CONTROLLED MARKOV-CHAINS WITH CONSTRAINTS

被引:7
作者
BORKAR, VS
机构
[1] Department of Electrical Engineering, Indian Institute of Science, Bangalore
来源
SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES | 1990年 / 15卷
关键词
CONTROLLED MARKOV CHAINS; ERGODIC CONTROL; CONTROL UNDER CONSTRAINTS; OPTIMAL STRATEGY; STATIONARY STRATEGY;
D O I
10.1007/BF02811335
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We consider the ergodic control of a Markov chain on a countable state space with a compact action space in presence of finitely many (say, m) ergodic constraints. Under a condition on the cost functions that penalizes instability, the existence of an optimal stable stationary strategy randomized at a maximum of m states is established using convex analytic arguments.
引用
收藏
页码:405 / 413
页数:9
相关论文
共 12 条
[1]  
Altman E., Shwartz A., Sensitivity of constrained Markov decision processes, (1990)
[2]  
Beutler F.J, Ross K.W, Optimal policies for controlled Markov chains with a constraint, J. Math. Anal. Appl., 112, pp. 236-252, (1985)
[3]  
Billingsley P., Convergence of probability measures, (1968)
[4]  
Borkar V.S, Control of Markov chains with long-run average cost criterion: the dynamic programmin equations, SIAM J. Control Optim., 27, pp. 642-657, (1989)
[5]  
Borkar V.S, Topics in controlled Markov chains, Pitman research notes in mathematics, (1991)
[6]  
Dubins L., On extreme points of convex sets, J. Math. Anal. Appl., 5, pp. 237-244, (1962)
[7]  
Hordijk A., Kallenberg L.C.M, Constrained undiscounted stochastic dynamic programming, Math. Oper. Res., 9, pp. 276-289, (1984)
[8]  
Luenberger D., Optimization by vector space methods, (1967)
[9]  
Phelps R., Lectures on Choquet’s theorem, (1966)
[10]  
Ross K.W, Randomized and past-dependent policies for Markov decision processes with multiple constraints, Oper. Res., 37, pp. 474-477, (1989)