This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) con...This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) constraint are resolved by integrating H_(2)/H_(∞) theory with Pareto game theory.First,a nonlinear stochastic bounded real lemma(SBRL)is derived,explicitly accounting for non-zero initial conditions.Through the analysis of four cross-coupled Hamilton-Jacobi equations(HJEs),we establish necessary and sufficient conditions for the existence of Pareto optimal strategies with the H_(∞) constraint.Secondly,to address the complexity of solving these nonlinear partial differential HJEs,we propose a neural network(NN)framework with synchronous tuning rules for the actor,critic,and disturbance components,based on a reinforcement learning(RL)approach.The designed tuning rules ensure convergence of the actor-critic-disturbance components to the desired values,enabling the realization of robust Pareto control strategies.The convergence of the proposed algorithm is rigorously analyzed using a constructed Lyapunov function for the NN weight errors.Finally,a numerical simulation example is provided to demonstrate the effectiveness of the proposed methods and main results.展开更多
Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous sta...Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.展开更多
The problem of the stability for a class of stochastic systems with time-varying interval delay and the norm-bounded uncertainty is investigated. Utilizing the information of both the lower and the upper bounds of the...The problem of the stability for a class of stochastic systems with time-varying interval delay and the norm-bounded uncertainty is investigated. Utilizing the information of both the lower and the upper bounds of the interval time-varying delay, a novel Lyapunov-Krasovskii functional is constructed. The delay-dependent sufficient criteria are derived in terms of linear matrix inequalities （LMIs）, which can be easily checked by the LMI in the Matlab toolbox. Based on the Jensen integral inequality, neither model transformations nor bounding techniques for cross terms is employed, so the derived criteria are less conservative than the existing results. Meanwhile, the computational complexity of the obtained stability conditions is reduced because no redundant matrix is introduced. A numerical example is given to show the effectiveness and the benefits of the proposed method.展开更多
This paper is concerned with the stability analysis for uncertain stochastic systems with interval time-varying delay.Improved delay-dependent robust stability criteria of uncertain stochastic systems with interval ti...This paper is concerned with the stability analysis for uncertain stochastic systems with interval time-varying delay.Improved delay-dependent robust stability criteria of uncertain stochastic systems with interval time-varying delay are proposed without ignoring any terms by considering the relationship among the time-varying delay,its upper bound,and their difference,and using both It6's differentied formula and Lyapunov stability theory.A numerical example is given to illustrate the effectiveness and the benefit of the proposed method.展开更多
A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza...A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.展开更多
This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions ...This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.展开更多
The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear st...The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.展开更多
The paper studies stochastic dynamics of a two-degree-of-freedom system,where a primary linear system is connected to a nonlinear energy sink with cubic stiffness nonlinearity and viscous damping.While the primary mas...The paper studies stochastic dynamics of a two-degree-of-freedom system,where a primary linear system is connected to a nonlinear energy sink with cubic stiffness nonlinearity and viscous damping.While the primary mass is subjected to a zero-mean Gaussian white noise excitation,the main objective of this study is to maximise the efficiency of the targeted energy transfer in the system.A surrogate optimisation algorithm is proposed for this purpose and adopted for the stochastic framework.The optimisations are conducted separately for the nonlinear stiffness coefficient alone as well as for both the nonlinear stiffness and damping coefficients together.Three different optimisation cost functions,based on either energy of the system’s components or the dissipated energy,are considered.The results demonstrate some clear trends in values of the nonlinear energy sink coefficients and show the effect of different cost functions on the optimal values of the nonlinear system’s coefficients.展开更多
In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control ...In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control law of the controller.Then,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response.To validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments.The results show that the novel PDF shape control approach is effective and feasible.Using an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial method.By comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control performance.For all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our method.The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.展开更多
