A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric varia...A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.展开更多
The controller designed according to classical or modern control theory will not satisfy the performance requirements when the controlled object in industrial field can not be described by exact mathematical model or...The controller designed according to classical or modern control theory will not satisfy the performance requirements when the controlled object in industrial field can not be described by exact mathematical model or the disturbance of the controlled system. In order to make the controlled system stable and having good performance, H∞ control theory was put forward to solve this practical problem. Taking the position of a rolling mill as the controlled object, it was rectified by optimal engineering way. Then, three different plans were put forward according to Bang-Bang control, LQ control and H∞ control, respectively. The result of the simulation shows that the controller designed according to H∞ method whose robust performance and ability to restrain colors disturbance is satisfactory.展开更多
This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in t...This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion.The Markov chain is assumed to be independent of Brownian motion,thus the market is incomplete.The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem.The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier.All the results are different from those in the problem with fixed time horizon.展开更多
Abstract: The current method to solve the problem of active suspension control for a vehicle is often dealt with a quarter-car or half-car model. But it is not enough to use this kind of model for practical applicatio...Abstract: The current method to solve the problem of active suspension control for a vehicle is often dealt with a quarter-car or half-car model. But it is not enough to use this kind of model for practical applications. In this paper, based on considering the influence of factors such as, seat and passengers, a MDOF(multi-degree-of-freedom) model describing the vehicle motion is set up. The MODF model, which is 8DOF of four independent suspensions and four wheel tracks, is more applicable by comparison of its analysis result with some conventional vehicle models. Therefore, it is more suitable to use the 8DOF full-car model than a conventional 4DOF half-car model in the active control design for car vibration. Based on the derived 8DOF model, a controller is designed by using LQ (linear quadratic ) control theory, and the appropriate control scheme is selected by testing various performance indexes. Computer simulation is carried out for a passenger car running on a road with step disturbance and random road disturbance expressed by Power Spectral Density (PSD). Vibrations corresponding to ride comfort are derived under the foregoing road disturbances. The response results for uncontrolled and controlled system are compared. The response of vehicle vibration is greatly suppressed and quickly damped, which testifies the effect of the active suspension. The results achieved for various controllers are compared to investigate the influence of different control schemes on the control effect.展开更多
This paper is concerned with a linear-quadrati stochastic Stackelberg differential game with one leader and two followers,where the game system is governed by a mean-field stochastic differential equatio.By maximum pr...This paper is concerned with a linear-quadrati stochastic Stackelberg differential game with one leader and two followers,where the game system is governed by a mean-field stochastic differential equatio.By maximum principle and verification theorem,the open-loop Stackelberg solution is expressed as a feedback form of the state and its mean with the help of three systems of Riccati equations.展开更多
In this paper,we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional,with two controllers—one can choose only deterministic time functions,called the deterministic contro...In this paper,we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional,with two controllers—one can choose only deterministic time functions,called the deterministic controller,while the other can choose adapted random processes,called the random controller.The optimal control is shown to exist under suitable assumptions.The optimal control is characterized via a system of fully coupled forward-backward stochastic differential equations(FBSDEs)of mean-field type.We solve the FBSDEs via solutions of two(but decoupled)Riccati equations,and give the respective optimal feedback law for both deterministic and random controllers,using solutions of both Riccati equations.The optimal state satisfies a linear stochastic differential equation(SDE)of mean-field type.Both the singular and infinite time-horizonal cases are also addressed.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11102031 and 11272076)the Fundamental Research Funds for Central Universities(No.DUT13LK25)+2 种基金the Key Laboratory Fund of Liaoning Province(No.L2013015)the China Postdoctoral Science Foundation(No.2014M550155)the State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-0114G02)
文摘A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.
文摘The controller designed according to classical or modern control theory will not satisfy the performance requirements when the controlled object in industrial field can not be described by exact mathematical model or the disturbance of the controlled system. In order to make the controlled system stable and having good performance, H∞ control theory was put forward to solve this practical problem. Taking the position of a rolling mill as the controlled object, it was rectified by optimal engineering way. Then, three different plans were put forward according to Bang-Bang control, LQ control and H∞ control, respectively. The result of the simulation shows that the controller designed according to H∞ method whose robust performance and ability to restrain colors disturbance is satisfactory.
基金supported by the Natural Science Foundation of China under Grant Nos.11831010,12001319 and 61961160732Shandong Provincial Natural Science Foundation under Grant Nos.ZR2019ZD42 and ZR2020QA025+2 种基金The Taishan Scholars Climbing Program of Shandong under Grant No.TSPD20210302Ruyi Liu acknowledges the Discovery Projects of Australian Research Council(DP200101550)the China Postdoctoral Science Foundation(2021TQ0196)。
文摘This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion.The Markov chain is assumed to be independent of Brownian motion,thus the market is incomplete.The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem.The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier.All the results are different from those in the problem with fixed time horizon.
文摘Abstract: The current method to solve the problem of active suspension control for a vehicle is often dealt with a quarter-car or half-car model. But it is not enough to use this kind of model for practical applications. In this paper, based on considering the influence of factors such as, seat and passengers, a MDOF(multi-degree-of-freedom) model describing the vehicle motion is set up. The MODF model, which is 8DOF of four independent suspensions and four wheel tracks, is more applicable by comparison of its analysis result with some conventional vehicle models. Therefore, it is more suitable to use the 8DOF full-car model than a conventional 4DOF half-car model in the active control design for car vibration. Based on the derived 8DOF model, a controller is designed by using LQ (linear quadratic ) control theory, and the appropriate control scheme is selected by testing various performance indexes. Computer simulation is carried out for a passenger car running on a road with step disturbance and random road disturbance expressed by Power Spectral Density (PSD). Vibrations corresponding to ride comfort are derived under the foregoing road disturbances. The response results for uncontrolled and controlled system are compared. The response of vehicle vibration is greatly suppressed and quickly damped, which testifies the effect of the active suspension. The results achieved for various controllers are compared to investigate the influence of different control schemes on the control effect.
基金supported in part by the Fund for Innovative Research Groups of NSFC under Grant No.61821004the Key Program of NSFC under Grant Nos.61633015 and 11831010the NSFC for Distinguished Young Scholars under Grant No.61925306。
文摘This paper is concerned with a linear-quadrati stochastic Stackelberg differential game with one leader and two followers,where the game system is governed by a mean-field stochastic differential equatio.By maximum principle and verification theorem,the open-loop Stackelberg solution is expressed as a feedback form of the state and its mean with the help of three systems of Riccati equations.
基金Lebesgue center of mathematics“Investissements d’avenir”program-ANR-11-LABX-0020-01,by CAESARS-ANR-15-CE05-0024MFG-ANR-16-CE40-0015-01.Tang acknowledges research supported by National Science Foundation of China(Grant No.11631004)Science and Technology Commission of Shanghai Municipality(Grant No.14XD1400400).
文摘In this paper,we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional,with two controllers—one can choose only deterministic time functions,called the deterministic controller,while the other can choose adapted random processes,called the random controller.The optimal control is shown to exist under suitable assumptions.The optimal control is characterized via a system of fully coupled forward-backward stochastic differential equations(FBSDEs)of mean-field type.We solve the FBSDEs via solutions of two(but decoupled)Riccati equations,and give the respective optimal feedback law for both deterministic and random controllers,using solutions of both Riccati equations.The optimal state satisfies a linear stochastic differential equation(SDE)of mean-field type.Both the singular and infinite time-horizonal cases are also addressed.