This paper describes a novel type of pendulum-like oscillation controller for micro air vehicle(MAV) hover and stare state in the presence of external disturbances,which is based on linear-quadratic regulator(LQR) and...This paper describes a novel type of pendulum-like oscillation controller for micro air vehicle(MAV) hover and stare state in the presence of external disturbances,which is based on linear-quadratic regulator(LQR) and particle swarm optimization(PSO).A linear mathematical model of pendulum phenomenon based upon actual wind tunnel test data representing the hover mode is established,and a hybrid LQR and PSO approach is proposed to stabilize oscillation.PSO is applied to parameter optimization of the designed LQR controller.A series of comparative experiments are conducted,and the results have verified the feasibility,effectiveness and robustness of our proposed approach.展开更多
A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,...A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).展开更多
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
This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost functional. Based on a weighted sum optimality method, the Pareto game is equi...This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost functional. Based on a weighted sum optimality method, the Pareto game is equivalently converted to an optimal control problem. In the first place,the feedback form of Pareto optimal strategy is derived by virtue of decoupling technology, which is represented by four Riccati equations, a mean-field forward stochastic differential equation(MF-FSDE),and a mean-field backward stochastic differential equation(MF-BSDE). In addition, the corresponding Pareto optimal solution is further obtained. Finally, the author solves a problem in mathematical finance to illustrate the application of the theoretical results.展开更多
This paper aims at solving the linear-quadratic optimal control problems(LQOCP)for time-varying descriptor systems in a real Hilbert space.By using the Moore-Penrose inverse theory and space decomposition technique,th...This paper aims at solving the linear-quadratic optimal control problems(LQOCP)for time-varying descriptor systems in a real Hilbert space.By using the Moore-Penrose inverse theory and space decomposition technique,the descriptor system can be rewritten as a new differential-algebraic equation(DAE),and then some novel sufficient conditions for the solvability of LQOCP are obtained.Especially,the methods proposed in this work are simpler and easier to verify and compute,and can solve LQOCP without the range inclusion condition.In addition,some numerical examples are shown to verify the results obtained.展开更多
The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential...The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.展开更多
The flight dynamics model of air-breathing hypersonic vehicles （AHVs） is highly nonlinear and multivariable cou- pling, and includes inertial uncertainties and external disturbances that require strong, robust, and ...The flight dynamics model of air-breathing hypersonic vehicles （AHVs） is highly nonlinear and multivariable cou- pling, and includes inertial uncertainties and external disturbances that require strong, robust, and high-accuracy controllers. In this paper, we propose a linear-quadratic regulator （LQR） design method based on stochastic robustness analysis for the longitudinal dynamics of AHVs. First, input/output feedback linearization is used to design LQRs. Second, subject to various system parameter uncertainties, system robustness is characterized by the probability of stability and desired performance. Then, the mapping rela- tionship between system robustness and LQR parameters is established. Particularly, to maximize system robustness, a novel hybrid particle swarm optimization algorithm is proposed to search for the optimal LQR parameters. During the search iteration, a Chernoff bound algorithm is applied to determine the finite sample size of Monte Carlo evaluation with the given prohabilily levels. Finally, simulation results show that the optimization algorithm can effectively find the optimal solution to the LQR parameters.展开更多
This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabiliza...This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabilizability condition which is weaker than the controllability,normally imposed in the similar problem for ordinary differential systems.In dealing with the turnpike problem,a crucial issue is to determine the corresponding static optimization problem.Intuitively mimicking the deterministic situations,it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization problem.However,this would lead us to a wrong direction.It is found that the correct static problem should contain the diffusion as a part of the objective function,which reveals a deep feature of the stochastic turnpike problem.展开更多
In this paper a class of iterative methods for the minimax problem i; proposed.We present a sequence of the extented linear-quadratic programming (ELQP) problems as subproblems of the original minimal problem and solv...In this paper a class of iterative methods for the minimax problem i; proposed.We present a sequence of the extented linear-quadratic programming (ELQP) problems as subproblems of the original minimal problem and solve the ELQP problem iteratively.The locally linear and su-perlinear convergence results of the algorithm are established.展开更多
We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of re...We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.展开更多
