This paper studies the fault tolerant control, adaptive approach, for linear time-invariant two-time-scale and three-time-scale singularly perturbed systems in presence of actuator faults and external disturbances. Fi...This paper studies the fault tolerant control, adaptive approach, for linear time-invariant two-time-scale and three-time-scale singularly perturbed systems in presence of actuator faults and external disturbances. First, the full order system will be controlled using v-dependent control law. The corresponding Lyapunov equation is ill-conditioned due to the presence of slow and fast phenomena. Secondly, a time-scale decomposition of the Lyapunov equation is carried out using singular perturbation method to avoid the numerical stiffness. A composite control law based on local controllers of the slow and fast subsystems is also used to make the control law ε-independent. The designed fault tolerant control guarantees the robust stability of the global closed-loop singularly perturbed system despite loss of effectiveness of actuators. The stability is proved based on the Lyapunov stability theory in the case where the singular perturbation parameter is sufficiently small. A numerical example is provided to illustrate the proposed method.展开更多
This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feed...This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.展开更多
The state feedback design for singularly perturbed systems described in Delta operator is considered. The composite state feedback controller for slow and fast subsystems is designed by using the direct method. The ob...The state feedback design for singularly perturbed systems described in Delta operator is considered. The composite state feedback controller for slow and fast subsystems is designed by using the direct method. The obtained results can bring previous conclusions of continuous and discrete time systems into the unified Delta framework. A simulation example is presented to demonstrate the validity and efficiency of the design.展开更多
This article studies the adaptive optimal output regulation problem for a class of interconnected singularly perturbed systems(SPSs) with unknown dynamics based on reinforcement learning(RL).Taking into account the sl...This article studies the adaptive optimal output regulation problem for a class of interconnected singularly perturbed systems(SPSs) with unknown dynamics based on reinforcement learning(RL).Taking into account the slow and fast characteristics among system states,the interconnected SPS is decomposed into the slow time-scale dynamics and the fast timescale dynamics through singular perturbation theory.For the fast time-scale dynamics with interconnections,we devise a decentralized optimal control strategy by selecting appropriate weight matrices in the cost function.For the slow time-scale dynamics with unknown system parameters,an off-policy RL algorithm with convergence guarantee is given to learn the optimal control strategy in terms of measurement data.By combining the slow and fast controllers,we establish the composite decentralized adaptive optimal output regulator,and rigorously analyze the stability and optimality of the closed-loop system.The proposed decomposition design not only bypasses the numerical stiffness but also alleviates the high-dimensionality.The efficacy of the proposed methodology is validated by a load-frequency control application of a two-area power system.展开更多
The optimal control design for singularly perturbed time-delay systems affected by external distur-bances is considered.Based on the decomposition theory of singular perturbation,the system is decom-posed into a fast ...The optimal control design for singularly perturbed time-delay systems affected by external distur-bances is considered.Based on the decomposition theory of singular perturbation,the system is decom-posed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances.Theoptimal disturbances rejection control law of the slow subsystem is obtained by using the successive ap-proximation approach(SAA)and feedforward compensation method.Further,the feedforward and feed-back composite control(FFCC)law for the original problem is developed.The FFCC law consists of lin-ear analytic terms and a time-delay compensation term which is the limit of the solution sequence of theadjoint vector equations.A disturbance observer is introduced to make the FFCC law physically realiz-able.Numerical examples show that the proposed algorithm is effective.展开更多
In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to pr...In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.展开更多
Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain l...Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain linear matrix equations are solvable. Once these equations are solvable, the state feedback regulator can easily be constructed.展开更多
The asymptotic behavior of solution for a n-dimensional nonlinear singularly perturbed system is studied. Under the appropriate assumptions, the existence of solution for the system is proved and the estimation of the...The asymptotic behavior of solution for a n-dimensional nonlinear singularly perturbed system is studied. Under the appropriate assumptions, the existence of solution for the system is proved and the estimation of the solution is given using the method of differential inequalities.展开更多
In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction...In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction of the sliding mode controller for singularly perturbed systems. The controller design is based on a linear diagonal transformation of the singularly perturbed model. Furthermore, the use of a single sliding mode controller designed for the slow component of the diagonalized system is investigated. Simulation results indicate the performance improvement of the proposed controllers.展开更多
Optimal deterministic disturbances rejection control problem for singularly perturbed linear systems is considered. By using the slow-fast decomposition theory of singular perturbation, the existent and unique conditi...Optimal deterministic disturbances rejection control problem for singularly perturbed linear systems is considered. By using the slow-fast decomposition theory of singular perturbation, the existent and unique conditions of the feedforward and feedback composite control （FFCC） laws for both infinite-time and finite-time are proposed, and the design approaches are given. A disturbance observer is introduced to make the FFCC laws realizable physically. Simulation results indicate that the FFCC laws are robust with respect to external disturbances.展开更多
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Unsing the iteration method and the comparison theorem, the existence, uniqueness and i...In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Unsing the iteration method and the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied.展开更多
The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using t...The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.展开更多
A class of nonlinear predator prey reaction diffusion systems for singularly pe rturbed problems are considered.Under suitable conditions, by using theory of di fferential inequalities the existence and asymptotic be...A class of nonlinear predator prey reaction diffusion systems for singularly pe rturbed problems are considered.Under suitable conditions, by using theory of di fferential inequalities the existence and asymptotic behavior of solution for in itial boundary value problems are studied.展开更多
A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems is studied.
