region of China“Research on orthogonal decomposition model order reduction methods for discrete control systems”.
文摘This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.
文摘1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).
基金Supported by the Science and Technology Plan Projects of the Educational Department of Shandong Province of China under Grant No. J08LI08
文摘Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.
基金Project supported by the National Natural Science Foundation of China (No.60034010)
文摘The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory of oscillatory matrix, the signoscillatory property of stiffness matrices of this system was proved, and the necessary and sufficient condition for the system to be positive was obtained completely.
基金Project supported by the National Natural Science Foundation of China (Nos.10372054 and 70431002)
文摘Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.
基金The project is supported by Henan Province Natural Science Fund
文摘In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.
基金the National Natural Science Foundation of China (10461006)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region (NJZZ07031)+1 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region (200408020103)the Natural Science Research Program of Inner Mongolia Normal University (QN005023)
文摘Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear （2 ＋ 1） dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.
文摘The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.
文摘This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.
文摘This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.
基金The author Adel Ouannas was supported by the Directorate General for Scientific Research and Technological Development of Algeria.The author Shaher Momani was supported by Ajman University in UAE.
文摘This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium.Through phase portrait,bifurcation diagrams,and largest Lyapunov exponents,it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors.Also,different tests are used to confirm the existence of chaos,such as 0-1 test and C0 complexity.In addition,the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique.Furthermore,based on the fractional linearization method,a one-dimensional controller to stabilize the new system is proposed.Numerical results are presented to validate the findings of the paper.
基金supported by National Natural Science Foundation of China(Nos.61273070 and 61203092)111 project(No.B12018)
文摘This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetitive processes is used to develop formulas for gain matrices design, together with convergent conditions in terms of linear matrix inequalities. An extension to deal with model uncertainty of the polytopic or norm bounded form is also developed and an illustrative example is given.
文摘In this paper, H ∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H ∞ performance indices is induced, and then a strategy for H ∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H ∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach. Keywords Multi-time-delay - discrete time system - LMI - delay-dependent - H ∞ control Bai-Da Qu received B. S. degree in electrical automation from Fuxin Mining Institute, China in 1982, M. Eng. degree from Hefei University of Polytechnology in 1990, and Ph.D from Northerneastern University in 1999. He was an electro-mechanical engineer at Erdaohezi Mine, Heilongjiang, China from 1982 to 1990, a Lecturer, Senior Engineer, Associate Professor and Professor in Shenyang Institue of Technology from 1990 to 2002. He is currently a professor in Communication and Control Engineering School, Southern Yangtze University. His research interests include control theory and applications (robust control, H ∞ control, time-delay systems, complex systems), system engineering (modeling, analysis and simulation, MIS,CMIS), power-electronics and electrical driving, signal detecting and process, industrial automation.
基金Supported by NSF of Zhejiang Province(2006A05192)
文摘In this paper, we study the nonlinear discrete systems and obtain several lyapunov inequalities for them. Then we give the application for lyapunov inequality.
文摘A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular model, called Forna- sini-Marchesini (FM) second model was proposed by Fornasini and Marchesini in 1978. The aim of this paper is to present a survey of the existing literature on the stability of FM second model.
文摘This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.
文摘A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This equation presents arbitrarily nearest-neighbor nonlinearities. We analyze the properties of such model both in connection to their modulational stability, as well as in regard to the generation of intrinsic localized modes. We present a generalized discrete Lange-Newell criterion. Numerical simulations are performed and we show that discrete breathers are generated through modulational instability.
文摘The flexible satellite batch production line is a complex discrete production system with multiple cross-disciplinary fields and mixed serial parallel tasks.As the source of the satellite batch production line process,the warehousing system has urgent needs such as uncertain production scale and rapid iteration and optimization of business processes.Therefore,the requirements and architecture of complex discrete warehousing systems such as flexible satellite batch production lines are studied.The physical system of intelligent equipment is abstracted as a digital model to form the underlying module,and a digital fusion framework of“business domain+middleware platform+intelligent equipment information model”is constructed.The granularity of microservice splitting is calculated based on the dynamic correlation relationship between user access instances and database table structures.The general warehousing functions of the platform are divided to achieve module customization,addition,and configuration.An open discrete warehousing system based on microservices is designed.Software architecture and design develop complex discrete warehousing systems based on the SpringCloud framework.This architecture achieves the decoupling of business logic and physical hardware,enhances the maintainability and scalability of the system,and greatly improves the system’s adaptability to different complex discrete warehousing business scenarios.
文摘This paper presents the dynamical properties of a discrete-time prey-predator model with refuge in prey under imprecise biological parameters.We consider the refuge concept of prey,which is proportional to the density of prey species with interval parameters.The model develops with natural interval parameters since the uncertainties of parameters of any ecological system are a widespread phenomenon in nature.The equilibria of the model are obtained,and the dynamic behaviours of the proposed system are examined.Simulations of the model are performed for different parameters of the model.Numerical simulations show that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.Our study,through analytical derivation and numerical example,presents the effect of refuge on population dynamics under imprecise biological parameters.
基金partially supported by the Science Technology Development Fund,Macao Special Administrative Region(0029/2023/RIA1)the National Research Foundation Singapore under its AI Singapore Programme(AISG2-GC-2023-007)
文摘With the development of cyber-physical systems,system security faces more risks from cyber-attacks.In this work,we study the problem that an external attacker implements covert sensor and actuator attacks with resource constraints(the total resource consumption of the attacks is not greater than a given initial resource of the attacker)to mislead a discrete event system under supervisory control to reach unsafe states.We consider that the attacker can implement two types of attacks:One by modifying the sensor readings observed by a supervisor and the other by enabling the actuator commands disabled by the supervisor.Each attack has its corresponding resource consumption and remains covert.To solve this problem,we first introduce a notion of combined-attackability to determine whether a closedloop system may reach an unsafe state after receiving attacks with resource constraints.We develop an algorithm to construct a corrupted supervisor under attacks,provide a verification method for combined-attackability in polynomial time based on a plant,a corrupted supervisor,and an attacker's initial resource,and propose a corresponding attack synthesis algorithm.The effectiveness of the proposed method is illustrated by an example.