Stochastic system state estimation subject to the unknown interference input widely exists in many fields,such as the control,communication,signal processing,and fault diagnosis.However,the research results are mostly...Stochastic system state estimation subject to the unknown interference input widely exists in many fields,such as the control,communication,signal processing,and fault diagnosis.However,the research results are mostly limited to the stochastic system in which only the dynamic state model or the measurement model concerns the individual unknown interference input,and the state model and the measurement model are both with the same unknown interference input.State estimate of the stochastic systems where the state model and the measurement model contain dual Unknown Interference inputs(dual-UI)with different physical meanings and mathematical definitions is concerned here.Firstly,the decoupling condition with the Unknown Interference input in the State model(S-UI)is shown,which introduces the decoupled system with the adjacent Measurement concerned Unknown Interference inputs(M-UI)appearing in the state model and the measurement model.Then,through defining the Differential term of the adjacent M-UI(M-UID),the equivalent system with only M-UID in the state model is obtained.Finally,considering the design freedom of the equivalent system,the decoupling filter in the minimum mean square error sense and the adaptive minimum upper filter with different applicable conditions are represented to obtain the optimal and sub-optimal state estimate,respectively.Two simulation cases verify the effectiveness and superiority compared with the traditional methods.展开更多
This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon ap...This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon approach. The explicit time-varying controller is designed if the condition is satisfied. The presented results are new to the best of our knowledge.展开更多
This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation an...This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.展开更多
The exponential stability in mean square and stabiliza- tion problems for It＆ stochastic switched systems with multiple time-delays are investigated. The system possesses the norm- bounded uncertainties and Markovian...The exponential stability in mean square and stabiliza- tion problems for It＆ stochastic switched systems with multiple time-delays are investigated. The system possesses the norm- bounded uncertainties and Markovian jumping parameters. By using an effective descriptor model transformation of the system and applying Ito＇s differential formula and Moon＇s inequality for bounding cross terms, a new delay-dependent sufficient condi- tion is derived in terms of linear matrix inequalities, and its states feedback controller is designed. Numerical examples are given to illustrate the efficiency and less conservation of the results.展开更多
This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Par...This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Parthasarathy quantum stochastic differential equation driven by quantum Wiener processes of bosonic fields in vacuum state. The Hamiltonian and system-field coupling operators, as functions of the system variables, are assumed to be represented in a Weyl quantization form. Using the Wigner-Moyal phase-space framework, we obtain a stochastic integro-differential equation for the posterior quasi-characteristic function （QCF） of the system conditioned on the measurements. This equation is a spatial Fourier domain representation of the Belavkin-Kushner-Stratonovich stochastic master equation driven by the innovation process associated with the measurements. We discuss a specific form of the posterior QCF dynamics in the case of linear system-field coupling and outline a Gaussian approximation of the posterior quantum state.展开更多
This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density fun...This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.展开更多
Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference schem...Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference scheme and the efficiency of the difference scheme in simulation of delay stochastic system with distributed parameter are analyzed. Examples are given to illustrate the application of the method.展开更多
In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed s...In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given.展开更多
Two easily verified delay-dependent criteria of mean-square exponential robust stability are obtained by constructing Lyapunov-Krasovskii functional and employing the decomposition technique of the continuous matrix-d...Two easily verified delay-dependent criteria of mean-square exponential robust stability are obtained by constructing Lyapunov-Krasovskii functional and employing the decomposition technique of the continuous matrix-discovered set of grey matrix and Ito formula.A numerical example shows the validity and practicality of the criteria presented in this paper.展开更多
This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals ...This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.展开更多
基金supported by the National Natural Science Foundation of China(12426609,62203220,62373229)the Taishan Scholar Project Foundation of Shandong Province(tsqnz20230619,tsqn202408110)+2 种基金the Fundamental Research Foundation of the Central Universities(23Cx06024A)the Natural Science Foundation of Shandong Province(ZR2024QF096)the Outstanding Youth Innovation Team in Shandong Higher Education Institutions(2023KJ061).