This paper investigates a linear-quadratic mean-field stochastic optimal control problem under both positive definite case and indefinite case where the controlled systems are mean-field stochastic differential equati...This paper investigates a linear-quadratic mean-field stochastic optimal control problem under both positive definite case and indefinite case where the controlled systems are mean-field stochastic differential equations driven by a Brownian motion and Teugels mar-tingales associated with Lévy processes.In either case,we obtain the optimality system for the optimal controls in open-loop form,and by means of a decoupling technique,we obtain the optimal controls in closed-loop form which can be represented by two Riccati differen-tial equations.Moreover,the solvability of the optimality system and the Riccati equations are also obtained under both positive definite case and indefinite case.展开更多
A defender–attacker–target problem with non-moving target is considered.This problem is modelled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional.In this game,the pu...A defender–attacker–target problem with non-moving target is considered.This problem is modelled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional.In this game,the pursuer is the defender,while the evader is the attacker.The objective of the pursuer is to minimise the cost functional,while the evader has two objectives:to maximise the cost functional and to keep a given terminal state inequality constraint.The open-loop saddle point solution of this game is obtained in the case where the transfer functions of the controllers for the defender and the attacker are of arbitrary orders.展开更多
A kind of linear-quadratic Stackelberg games with the multilevel hierarchy driven by both Brownian motion and Poisson processes is considered.The Stackelberg equilibrium is presented by linear forward-backward stochas...A kind of linear-quadratic Stackelberg games with the multilevel hierarchy driven by both Brownian motion and Poisson processes is considered.The Stackelberg equilibrium is presented by linear forward-backward stochastic differential equations(FBSDEs)with Poisson processes(FBSDEPs)in a closed form.By the continuity method,the unique solvability of FBSDEPs with a multilevel self-similar domination-monotonicity structure is obtained.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 61273054,60975072,60604009)the Program for New Century Excellent Talents in University of China (Grant No. NCET-10-0021)+1 种基金the Aeronautical Foundation of China (Grant No. 20115151019)the Opening Foundation of State Key Laboratory of Virtual Reality Technology and Systems of China (Grant No. VR-2011-ZZ-01)
文摘This paper describes a novel type of pendulum-like oscillation controller for micro air vehicle(MAV) hover and stare state in the presence of external disturbances,which is based on linear-quadratic regulator(LQR) and particle swarm optimization(PSO).A linear mathematical model of pendulum phenomenon based upon actual wind tunnel test data representing the hover mode is established,and a hybrid LQR and PSO approach is proposed to stabilize oscillation.PSO is applied to parameter optimization of the designed LQR controller.A series of comparative experiments are conducted,and the results have verified the feasibility,effectiveness and robustness of our proposed approach.
基金supported by National Natural Science Foundation of China (Grant Nos.12025105, 11971334 and 11931011)the Chang Jiang Scholars Program and the Science Development Project of Sichuan University (Grant Nos. 2020SCUNL101 and 2020SCUNL201)。
文摘A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).
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.
基金supported by the National Key R&D Program of China under Grant No. 2022YFA1006103the National Natural Science Foundation of China under Grant Nos. 61821004, 61925306, and 11831010the Natural Science Foundation of Shandong Province under Grant Nos. ZR2019ZD42 and ZR2020ZD24。
文摘This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost functional. Based on a weighted sum optimality method, the Pareto game is equivalently converted to an optimal control problem. In the first place,the feedback form of Pareto optimal strategy is derived by virtue of decoupling technology, which is represented by four Riccati equations, a mean-field forward stochastic differential equation(MF-FSDE),and a mean-field backward stochastic differential equation(MF-BSDE). In addition, the corresponding Pareto optimal solution is further obtained. Finally, the author solves a problem in mathematical finance to illustrate the application of the theoretical results.
基金supported by the National Natural Science Foundation of China(11961052,62173355)the Natural Science Foundation of Inner Mongolia(2021MS01006)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT2317)。
文摘This paper aims at solving the linear-quadratic optimal control problems(LQOCP)for time-varying descriptor systems in a real Hilbert space.By using the Moore-Penrose inverse theory and space decomposition technique,the descriptor system can be rewritten as a new differential-algebraic equation(DAE),and then some novel sufficient conditions for the solvability of LQOCP are obtained.Especially,the methods proposed in this work are simpler and easier to verify and compute,and can solve LQOCP without the range inclusion condition.In addition,some numerical examples are shown to verify the results obtained.
基金Project supported by the 973 National Basic Research Program of China (No. 2007CB814904)the National Natural Science Foundations of China (No. 10921101)+2 种基金the Shandong Provincial Natural Science Foundation of China (No. 2008BS01024)the Science Fund for Distinguished Young Scholars of Shandong Province (No. JQ200801)the Shandong University Science Fund for Distinguished Young Scholars(No. 2009JQ004)
文摘The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.
