This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s...This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s),u(s))dB(s)+∫_(0)^(t)h(t,s)dξ(s).by Here d B(s)denotes the Brownian motion It?type differential,ξdenotes the singular control(singular in time t with respect to Lebesgue measure)and u denotes the regular control(absolutely continuous with respect to Lebesgue measure).Such systems may for example be used to model harvesting of populations with memory,where X(t)represents the population density at time t,and the singular control processξrepresents the harvesting effort rate.The total income from the harvesting is represented by J(u, ξ) = E[∫_(0)^(t) f_(0)(t,X(t), u(t))dt + ∫_(0)^(t)f_(1)(t,X(t))dξ(t) + g(X(T))] for the given functions f0,f1 and g,where T>0 is a constant denoting the terminal time of the harvesting.Note that it is important to allow the controls to be singular,because in some cases the optimal controls are of this type.Using Hida-Malliavin calculus,we prove sufficient conditions and necessary conditions of optimality of controls.As a consequence,we obtain a new type of backward stochastic Volterra integral equations with singular drift.Finally,to illustrate our results,we apply them to discuss optimal harvesting problems with possibly density dependent prices.展开更多
This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the ty...This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.展开更多
Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for dela...Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.展开更多
This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diff...This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion coefficient.This control problem is difficult to solve with the classical method of spike variation.The authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control problem.Sufficient optimality conditions are also investigated.展开更多
A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in al...A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.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
The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singu...The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.展开更多
The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is propo...The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.展开更多
A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a suffic...A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a sufficient condition for the solvability of the H-infinity control problem for SISSs is given which generalizes the H-infinity control theory for singular systems to switched singular systems with impulsive effects. Then the sufficient condition of solvablity of the H-infinity control problem is presented in terms of linear matrix inequalities. Finally, the effectiveness of the developed aooroach for switched and imoulsive singular svstems is illustrated by a numerical example.展开更多
The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and n...The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.展开更多
To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system wi...To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.展开更多
Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semi...Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.展开更多
为不明确的 Lur' e 的一个班追踪控制的可靠柔韧的 H 的问题单个系统被学习。致动器和传感器的一个实际、一般的失败模型被使用凸的 polytopic 无常描述控制表面缺陷考虑。一些足够的条件以线性矩阵不平等(LMI ) 为致动器，传感器...为不明确的 Lur' e 的一个班追踪控制的可靠柔韧的 H 的问题单个系统被学习。致动器和传感器的一个实际、一般的失败模型被使用凸的 polytopic 无常描述控制表面缺陷考虑。一些足够的条件以线性矩阵不平等(LMI ) 为致动器，传感器和控制表面失败的案例被介绍。结果的控制系统是可靠的因为他们与当所有控制部件象一些控制部件什么时候经历失败一样是运作的时，没有不变的错误，追踪引用信号的 H 性能和输出保证靠近环的系统得到柔韧的稳定性。最后，一个数字例子被给显示出建议方法的有效性。展开更多
Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in usi...Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.展开更多
This paper presents a new design approach to achieve decentralized optimal control of high-dimension complex singular systems with dynamic uncertainties. Based on robust adaptive dynamic programming(robust ADP) method...This paper presents a new design approach to achieve decentralized optimal control of high-dimension complex singular systems with dynamic uncertainties. Based on robust adaptive dynamic programming(robust ADP) method, controllers for solving the singular systems optimal control problem are designed. The proposed algorithm can work well when the system model is not exactly known but the input and output data can be measured. The policy iteration of each controller only uses their own states and input information for learning,and do not need to know the whole system dynamics. Simulation results on the New England 10-machine 39-bus test system show the effectiveness of the designed controller.展开更多
This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular ...This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.展开更多