文摘This paper investigates a multiplayer Pareto game for affine nonlinear stochastic systems disturbed by both external and the internal multiplicative noises.The Pareto cooperative optimal strategies with the H_(∞) constraint are resolved by integrating H_(2)/H_(∞) theory with Pareto game theory.First,a nonlinear stochastic bounded real lemma(SBRL)is derived,explicitly accounting for non-zero initial conditions.Through the analysis of four cross-coupled Hamilton-Jacobi equations(HJEs),we establish necessary and sufficient conditions for the existence of Pareto optimal strategies with the H_(∞) constraint.Secondly,to address the complexity of solving these nonlinear partial differential HJEs,we propose a neural network(NN)framework with synchronous tuning rules for the actor,critic,and disturbance components,based on a reinforcement learning(RL)approach.The designed tuning rules ensure convergence of the actor-critic-disturbance components to the desired values,enabling the realization of robust Pareto control strategies.The convergence of the proposed algorithm is rigorously analyzed using a constructed Lyapunov function for the NN weight errors.Finally,a numerical simulation example is provided to demonstrate the effectiveness of the proposed methods and main results.
基金supported by the National Natural Science Foundation of China(62403393,12202058,62103118)the China Postdoctoral Science Foundation(2021T140160,2023 T160051)the Natural Science Foundation of Chongqing(CSTB 2023NSCQ-MSX0152)
文摘Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.
基金The National Natural Science Foundation of China(No.60874030,60574006,60404006)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.07KJB510125)
文摘The problem of the stability for a class of stochastic systems with time-varying interval delay and the norm-bounded uncertainty is investigated. Utilizing the information of both the lower and the upper bounds of the interval time-varying delay, a novel Lyapunov-Krasovskii functional is constructed. The delay-dependent sufficient criteria are derived in terms of linear matrix inequalities （LMIs）, which can be easily checked by the LMI in the Matlab toolbox. Based on the Jensen integral inequality, neither model transformations nor bounding techniques for cross terms is employed, so the derived criteria are less conservative than the existing results. Meanwhile, the computational complexity of the obtained stability conditions is reduced because no redundant matrix is introduced. A numerical example is given to show the effectiveness and the benefits of the proposed method.
基金Supported by National Natural Science Foundation of China(60425310,60574014)the Doctor Subject Foundation of China(20050533015,200805330004)+1 种基金the Program for New Century Excellent Talents in University(NCET-06-0679)the Natural Science Foundation of Hunan Province(08JJ1010)
文摘This paper is concerned with the stability analysis for uncertain stochastic systems with interval time-varying delay.Improved delay-dependent robust stability criteria of uncertain stochastic systems with interval time-varying delay are proposed without ignoring any terms by considering the relationship among the time-varying delay,its upper bound,and their difference,and using both It6's differentied formula and Lyapunov stability theory.A numerical example is given to illustrate the effectiveness and the benefit of the proposed method.
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.
基金This work was supported by the National Natural Science Foundation of China(No.60074007).
文摘This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.
基金the National Natural Science Foundation of China(No.61273127)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(No.12JK0524)
文摘The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.
基金funding for this work from NSF-CMMI 2009270 and EPSRC EP/V034391/1.
文摘The paper studies stochastic dynamics of a two-degree-of-freedom system,where a primary linear system is connected to a nonlinear energy sink with cubic stiffness nonlinearity and viscous damping.While the primary mass is subjected to a zero-mean Gaussian white noise excitation,the main objective of this study is to maximise the efficiency of the targeted energy transfer in the system.A surrogate optimisation algorithm is proposed for this purpose and adopted for the stochastic framework.The optimisations are conducted separately for the nonlinear stiffness coefficient alone as well as for both the nonlinear stiffness and damping coefficients together.Three different optimisation cost functions,based on either energy of the system’s components or the dissipated energy,are considered.The results demonstrate some clear trends in values of the nonlinear energy sink coefficients and show the effect of different cost functions on the optimal values of the nonlinear system’s coefficients.
基金supported in part by the National Natural Science Foundation of China(61903298,62073259,61773016)。
文摘In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control law of the controller.Then,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response.To validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments.The results show that the novel PDF shape control approach is effective and feasible.Using an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial method.By comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control performance.For all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our method.The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.
