This paper aims to provide a systematic approach to investigate the optimal feedback control systems governed by the fractional neutral evolution system with fixed delay in the sense of Caputo fractional derivatives i...This paper aims to provide a systematic approach to investigate the optimal feedback control systems governed by the fractional neutral evolution system with fixed delay in the sense of Caputo fractional derivatives in separable reflexive Banach spaces.Initially,we study the existence result of mild solutions for the system by applying fixed point theorem for a condensing map due to Martelli.The existence of feasible pairs is obtained by using the Filippov theorem and the Cesari property.Furthermore,the existence of optimal feedback control and time optimal control are studied for the corresponding control problem.Finally,an example is given to validate our findings.展开更多
This paper considers optimal feedback control for a general continuous time finite-dimensional deterministic system with finite horizon cost functional. A practically feasible algorithm to calculate the numerical solu...This paper considers optimal feedback control for a general continuous time finite-dimensional deterministic system with finite horizon cost functional. A practically feasible algorithm to calculate the numerical solution of the optimal feedback control by dynamic programming approach is developed. The highlights of this algorithm are: a) It is based on a convergent constructive algorithm for optimal feedback control law which was proposed by the authors before through an approximation for the viscosity solution of the time-space discretization scheme developed by dynamic programming method; b) The computation complexity is significantly reduced since only values of viscosity solution on some local cones around the optimal trajectory are calculated. Two numerical experiments are presented to illustrate the effectiveness and fastness of the algorithm.展开更多
A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the p...A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It6 stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov （FPK） equation associated with the It6 equations is obtained. The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under E1 Centro, Hachinohe, Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.展开更多
Optimal feedback control of nonlinear system with free terminal time present many challenges including nonsmooth in the value function and control laws,and existence of multiple local or even global optimal trajectori...Optimal feedback control of nonlinear system with free terminal time present many challenges including nonsmooth in the value function and control laws,and existence of multiple local or even global optimal trajectories.To mitigate these issues,the authors introduce an actor-critic method along with some enhancements.The authors demonstrate the algorithm's effectiveness on a prototypical example featuring each of the main pathological issues present in problems of this type as well as a higher dimensional example to show that the solution method presented can scale.展开更多
The author studies a stochastic linear quadratic(SLQ for short)optimal control problem for systems governed by stochastic evolution equations,where the control operator in the drift term may be unbounded.Under the con...The author studies a stochastic linear quadratic(SLQ for short)optimal control problem for systems governed by stochastic evolution equations,where the control operator in the drift term may be unbounded.Under the condition that the cost functional is uniformly convex,the well-posedness of the operator-valued Riccati equation is proved.Based on that,the optimal feedback control of the control problem is given.展开更多
This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the so...This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the solution to the equation are also studied.展开更多
文摘This paper aims to provide a systematic approach to investigate the optimal feedback control systems governed by the fractional neutral evolution system with fixed delay in the sense of Caputo fractional derivatives in separable reflexive Banach spaces.Initially,we study the existence result of mild solutions for the system by applying fixed point theorem for a condensing map due to Martelli.The existence of feasible pairs is obtained by using the Filippov theorem and the Cesari property.Furthermore,the existence of optimal feedback control and time optimal control are studied for the corresponding control problem.Finally,an example is given to validate our findings.
文摘This paper considers optimal feedback control for a general continuous time finite-dimensional deterministic system with finite horizon cost functional. A practically feasible algorithm to calculate the numerical solution of the optimal feedback control by dynamic programming approach is developed. The highlights of this algorithm are: a) It is based on a convergent constructive algorithm for optimal feedback control law which was proposed by the authors before through an approximation for the viscosity solution of the time-space discretization scheme developed by dynamic programming method; b) The computation complexity is significantly reduced since only values of viscosity solution on some local cones around the optimal trajectory are calculated. Two numerical experiments are presented to illustrate the effectiveness and fastness of the algorithm.
基金Project supported by the National Natural Science Foundation of China under a key grant (No.10332030)the Research Fund for the Doctoral Program of Higher Education of China (No.20060335125)the Zhejiang Provincial Natural Science Foundation of China (No.Y607087).
文摘A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It6 stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov （FPK） equation associated with the It6 equations is obtained. The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under E1 Centro, Hachinohe, Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.
基金supported in part by the Air Force Office of Scientific Research(AFOSR),USA under Grant No.FA9550-21-1-0113the National Science Foundation(NSF),USA under Grant Nos.2134235 and 2202668。
文摘Optimal feedback control of nonlinear system with free terminal time present many challenges including nonsmooth in the value function and control laws,and existence of multiple local or even global optimal trajectories.To mitigate these issues,the authors introduce an actor-critic method along with some enhancements.The authors demonstrate the algorithm's effectiveness on a prototypical example featuring each of the main pathological issues present in problems of this type as well as a higher dimensional example to show that the solution method presented can scale.
基金supported by the National Natural Science Foundation of China(Nos.11971334,12025105)。
文摘The author studies a stochastic linear quadratic(SLQ for short)optimal control problem for systems governed by stochastic evolution equations,where the control operator in the drift term may be unbounded.Under the condition that the cost functional is uniformly convex,the well-posedness of the operator-valued Riccati equation is proved.Based on that,the optimal feedback control of the control problem is given.
基金partially supported by a grant from the Simons Foundation #209206
文摘This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the solution to the equation are also studied.