This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-...This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.展开更多
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic beh...The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.展开更多
The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is construc...The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is constructed and introducing two auxiliary functions the existence and uniqueness theorem of solution for the basic reaction diffusion system is proved. Using the singularly perturbed method the formal asymptotic expressions of the solution are constructed with power series theory. By using the comparison theorem the existence and its asymptotic behavior of solution for the original problem are studied. Finally, using method of estimate inequalities, the structure of solutions for the problem is discussed thoroughly in three cases and asymptotic solution of the original problem is given. The asymptotic behavior of solution in the three cases is proved.展开更多
In this paper, we consider a class of optimal control problem for the singularly perturbed hybrid dynamical systems. By means of variational method, we obtain the necessary conditions of the hybrid dynamical systems. ...In this paper, we consider a class of optimal control problem for the singularly perturbed hybrid dynamical systems. By means of variational method, we obtain the necessary conditions of the hybrid dynamical systems. Meanwhile, the existence of solution for the hybrid dynamical system is proved by the sewing method and the uniformly valid asymptotic expansion of the optimal trajectory is constructed by the boundary function method. Finally,an example is presented to illustrate the result.展开更多
The problems of the nonlocal boundary conditions for the singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for ...The problems of the nonlocal boundary conditions for the singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems are studied.展开更多
The singularly perturbed initial boudary value problem for the nonlocal reaction diffusion systems was considered. Using iteration method the comparison theorem was obtained. Introducing stretched variable the formal ...The singularly perturbed initial boudary value problem for the nonlocal reaction diffusion systems was considered. Using iteration method the comparison theorem was obtained. Introducing stretched variable the formal asymptotic solution was constructed. And the existence and its asymptotic behavior of solution for the problem were studied by using the method of the upper and lower solution.展开更多
文摘This paper studies the fault tolerant control, adaptive approach, for linear time-invariant two-time-scale and three-time-scale singularly perturbed systems in presence of actuator faults and external disturbances. First, the full order system will be controlled using v-dependent control law. The corresponding Lyapunov equation is ill-conditioned due to the presence of slow and fast phenomena. Secondly, a time-scale decomposition of the Lyapunov equation is carried out using singular perturbation method to avoid the numerical stiffness. A composite control law based on local controllers of the slow and fast subsystems is also used to make the control law ε-independent. The designed fault tolerant control guarantees the robust stability of the global closed-loop singularly perturbed system despite loss of effectiveness of actuators. The stability is proved based on the Lyapunov stability theory in the case where the singular perturbation parameter is sufficiently small. A numerical example is provided to illustrate the proposed method.
基金supported by Russian Foundation for Basic Research(No.15-08-06859a)and by the Ministry of Education and Science of the Russian Federation in the framework of the basic part of the state order(No.2.8629.2017).
文摘This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.
基金This work was supported by the National Natural Science Foundation of China (No. 60474078,60304001).
文摘The state feedback design for singularly perturbed systems described in Delta operator is considered. The composite state feedback controller for slow and fast subsystems is designed by using the direct method. The obtained results can bring previous conclusions of continuous and discrete time systems into the unified Delta framework. A simulation example is presented to demonstrate the validity and efficiency of the design.
基金supported by the National Natural Science Foundation of China (62073327,62273350)the Natural Science Foundation of Jiangsu Province (BK20221112)。
文摘This article studies the adaptive optimal output regulation problem for a class of interconnected singularly perturbed systems(SPSs) with unknown dynamics based on reinforcement learning(RL).Taking into account the slow and fast characteristics among system states,the interconnected SPS is decomposed into the slow time-scale dynamics and the fast timescale dynamics through singular perturbation theory.For the fast time-scale dynamics with interconnections,we devise a decentralized optimal control strategy by selecting appropriate weight matrices in the cost function.For the slow time-scale dynamics with unknown system parameters,an off-policy RL algorithm with convergence guarantee is given to learn the optimal control strategy in terms of measurement data.By combining the slow and fast controllers,we establish the composite decentralized adaptive optimal output regulator,and rigorously analyze the stability and optimality of the closed-loop system.The proposed decomposition design not only bypasses the numerical stiffness but also alleviates the high-dimensionality.The efficacy of the proposed methodology is validated by a load-frequency control application of a two-area power system.
