Observability is a fundamental property of a partially observed dynamical system,which means whether one can use an input sequence and the corresponding output sequence to determine the initial state.Observability pro...Observability is a fundamental property of a partially observed dynamical system,which means whether one can use an input sequence and the corresponding output sequence to determine the initial state.Observability provides bases for many related problems,such as state estimation,identification,disturbance decoupling,controller synthesis,etc.Until now,fundamental improvement has been obtained in observability of Boolean control networks(BCNs)mainly based on two methods-Edward F.Moore's partition and our observability graph or their equivalent representations found later based on the semitensor product(STP)of matrices(where the STP was proposed by Daizhan Cheng),including necessary and sufficient conditions for different types of observability,extensions to probabilistic Boolean networks(PBNs)and singular BCNs,even to nondeterministic finite-transition systems(NFTSs);and the development(with the help of the STP of matrices)in related topics,such as com-putation of smallest invariant dual subspaces of BNs containing a set of Boolean functions,multiple-experiment observability verification/decomposition in BCNs,disturbance decoupling in BCNs,etc.This paper provides a thorough survey for these topics.The contents of the paper are guided by the above two methods.First,we show that Moore's partition-based method closely relates the following problems:computation of smallest invariant dual subspaces of BNs,multiple-experiment observ-ability verification/decomposition in BCNs,and disturbance decoupling in BCNs.However,this method does not apply to other types of observability or nondeterministic systems.Second,we show that based on our observability graph,four different types of observability have been verified in BCNs,verification results have also been extended to PBNs,singular BCNs,and NFTSs.In addition,Moore's partition also shows similarities between BCNs and linear time-invariant(LTI)control systems,e.g.,smallest invariant dual subspaces of BNs containing a set of Boolean functions in BCNs vs unobservable subspaces of LTI control systems,the forms of quotient systems based on observability decomposition in both types of systems.However,there are essential differences between the two types of systems,e.g.,"all plausible definitions of observability in LTI control systems turn out to be equivalent"(by Walter M.Wonham 1985),but there exist nonequivalent definitions of observability in BCNs;the quotient system based on observability decomposition always exists in an LTI control system,while a quotient system based on multiple-experiment observability decomposition does not always exist in a BCN.展开更多
Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control s...Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.展开更多
This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is co...This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output- decomposed form by constructing a set of consistent outputfriendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan＇s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan＇s problem is obtained.展开更多
In this paper,the problem of controllability of Boolean control networks(BCNs)with multiple time delays in both states and controls is investigated.First,the controllability problem of BCNs with multiple time delays i...In this paper,the problem of controllability of Boolean control networks(BCNs)with multiple time delays in both states and controls is investigated.First,the controllability problem of BCNs with multiple time delays in controls is considered.For this controllability problem,a controllability matrix is constructed by defining a new product of matrices,based on which a necessary and sufficient controllability condition is obtained.Then,the controllability of BCNs with multiple time delays in states is studied by giving a necessary and sufficient condition.Subsequently,based on these results,a controllability matrix for BCNs with multiple time delays in both states and controls is proposed that provides a concise controllability condition.Finally,two examples are given to illustrate the main results.展开更多
Recently there has been great interest in the idea that evolvable system based on the principle of artifcial intelligence can be used to continuously and autonomously adapt the behaviour of physically embedded systems...Recently there has been great interest in the idea that evolvable system based on the principle of artifcial intelligence can be used to continuously and autonomously adapt the behaviour of physically embedded systems such as autonomous mobile robots and intelligent home devices. Meanwhile, we have seen the introduction of evolvable hardware(EHW): new integrated electronic circuits that are able to continuously evolve to adapt the chages in the environment implemented by evolutionary algorithms such as genetic algorithm(GA) and reinforcement learning. This paper concentrates on developing a robotic navigation system whose basic behaviours are obstacle avoidance and light source navigation. The results demonstrate that the intrinsic evolvable hardware system is able to create the stable robotiiuc behaviours as required in the real world instead of the traditional hardware systems.展开更多
This paper gives an equivalent condition for the observability of Boolean control networks（BCNs） with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of ...This paper gives an equivalent condition for the observability of Boolean control networks（BCNs） with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of the semi-tensor product of matrices. First, the BCN under consideration is split into a finite number of subsystems with no time delays. Second, the observability of the BCN is verified by testing the observability of the so-called observability constructed path（a special subsystem without time delays） based on graph theory. These results extend the recent related results on the observability of BCNs. Examples are shown to illustrate the effectiveness of the results.展开更多