The objective of this paper is to study systematically the dynamics and control strategy of a singular biological economic model that is described by a differential-algebraic equation. It is shown that when the econom...The objective of this paper is to study systematically the dynamics and control strategy of a singular biological economic model that is described by a differential-algebraic equation. It is shown that when the economic profit passes through zero, this model exhibits the transcritical bifurcation, the Hopf bifurcation, and the limit cycle. In particular, the system undergoes the singularity induced bifurcation at the positive equilibrium, which can result in impulse. Then, state feedback controllers closer to the actual control strategies are designed to eliminate the unexpected singularity induced bifurcation and stabilize the positive equilibrium under the positive profit. Finally, numerical simulations verify the results and illustrate the effectiveness of the controllers. Also, the model with positive economic profit is shown numerically to have different dynamics.展开更多
A designing method is presented to find stabilizing saturated linear controllers for linear continuous time and discrete time singular systems with control constraints. The idea is as follows: The system is first stab...A designing method is presented to find stabilizing saturated linear controllers for linear continuous time and discrete time singular systems with control constraints. The idea is as follows: The system is first stabilized by a low-gain linear state feedback control. A general Lyapunov function is found, on the basis of which another linear state feedback control is computed. The second step is very similar to a relay control design. The two controls are added and saturated.展开更多
Selecting a proper initial input for Iterative Learning Control (ILC) algorithms has been shown to offer faster learning speed compared to the same theories if a system starts from blind. Iterative Learning Control is...Selecting a proper initial input for Iterative Learning Control (ILC) algorithms has been shown to offer faster learning speed compared to the same theories if a system starts from blind. Iterative Learning Control is a control technique that uses previous successive projections to update the following execution/trial input such that a reference is followed to a high precision. In ILC, convergence of the error is generally highly dependent on the initial choice of input applied to the plant, thus a good choice of initial start would make learning faster and as a consequence the error tends to zero faster as well. Here in this paper, an upper limit to the initial choice construction for the input signal for trial 1 is set such that the system would not tend to respond aggressively due to the uncertainty that lies in high frequencies. The provided limit is found in term of singular values and simulation results obtained illustrate the theory behind.展开更多
基金the financial support provided by the Swedish Research Council grant(2020-04697)the Norwegian Research Council grant(250768/F20),respectively。
文摘This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s),u(s))dB(s)+∫_(0)^(t)h(t,s)dξ(s).by Here d B(s)denotes the Brownian motion It?type differential,ξdenotes the singular control(singular in time t with respect to Lebesgue measure)and u denotes the regular control(absolutely continuous with respect to Lebesgue measure).Such systems may for example be used to model harvesting of populations with memory,where X(t)represents the population density at time t,and the singular control processξrepresents the harvesting effort rate.The total income from the harvesting is represented by J(u, ξ) = E[∫_(0)^(t) f_(0)(t,X(t), u(t))dt + ∫_(0)^(t)f_(1)(t,X(t))dξ(t) + g(X(T))] for the given functions f0,f1 and g,where T>0 is a constant denoting the terminal time of the harvesting.Note that it is important to allow the controls to be singular,because in some cases the optimal controls are of this type.Using Hida-Malliavin calculus,we prove sufficient conditions and necessary conditions of optimality of controls.As a consequence,we obtain a new type of backward stochastic Volterra integral equations with singular drift.Finally,to illustrate our results,we apply them to discuss optimal harvesting problems with possibly density dependent prices.
基金co-supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF21-BJ-J-1180)。
文摘This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.
基金the National Natural Science Foundation of China (60574011)the National Natural Science Foundation of Liaoning Province (2050770).
文摘Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.
基金supported by the National Natural Science Foundation of China under Grant Nos.11201268and 61105077the Natural Science Foundation of Shandong Province under Grant Nos.ZR2011AQ018 andZR2012AQ013
文摘This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion coefficient.This control problem is difficult to solve with the classical method of spike variation.The authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control problem.Sufficient optimality conditions are also investigated.
基金Supported by the National Science Foundation of China.
文摘A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.
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.
基金This work was supported by the National Creative Research Groups Science Foundation of China (No. 60421002) and the New Century 151 Talent Projectof Zhejiang Province.
文摘The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(60774016).
文摘The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.
