This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on ...This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.展开更多
The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval(possibly unknown)minimising a cost functional,while satisfying hard...The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval(possibly unknown)minimising a cost functional,while satisfying hard constraints on the input.In this framework,the minimum-time optimal control problem and some related problems are of interest for both theory and applications.For linear systems,the solution of the problem often relies upon the use of bang-bang control signals.For nonlinear systems,the“shape”of the optimal input is in general not known.The control input can be found solving a Hamilton–Jacobi–Bellman(HJB)partial differential equation(PDE):it typically consists of a combination of bang-bang controls and singular arcs.In this paper,a methodology to approximate the solution of the HJB PDE is proposed.This approximation yields a dynamic state feedback law.The theory is illustrated by means of two examples:the minimum-time optimal control problem for an industrial wastewater treatment plant and the Goddard problem,i.e.a maximum-range optimal control problem.展开更多
The suboptimal control program via memoryless state feedback strategies for LQ differential games with multiple players is studied in this paper. Sufficient conditions for the existence of the suboptimal strategies fo...The suboptimal control program via memoryless state feedback strategies for LQ differential games with multiple players is studied in this paper. Sufficient conditions for the existence of the suboptimal strategies for LQ differential games are presented. It is shown that the suboptimal strategies of LQ differential games are associated with a coupled algebraic Riccati inequality. Furthermore, the problem of designing suboptimal strategies is considered. A non-convex optimization problem with BMI constrains is formulated to design the suboptimal strategies which minimizes the performance indices of the closed-loop LQ differential games and can be solved by using LMI Toolbox of MATLAB. An example is given to illustrate the proposed results.展开更多
In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equatio...In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the Fokker-Planck formalism allows considering a larger classof objectives. To illustratethe connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.展开更多
文摘This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.
文摘The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval(possibly unknown)minimising a cost functional,while satisfying hard constraints on the input.In this framework,the minimum-time optimal control problem and some related problems are of interest for both theory and applications.For linear systems,the solution of the problem often relies upon the use of bang-bang control signals.For nonlinear systems,the“shape”of the optimal input is in general not known.The control input can be found solving a Hamilton–Jacobi–Bellman(HJB)partial differential equation(PDE):it typically consists of a combination of bang-bang controls and singular arcs.In this paper,a methodology to approximate the solution of the HJB PDE is proposed.This approximation yields a dynamic state feedback law.The theory is illustrated by means of two examples:the minimum-time optimal control problem for an industrial wastewater treatment plant and the Goddard problem,i.e.a maximum-range optimal control problem.
基金Supported by National Natural Science Foundation of P. R. China (10272001, 60334030, and 60474029)
文摘The suboptimal control program via memoryless state feedback strategies for LQ differential games with multiple players is studied in this paper. Sufficient conditions for the existence of the suboptimal strategies for LQ differential games are presented. It is shown that the suboptimal strategies of LQ differential games are associated with a coupled algebraic Riccati inequality. Furthermore, the problem of designing suboptimal strategies is considered. A non-convex optimization problem with BMI constrains is formulated to design the suboptimal strategies which minimizes the performance indices of the closed-loop LQ differential games and can be solved by using LMI Toolbox of MATLAB. An example is given to illustrate the proposed results.
基金the support by the European Science Foundation Exchange OPTPDE Grantthe support of CADMOS(Center for Advances Modeling and Science)Supported in part by the European Union under Grant Agreement“Multi-ITN STRIKE-Novel Methods in Computational Finance”.Fund Project No.304617 Marie Curie Research Training Network.
文摘In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the Fokker-Planck formalism allows considering a larger classof objectives. To illustratethe connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.