基金the National Natural Science Foundation of China(No.60574023,40776051)the Natural Science Foundation of Zhejiang Province(No.Y107232)+1 种基金the Scientific Research Found of Zhejiang Provincial Education Department(No.Y200702660)the 123 Talent Funding Project of China Jiliang University(No.2006RC17)
文摘The optimal control design for singularly perturbed time-delay systems affected by external distur-bances is considered.Based on the decomposition theory of singular perturbation,the system is decom-posed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances.Theoptimal disturbances rejection control law of the slow subsystem is obtained by using the successive ap-proximation approach(SAA)and feedforward compensation method.Further,the feedforward and feed-back composite control(FFCC)law for the original problem is developed.The FFCC law consists of lin-ear analytic terms and a time-delay compensation term which is the limit of the solution sequence of theadjoint vector equations.A disturbance observer is introduced to make the FFCC law physically realiz-able.Numerical examples show that the proposed algorithm is effective.
基金the National Natural Science Foundation of China (No. 10671069, 60674046)
文摘In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.
文摘Based on the T-S model, the output regulation of nonlinear singularly perturbed systems via state feedback is discussed. It is shown that, under standard assumptions, this problean is solvable if and only if certain linear matrix equations are solvable. Once these equations are solvable, the state feedback regulator can easily be constructed.
基金Supported by the National Natural Science Foundation(10471039)Supported by the Natural Science Foundation of Zhejiang Province(102009)
文摘The asymptotic behavior of solution for a n-dimensional nonlinear singularly perturbed system is studied. Under the appropriate assumptions, the existence of solution for the system is proved and the estimation of the solution is given using the method of differential inequalities.
文摘In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction of the sliding mode controller for singularly perturbed systems. The controller design is based on a linear diagonal transformation of the singularly perturbed model. Furthermore, the use of a single sliding mode controller designed for the slow component of the diagonalized system is investigated. Simulation results indicate the performance improvement of the proposed controllers.
基金This project was supported by the National Natural Science Foundation of China (60574023), the Natural Science Foundation of Shandong Province (Z2005G01), and the Natural Science Foundation of Qingdao City (05-1-JC-94).
文摘Optimal deterministic disturbances rejection control problem for singularly perturbed linear systems is considered. By using the slow-fast decomposition theory of singular perturbation, the existent and unique conditions of the feedforward and feedback composite control （FFCC） laws for both infinite-time and finite-time are proposed, and the design approaches are given. A disturbance observer is introduced to make the FFCC laws realizable physically. Simulation results indicate that the FFCC laws are robust with respect to external disturbances.
基金The project is supported by The National Natural Science Foundation of China(10071048)"Hundred People Project" of Chinese Academy of Sciences
文摘In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Unsing the iteration method and the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied.
基金the NNSF of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)part by E-Institutes of Shanghai Municipal Education Commission(E03004)
文摘The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.
基金Supported by important study project of the National Natural Science Foundation of China(9 0 2 1 1 0 0 4 ) and by the"Hundred Talents'Project"of Chinese Academy of Sciences
文摘A class of nonlinear predator prey reaction diffusion systems for singularly pe rturbed problems are considered.Under suitable conditions, by using theory of di fferential inequalities the existence and asymptotic behavior of solution for in itial boundary value problems are studied.
文摘A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems is studied.
基金Project supported by the National Natural Science Foundation of China (No. 10671214)the Chongqing Natural Science Foundation of China (No. 2005cc14)Shanghai Shuguang Genzong Project (No.04SGG05)
文摘This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.
文摘The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
基金Supported by the National Natural Science Foundation of China (40676016 and 10471039)the National Program for Basic Science Researches of China (2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)E-Insitutes of Shanghai Municipal Education Commission (N.E03004)
文摘The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is constructed and introducing two auxiliary functions the existence and uniqueness theorem of solution for the basic reaction diffusion system is proved. Using the singularly perturbed method the formal asymptotic expressions of the solution are constructed with power series theory. By using the comparison theorem the existence and its asymptotic behavior of solution for the original problem are studied. Finally, using method of estimate inequalities, the structure of solutions for the problem is discussed thoroughly in three cases and asymptotic solution of the original problem is given. The asymptotic behavior of solution in the three cases is proved.
基金supported by the National Natural Science Foundation of China(11471118,11401385 and 11371140)Natural Science Foundation of Hebei Province(A2015407063)Doctoral Foundation of Hebei Normal University of Science and Technology(2013YB008)
文摘In this paper, we consider a class of optimal control problem for the singularly perturbed hybrid dynamical systems. By means of variational method, we obtain the necessary conditions of the hybrid dynamical systems. Meanwhile, the existence of solution for the hybrid dynamical system is proved by the sewing method and the uniformly valid asymptotic expansion of the optimal trajectory is constructed by the boundary function method. Finally,an example is presented to illustrate the result.
文摘The problems of the nonlocal boundary conditions for the singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems are studied.
文摘The singularly perturbed initial boudary value problem for the nonlocal reaction diffusion systems was considered. Using iteration method the comparison theorem was obtained. Introducing stretched variable the formal asymptotic solution was constructed. And the existence and its asymptotic behavior of solution for the problem were studied by using the method of the upper and lower solution.