基金the National Natural Science Foundation of China (No.60574013)the Science and Technology Foundation of theEducation Department of Liaoning Province (No.20060823)
文摘A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a sufficient condition for the solvability of the H-infinity control problem for SISSs is given which generalizes the H-infinity control theory for singular systems to switched singular systems with impulsive effects. Then the sufficient condition of solvablity of the H-infinity control problem is presented in terms of linear matrix inequalities. Finally, the effectiveness of the developed aooroach for switched and imoulsive singular svstems is illustrated by a numerical example.
基金supported by the National Natural Science Foundation of China (60564001)the Program for New Century Excellent Talentsin University (NCET-06-0756)
文摘The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.
基金the National Natural Science Foundation of China (60574088,60274014).
文摘To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(60674018)
文摘Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.
文摘为不明确的 Lur' e 的一个班追踪控制的可靠柔韧的 H 的问题单个系统被学习。致动器和传感器的一个实际、一般的失败模型被使用凸的 polytopic 无常描述控制表面缺陷考虑。一些足够的条件以线性矩阵不平等(LMI ) 为致动器，传感器和控制表面失败的案例被介绍。结果的控制系统是可靠的因为他们与当所有控制部件象一些控制部件什么时候经历失败一样是运作的时，没有不变的错误，追踪引用信号的 H 性能和输出保证靠近环的系统得到柔韧的稳定性。最后，一个数字例子被给显示出建议方法的有效性。
基金support from the National Natural Science Foundation of China (No. 61403197)the National Key Research and Development Plan of China (No. 2016YFB0500901)
文摘Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.
基金supported in part by the National Natural Science Foundation of China(61473070,61433004,61627809)SAPI Fundamental Research Funds(2018ZCX22)
文摘This paper presents a new design approach to achieve decentralized optimal control of high-dimension complex singular systems with dynamic uncertainties. Based on robust adaptive dynamic programming(robust ADP) method, controllers for solving the singular systems optimal control problem are designed. The proposed algorithm can work well when the system model is not exactly known but the input and output data can be measured. The policy iteration of each controller only uses their own states and input information for learning,and do not need to know the whole system dynamics. Simulation results on the New England 10-machine 39-bus test system show the effectiveness of the designed controller.
文摘This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.
基金supported by National Natural Science Foundation of China (No.60974004)Science Foundation of Ministry of Housing and Urban-Rural Development (No.2011-K5-31)
文摘The objective of this paper is to study systematically the dynamics and control strategy of a singular biological economic model that is described by a differential-algebraic equation. It is shown that when the economic profit passes through zero, this model exhibits the transcritical bifurcation, the Hopf bifurcation, and the limit cycle. In particular, the system undergoes the singularity induced bifurcation at the positive equilibrium, which can result in impulse. Then, state feedback controllers closer to the actual control strategies are designed to eliminate the unexpected singularity induced bifurcation and stabilize the positive equilibrium under the positive profit. Finally, numerical simulations verify the results and illustrate the effectiveness of the controllers. Also, the model with positive economic profit is shown numerically to have different dynamics.
文摘A designing method is presented to find stabilizing saturated linear controllers for linear continuous time and discrete time singular systems with control constraints. The idea is as follows: The system is first stabilized by a low-gain linear state feedback control. A general Lyapunov function is found, on the basis of which another linear state feedback control is computed. The second step is very similar to a relay control design. The two controls are added and saturated.
文摘Selecting a proper initial input for Iterative Learning Control (ILC) algorithms has been shown to offer faster learning speed compared to the same theories if a system starts from blind. Iterative Learning Control is a control technique that uses previous successive projections to update the following execution/trial input such that a reference is followed to a high precision. In ILC, convergence of the error is generally highly dependent on the initial choice of input applied to the plant, thus a good choice of initial start would make learning faster and as a consequence the error tends to zero faster as well. Here in this paper, an upper limit to the initial choice construction for the input signal for trial 1 is set such that the system would not tend to respond aggressively due to the uncertainty that lies in high frequencies. The provided limit is found in term of singular values and simulation results obtained illustrate the theory behind.
