Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise

2013 ◽  
Vol 11 (4) ◽  
pp. 629-633 ◽  
Author(s):  
Huainian Zhu ◽  
Chengke Zhang
Keyword(s):  
Differential Games ◽  
Time Horizon ◽  
Stochastic Differential Games ◽  
Linear Quadratic ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
And Control

scholarly journals Linear Quadratic Nash Differential Games of Stochastic Singular Systems

2014 ◽  
Vol 2 (6) ◽  
pp. 553-560
Author(s):  
Haiying Zhou ◽  
Huainian Zhu ◽  
Chengke Zhang
Keyword(s):  
Differential Games ◽  
Finite Time ◽  
Time Horizon ◽  
Singular Systems ◽  
Existence Condition ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
Finite Time Horizon ◽  
Stochastic Singular Systems ◽  
Nash Differential Games

AbstractIn this paper, we deal with the Nash differential games of stochastic singular systems governed by Itô-type equation in finite-time horizon and infinite-time horizon, respectively. Firstly, the Nash differential game problem of stochastic singular systems in finite time horizon is formulated. By applying the results of stochastic optimal control problem, the existence condition of the Nash strategy is presented by means of a set of cross-coupled Riccati differential equations. Similarly, under the assumption of the admissibility of the stochastic singular systems, the existence condition of the Nash strategy in infinite-time horizon is presented by means of a set of cross-coupled Riccati algebraic equations. The results show that the strategies of each players interact.

scholarly journals Infinite time horizon optimal current control of a stepper motor exploiting a finite element model

2014 ◽  
Vol 62 (4) ◽  
pp. 835-841 ◽  
Author(s):  
J. Bernat ◽  
S. Stępień ◽  
A. Stranz ◽  
G. Szymański ◽  
J.K. Sykulski
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Time Horizon ◽  
Element Model ◽  
Current Control ◽  
Stepper Motor ◽  
Linear Quadratic ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
Optimal Current

Abstract An optimal control theory based method is presented aiming at minimizing the energy delivered from source and the power loss in a stepper motor circuit. A linear quadratic current regulator with an infinite time horizon is employed and its appropriateness for this type of a problem explained. With the purpose of improving the accuracy of the control system, the self and mutual inductances of windings are calculated using a finite element model. The numerically computed results are verified experimentally.

scholarly journals Constrained stochastic LQ control on infinite time horizon with regime switching

2021 ◽  
Author(s):  
Ying Hu ◽  
Xiaomin Shi ◽  
Zuo Quan Xu
Keyword(s):  
Regime Switching ◽  
Time Horizon ◽  
Random Coefficients ◽  
State Feedback Control ◽  
Linear Quadratic ◽  
Infinite Time ◽  
Approximation Techniques ◽  
Infinite Time Horizon ◽  
Nonnegative Solutions ◽  
Optimal State Feedback

This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. To tackle the problem, two new extended stochastic Riccati equations (ESREs) on infinite time horizon are introduced. The existence of the nonnegative solutions, in both standard and singular cases, is proved through a sequence of ESREs on finite time horizon. Based on this result and some approximation techniques, we obtain the optimal state feedback control and optimal value for the stochastic LQ problem explicitly. Finally, we apply these results to solve a lifetime portfolio selection problem of tracking a given wealth level with regime switching and portfolio constraint.

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