Relaxed long run average continuous control of piecewise deterministic Markov processes

2007 ◽  
Author(s):  
Oswaldo L. V. Costa ◽  
F. Dufour
Keyword(s):  
Markov Processes ◽  
Continuous Control ◽  
Long Run ◽  
Piecewise Deterministic Markov Processes

scholarly journals The Vanishing Discount Approach for the Average Continuous Control of Piecewise Deterministic Markov Processes

2009 ◽  
Vol 46 (04) ◽  
pp. 1157-1183 ◽  
Author(s):  
O. L. V. Costa ◽  
F. Dufour
Keyword(s):  
Optimal Control ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Relative Difference ◽  
Continuous Control ◽  
Value Functions ◽  
Optimal Control Strategy ◽  
Long Run ◽  
Piecewise Deterministic Markov Processes ◽  
Vanishing Discount Approach

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the α-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

scholarly journals The Vanishing Discount Approach for the Average Continuous Control of Piecewise Deterministic Markov Processes

2009 ◽  
Vol 46 (4) ◽  
pp. 1157-1183 ◽  
Author(s):  
O. L. V. Costa ◽  
F. Dufour
Keyword(s):  
Optimal Control ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Relative Difference ◽  
Continuous Control ◽  
Value Functions ◽  
Optimal Control Strategy ◽  
Long Run ◽  
Piecewise Deterministic Markov Processes ◽  
Vanishing Discount Approach

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the α-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

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