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

Author(s):  
Ying Hu ◽  
Xiaomin Shi ◽  
Zuo Quan Xu

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.

2014 ◽  
Vol 62 (4) ◽  
pp. 835-841 ◽  
Author(s):  
J. Bernat ◽  
S. Stępień ◽  
A. Stranz ◽  
G. Szymański ◽  
J.K. Sykulski

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.


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