基金supported by the National Natural Science Foundation of China(Nos.61603040 and 61433003)Yunnan Applied Basic Research Project of China(No.201701CF00037)+1 种基金Guangdong Province Science and Technology Innovation Strategy Special Fund Project,China(No.skjtdzxrwqd2018001)Yunnan Provincial Science and Technology Department Key Research Program(Engineering),China(No.2018BA070)。
文摘Stochastic system state estimation subject to the unknown interference input widely exists in many fields,such as the control,communication,signal processing,and fault diagnosis.However,the research results are mostly limited to the stochastic system in which only the dynamic state model or the measurement model concerns the individual unknown interference input,and the state model and the measurement model are both with the same unknown interference input.State estimate of the stochastic systems where the state model and the measurement model contain dual Unknown Interference inputs(dual-UI)with different physical meanings and mathematical definitions is concerned here.Firstly,the decoupling condition with the Unknown Interference input in the State model(S-UI)is shown,which introduces the decoupled system with the adjacent Measurement concerned Unknown Interference inputs(M-UI)appearing in the state model and the measurement model.Then,through defining the Differential term of the adjacent M-UI(M-UID),the equivalent system with only M-UID in the state model is obtained.Finally,considering the design freedom of the equivalent system,the decoupling filter in the minimum mean square error sense and the adaptive minimum upper filter with different applicable conditions are represented to obtain the optimal and sub-optimal state estimate,respectively.Two simulation cases verify the effectiveness and superiority compared with the traditional methods.
基金This work was supported by the Taishan Scholar Construction Engineering by Shandong Government and the National Natural Science Foundation of China （Nos. 61120106011, 61203029）.
文摘This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon approach. The explicit time-varying controller is designed if the condition is satisfied. The presented results are new to the best of our knowledge.
基金supported by the National Natural Science Foundation of China (No.60525303, 60604004, 60704009) Natural Science Foundationof Hebei Province, China (No.F2005000390, F2006000270)
文摘This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.
文摘The exponential stability in mean square and stabiliza- tion problems for It＆ stochastic switched systems with multiple time-delays are investigated. The system possesses the norm- bounded uncertainties and Markovian jumping parameters. By using an effective descriptor model transformation of the system and applying Ito＇s differential formula and Moon＇s inequality for bounding cross terms, a new delay-dependent sufficient condi- tion is derived in terms of linear matrix inequalities, and its states feedback controller is designed. Numerical examples are given to illustrate the efficiency and less conservation of the results.
文摘This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Parthasarathy quantum stochastic differential equation driven by quantum Wiener processes of bosonic fields in vacuum state. The Hamiltonian and system-field coupling operators, as functions of the system variables, are assumed to be represented in a Weyl quantization form. Using the Wigner-Moyal phase-space framework, we obtain a stochastic integro-differential equation for the posterior quasi-characteristic function （QCF） of the system conditioned on the measurements. This equation is a spatial Fourier domain representation of the Belavkin-Kushner-Stratonovich stochastic master equation driven by the innovation process associated with the measurements. We discuss a specific form of the posterior QCF dynamics in the case of linear system-field coupling and outline a Gaussian approximation of the posterior quantum state.
文摘This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.
文摘Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference scheme and the efficiency of the difference scheme in simulation of delay stochastic system with distributed parameter are analyzed. Examples are given to illustrate the application of the method.
基金This project was supported by the National Natural Science Foundation of China (No. 69874015) and Natural Science Foundation of
文摘In this paper, we investigate the decentralized stabilization of some time-varying uncertain large-scale stochastic systems with delays under matching conditions. A type of decentralized controllers with guaranteed stabilization and sub-optimality are also given.
基金Supported by the Natural Science Foundation of Henan Province（061105440） Supported by the Natural Science Foundation of the Education Department of Henan Province（2008A1100150）
文摘Two easily verified delay-dependent criteria of mean-square exponential robust stability are obtained by constructing Lyapunov-Krasovskii functional and employing the decomposition technique of the continuous matrix-discovered set of grey matrix and Ito formula.A numerical example shows the validity and practicality of the criteria presented in this paper.
基金supported by the National Key Research and Development Program of China(2022YFA1006103,2023YFA1009203)the National Natural Science Foundation of China(61925306,61821004,11831010,61977043,12001320)+2 种基金the Natural Science Foundation of Shandong Province(ZR2019ZD42,ZR2020ZD24)the Taishan Scholars Young Program of Shandong(TSQN202211032)the Young Scholars Program of Shandong University。
文摘This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.
