Optimal control for probabilistic Boolean networks using discrete-time Markov decision processes

2018 ◽  
Vol 503 ◽  
pp. 1297-1307
Author(s):  
Qiuli Liu ◽  
Yu He ◽  
Junwei Wang
Keyword(s):  
Optimal Control ◽  
Markov Decision Processes ◽  
Discrete Time ◽  
Boolean Networks ◽  
Decision Processes ◽  
Markov Decision ◽  
Probabilistic Boolean Networks

scholarly journals Optimal Intervention in Semi-Markov-Based Asynchronous Probabilistic Boolean Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Qiuli Liu ◽  
Qingguo Zeng ◽  
Jinghao Huang ◽  
Deliang Li
Keyword(s):  
Optimal Control ◽  
Markov Decision Processes ◽  
Value At Risk ◽  
Boolean Networks ◽  
Decision Processes ◽  
Finite Horizon ◽  
Average Value ◽  
Markov Decision ◽  
Probabilistic Boolean Networks ◽  
Average Value At Risk

Synchronous probabilistic Boolean networks (PBNs) and generalized asynchronous PBNs have received significant attention over the past decade as a tool for modeling complex genetic regulatory networks. From a biological perspective, the occurrence of interactions among genes, such as transcription, translation, and degradation, may require a few milliseconds or even up to a few seconds. Such a time delay can be best characterized by generalized asynchronous PBNs. This paper attempts to study an optimal control problem in a generalized asynchronous PBN by employing the theory of average value-at-risk (AVaR) for finite horizon semi-Markov decision processes. Specifically, we first formulate a control model for a generalized asynchronous PBN as an AVaR model for finite horizon semi-Markov decision processes and then solve an optimal control problem for minimizing average value-at-risk criterion over a finite horizon. In order to illustrate the validity of our approach, a numerical example is also displayed.

scholarly journals Impulsive Control for Continuous-Time Markov Decision Processes

2015 ◽  
Vol 47 (1) ◽  
pp. 106-127 ◽  
Author(s):  
François Dufour ◽  
Alexei B. Piunovskiy
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Markov Decision Processes ◽  
Control Strategy ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Optimal Control Strategy ◽  
Optimality Equation ◽  
Markov Decision

In this paper our objective is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite time horizon discounted cost. The continuous-time controlled process is shown to be nonexplosive under appropriate hypotheses. The so-called Bellman equation associated to this control problem is studied. Sufficient conditions ensuring the existence and the uniqueness of a bounded measurable solution to this optimality equation are provided. Moreover, it is shown that the value function of the optimization problem under consideration satisfies this optimality equation. Sufficient conditions are also presented to ensure on the one hand the existence of an optimal control strategy, and on the other hand the existence of a ε-optimal control strategy. The decomposition of the state space into two disjoint subsets is exhibited where, roughly speaking, one should apply a gradual action or an impulsive action correspondingly to obtain an optimal or ε-optimal strategy. An interesting consequence of our previous results is as follows: the set of strategies that allow interventions at time t = 0 and only immediately after natural jumps is a sufficient set for the control problem under consideration.

scholarly journals Impulsive Control for Continuous-Time Markov Decision Processes

2015 ◽  
Vol 47 (01) ◽  
pp. 106-127 ◽  
Author(s):  
François Dufour ◽  
Alexei B. Piunovskiy
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Markov Decision Processes ◽  
Control Strategy ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Optimal Control Strategy ◽  
Optimality Equation ◽  
Markov Decision

In this paper our objective is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite time horizon discounted cost. The continuous-time controlled process is shown to be nonexplosive under appropriate hypotheses. The so-called Bellman equation associated to this control problem is studied. Sufficient conditions ensuring the existence and the uniqueness of a bounded measurable solution to this optimality equation are provided. Moreover, it is shown that the value function of the optimization problem under consideration satisfies this optimality equation. Sufficient conditions are also presented to ensure on the one hand the existence of an optimal control strategy, and on the other hand the existence of a ε-optimal control strategy. The decomposition of the state space into two disjoint subsets is exhibited where, roughly speaking, one should apply a gradual action or an impulsive action correspondingly to obtain an optimal or ε-optimal strategy. An interesting consequence of our previous results is as follows: the set of strategies that allow interventions at time t = 0 and only immediately after natural jumps is a sufficient set for the control problem under consideration.

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