The aim of this survey paper is to provide the state of the art of the research on control and optimal control of Boolean control networks,under the assumption that all the state variables are accessible and hence ava...The aim of this survey paper is to provide the state of the art of the research on control and optimal control of Boolean control networks,under the assumption that all the state variables are accessible and hence available for feedback.Necessary and sufficient conditions for stabilisability to a limit cycle or to an equilibrium point are given.Additionally,it is shown that when such conditions are satisfied,stabilisation can always be achieved by means of state feedback.Analogous results are obtained for the safe control problem that is investigated for the first time in this survey.Finite and infinite horizon optimal control are subsequently considered,and solution algorithms are provided,based on suitable adaptations of theRiccati difference and algebraic equations.Finally,an appropriate definition of the cost function allows to restate and to solve both stabilisation and safe control as infinite horizon optimal control problems.展开更多
This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, ...This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.展开更多
In this paper,observability is studied for periodically switched Boolean control networks(PSBCNs),which are managed with periodic switching signal and consist of some Boolean control networks.Firstly,via semi-tensor p...In this paper,observability is studied for periodically switched Boolean control networks(PSBCNs),which are managed with periodic switching signal and consist of some Boolean control networks.Firstly,via semi-tensor product of matrices,PSBCNs are expressed as algebraic forms.Secondly,a parallel system is constructed by combining two same PSBCNs,based on which,the observability problem of the original PSBCN can be transformed into the set reachability problem of this parallel system.Then,two necessary and sufficient conditions are obtained to detect reachability of parallel systems and observability of PSBCNs.In addition,the proposed conditions are extended to the case of state constraints.Finally,a practical example and a numerical example are provided to illustrate the results.展开更多
This paper investigates the optimal output regulation of switched Boolean control networks by using a dynamic programming method.The reference signal studied in this paper is generated by the output trajectory of a sw...This paper investigates the optimal output regulation of switched Boolean control networks by using a dynamic programming method.The reference signal studied in this paper is generated by the output trajectory of a switched Boolean network.First,a per-step cost vector is proposed based on the largest control invariant set of the augmented auxiliary system.Then,a novel criterion is derived for determining the solvability of the output regulation.The proposed criterion transforms the solvability of output regulation of switched Boolean control networks into an optimization problem,providing a new perspective for addressing output regulation through optimal control.Based on this,an optimal state feedback control is proposed to enable the output trajectory of the original network to completely track the reference signal.An algorithm is presented to calculate the optimal feedback gain matrix and the optimal value for each state.Compared with existing results,the optimal state feedback control presented in this paper offers a generalized optimization principle and effectively reduces the computational complexity associated with designing state feedback control.Finally,an illustrative example is provided to validate the effectiveness of the results obtained.展开更多
文摘Observability is a fundamental property of a partially observed dynamical system,which means whether one can use an input sequence and the corresponding output sequence to determine the initial state.Observability provides bases for many related problems,such as state estimation,identification,disturbance decoupling,controller synthesis,etc.Until now,fundamental improvement has been obtained in observability of Boolean control networks(BCNs)mainly based on two methods-Edward F.Moore's partition and our observability graph or their equivalent representations found later based on the semitensor product(STP)of matrices(where the STP was proposed by Daizhan Cheng),including necessary and sufficient conditions for different types of observability,extensions to probabilistic Boolean networks(PBNs)and singular BCNs,even to nondeterministic finite-transition systems(NFTSs);and the development(with the help of the STP of matrices)in related topics,such as com-putation of smallest invariant dual subspaces of BNs containing a set of Boolean functions,multiple-experiment observability verification/decomposition in BCNs,disturbance decoupling in BCNs,etc.This paper provides a thorough survey for these topics.The contents of the paper are guided by the above two methods.First,we show that Moore's partition-based method closely relates the following problems:computation of smallest invariant dual subspaces of BNs,multiple-experiment observ-ability verification/decomposition in BCNs,and disturbance decoupling in BCNs.However,this method does not apply to other types of observability or nondeterministic systems.Second,we show that based on our observability graph,four different types of observability have been verified in BCNs,verification results have also been extended to PBNs,singular BCNs,and NFTSs.In addition,Moore's partition also shows similarities between BCNs and linear time-invariant(LTI)control systems,e.g.,smallest invariant dual subspaces of BNs containing a set of Boolean functions in BCNs vs unobservable subspaces of LTI control systems,the forms of quotient systems based on observability decomposition in both types of systems.However,there are essential differences between the two types of systems,e.g.,"all plausible definitions of observability in LTI control systems turn out to be equivalent"(by Walter M.Wonham 1985),but there exist nonequivalent definitions of observability in BCNs;the quotient system based on observability decomposition always exists in an LTI control system,while a quotient system based on multiple-experiment observability decomposition does not always exist in a BCN.
基金supported by the National Natural Science Foundation of China (62273201,62173209,72134004,62303170)the Research Fund for the Taishan Scholar Project of Shandong Province of China (TSTP20221103)。
文摘Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.
文摘This paper investigates the Morgan＇s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output- decomposed form by constructing a set of consistent outputfriendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan＇s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan＇s problem is obtained.