基金the National Natural Science Foundation of China （No. 11672235）
文摘The flight dynamics model of air-breathing hypersonic vehicles （AHVs） is highly nonlinear and multivariable cou- pling, and includes inertial uncertainties and external disturbances that require strong, robust, and high-accuracy controllers. In this paper, we propose a linear-quadratic regulator （LQR） design method based on stochastic robustness analysis for the longitudinal dynamics of AHVs. First, input/output feedback linearization is used to design LQRs. Second, subject to various system parameter uncertainties, system robustness is characterized by the probability of stability and desired performance. Then, the mapping rela- tionship between system robustness and LQR parameters is established. Particularly, to maximize system robustness, a novel hybrid particle swarm optimization algorithm is proposed to search for the optimal LQR parameters. During the search iteration, a Chernoff bound algorithm is applied to determine the finite sample size of Monte Carlo evaluation with the given prohabilily levels. Finally, simulation results show that the optimization algorithm can effectively find the optimal solution to the LQR parameters.
基金supported by the National Natural Science Foundation of China(No.11901280,12271242,12201424)Guangdong Basic and Applied Basic Research Foundation(No.2021A1515010031)+1 种基金Shenzhen Fundamental Research General Program(No.JCYJ20220530112814032)NSF(No.DMS-1812921)。
文摘This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabilizability condition which is weaker than the controllability,normally imposed in the similar problem for ordinary differential systems.In dealing with the turnpike problem,a crucial issue is to determine the corresponding static optimization problem.Intuitively mimicking the deterministic situations,it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization problem.However,this would lead us to a wrong direction.It is found that the correct static problem should contain the diffusion as a part of the objective function,which reveals a deep feature of the stochastic turnpike problem.
文摘In this paper a class of iterative methods for the minimax problem i; proposed.We present a sequence of the extented linear-quadratic programming (ELQP) problems as subproblems of the original minimal problem and solve the ELQP problem iteratively.The locally linear and su-perlinear convergence results of the algorithm are established.
基金supported by National Natural Science Foundation of China (Grant Nos. 61573217,11471192 and 11626142)the National High-Level Personnel of Special Support Program,the Chang Jiang Scholar Program of Chinese Education Ministry+2 种基金the Natural Science Foundation of Shandong Province (Grant Nos. JQ201401 and ZR2016AB08)the Colleges and Universities Science and Technology Plan Project of Shandong Province (Grant No. J16LI55)the Fostering Project of Dominant Discipline and Talent Team of Shandong University of Finance and Economics
文摘We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.
基金supported by the Key Projects of Natural Science Foundation of Zhejiang Province of China(no.Z22A013952)the National Natural Science Foundation of China(no.11871121)supported by the Natural Science Foundation of Zhejiang Province of China(no.LY21A010001).
文摘This paper investigates a linear-quadratic mean-field stochastic optimal control problem under both positive definite case and indefinite case where the controlled systems are mean-field stochastic differential equations driven by a Brownian motion and Teugels mar-tingales associated with Lévy processes.In either case,we obtain the optimality system for the optimal controls in open-loop form,and by means of a decoupling technique,we obtain the optimal controls in closed-loop form which can be represented by two Riccati differen-tial equations.Moreover,the solvability of the optimality system and the Riccati equations are also obtained under both positive definite case and indefinite case.
文摘A defender–attacker–target problem with non-moving target is considered.This problem is modelled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional.In this game,the pursuer is the defender,while the evader is the attacker.The objective of the pursuer is to minimise the cost functional,while the evader has two objectives:to maximise the cost functional and to keep a given terminal state inequality constraint.The open-loop saddle point solution of this game is obtained in the case where the transfer functions of the controllers for the defender and the attacker are of arbitrary orders.
基金supported by National Natural Science Foundation of China(Grant Nos.11871310,11801317,61873325 and 11831010)the Natural Science Foundation of Shandong Province(Grant No.ZR2019MA013)+1 种基金the National Key R&D Program of China(Grant No.2018YFA0703900)the Colleges and Universities Youth Innovation Technology Program of Shandong Province(Grant No.2019KJI011)。
文摘A kind of linear-quadratic Stackelberg games with the multilevel hierarchy driven by both Brownian motion and Poisson processes is considered.The Stackelberg equilibrium is presented by linear forward-backward stochastic differential equations(FBSDEs)with Poisson processes(FBSDEPs)in a closed form.By the continuity method,the unique solvability of FBSDEPs with a multilevel self-similar domination-monotonicity structure is obtained.