基金supported by the Natural Science Foundation of Chongqing,China(No.CSTB2022NSCQ-MSX2869)the Science and Technology Research Program of Chongqing Municipal Education Commission,China(No.KJQN202200524)+1 种基金the Research Project of National Center for Applied Mathematics in Chongqing,China(No.ncamc2022-msxm05)the Program of Chongqing Normal University,China(No.21XLB045)。
文摘In this paper,the problem of controllability of Boolean control networks(BCNs)with multiple time delays in both states and controls is investigated.First,the controllability problem of BCNs with multiple time delays in controls is considered.For this controllability problem,a controllability matrix is constructed by defining a new product of matrices,based on which a necessary and sufficient controllability condition is obtained.Then,the controllability of BCNs with multiple time delays in states is studied by giving a necessary and sufficient condition.Subsequently,based on these results,a controllability matrix for BCNs with multiple time delays in both states and controls is proposed that provides a concise controllability condition.Finally,two examples are given to illustrate the main results.
文摘Recently there has been great interest in the idea that evolvable system based on the principle of artifcial intelligence can be used to continuously and autonomously adapt the behaviour of physically embedded systems such as autonomous mobile robots and intelligent home devices. Meanwhile, we have seen the introduction of evolvable hardware(EHW): new integrated electronic circuits that are able to continuously evolve to adapt the chages in the environment implemented by evolutionary algorithms such as genetic algorithm(GA) and reinforcement learning. This paper concentrates on developing a robotic navigation system whose basic behaviours are obstacle avoidance and light source navigation. The results demonstrate that the intrinsic evolvable hardware system is able to create the stable robotiiuc behaviours as required in the real world instead of the traditional hardware systems.
基金supported by the National Natural Science Foundation of China under Grant Nos.61603109and 51209051the Natural Science Foundation of Heilongjiang Province of China under Grant No.LC2016023+1 种基金the Fundamental Research Funds for the Central Universities under Grant Nos.HEUCFM170406 and HEUCFM170112the State Key Laboratory of Ocean Engineering(Shanghai Jiao Tong University)under Grant No.1415
文摘This paper gives an equivalent condition for the observability of Boolean control networks（BCNs） with time-variant delays in states under a mild assumption by using the graph-theoretic method under the framework of the semi-tensor product of matrices. First, the BCN under consideration is split into a finite number of subsystems with no time delays. Second, the observability of the BCN is verified by testing the observability of the so-called observability constructed path（a special subsystem without time delays） based on graph theory. These results extend the recent related results on the observability of BCNs. Examples are shown to illustrate the effectiveness of the results.
文摘The aim of this survey paper is to provide the state of the art of the research on control and optimal control of Boolean control networks,under the assumption that all the state variables are accessible and hence available for feedback.Necessary and sufficient conditions for stabilisability to a limit cycle or to an equilibrium point are given.Additionally,it is shown that when such conditions are satisfied,stabilisation can always be achieved by means of state feedback.Analogous results are obtained for the safe control problem that is investigated for the first time in this survey.Finite and infinite horizon optimal control are subsequently considered,and solution algorithms are provided,based on suitable adaptations of theRiccati difference and algebraic equations.Finally,an appropriate definition of the cost function allows to restate and to solve both stabilisation and safe control as infinite horizon optimal control problems.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61673012,11271194a Project on the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.
基金supported by the National Natural Science Foundation of China under Grant Nos.12101366, 62103176 and 72134004the Natural Science Foundation of Shandong Province under Grant Nos. ZR2020QF117 and ZR2019BF023
文摘In this paper,observability is studied for periodically switched Boolean control networks(PSBCNs),which are managed with periodic switching signal and consist of some Boolean control networks.Firstly,via semi-tensor product of matrices,PSBCNs are expressed as algebraic forms.Secondly,a parallel system is constructed by combining two same PSBCNs,based on which,the observability problem of the original PSBCN can be transformed into the set reachability problem of this parallel system.Then,two necessary and sufficient conditions are obtained to detect reachability of parallel systems and observability of PSBCNs.In addition,the proposed conditions are extended to the case of state constraints.Finally,a practical example and a numerical example are provided to illustrate the results.
基金supported by the National Natural Science Foundation of China under Grant No.62203172the Hebei Natural Science Foundation under Grant No.F2024502008the Fundamental Research Funds for the Central Universities under Grant No.2024MS141。
文摘This paper investigates the optimal output regulation of switched Boolean control networks by using a dynamic programming method.The reference signal studied in this paper is generated by the output trajectory of a switched Boolean network.First,a per-step cost vector is proposed based on the largest control invariant set of the augmented auxiliary system.Then,a novel criterion is derived for determining the solvability of the output regulation.The proposed criterion transforms the solvability of output regulation of switched Boolean control networks into an optimization problem,providing a new perspective for addressing output regulation through optimal control.Based on this,an optimal state feedback control is proposed to enable the output trajectory of the original network to completely track the reference signal.An algorithm is presented to calculate the optimal feedback gain matrix and the optimal value for each state.Compared with existing results,the optimal state feedback control presented in this paper offers a generalized optimization principle and effectively reduces the computational complexity associated with designing state feedback control.Finally,an illustrative example is provided to validate the effectiveness of the results obtained.
