Stochastic Control in Discrete and Continuous Time

Seierstad, Atle

doi:10.1007/978-0-387-76617-1

Cited by 45 publications

(35 citation statements)

References 1 publication

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“…As an illustration, we begin with an example (see [17]) to show the difficulty of designing penalty functions. Consider the following state equation:…”

Section: A Canonical Examplementioning

confidence: 99%

Parameterized penalties in the dual representation of Markov decision processes

Fan

Zhou

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Duality in Markov decision processes (MDPs) has been studied recently by several researchers with the goal to derive dual bounds on the value function. In this paper we propose the idea of using parameterized penalty functions in the dual representation of MDPs, which allows us to integrate different types of penalty functions and guarantees a tighter dual bound with more penalties used. To complement and diversify the existing linear penalties developed in the literature, we also introduce a new class of nonlinear penalties that can be used for a broad class of problems and are also easy to implement in practice. Based on this new class of penalties, our framework of parameterized penalties is a promising method to produce tighter dual bounds than existing dualitybased methods. We compare the performance of the dual bounds induced by different penalties on a numerical example, demonstrating the effectiveness of our method.

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“…As an illustration, we begin with an example (see [17]) to show the difficulty of designing penalty functions. Consider the following state equation:…”

Section: A Canonical Examplementioning

confidence: 99%

Parameterized penalties in the dual representation of Markov decision processes

Fan

Zhou

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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“…By (22), (23), taking lim sup as T → t 1 , gives h(x * (t 1 )) h(x(t 1 )), so (x * (t), u * (t)) is optimal. For the general case ({ i } i larger than { i } i ) see Proof of Remark 2.10 in Chapter 2 in [12] (in this case the local Lipschitz property is needed).…”

Section: Example 4 (Growth Causing Pollution With Negative Effects)mentioning

confidence: 99%

Control problems with surfaces triggering jumps in the state variables

Seierstad

Stabrun

2009

Optim Control Appl Methods

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By means of some simple examples from economics, we elucidate certain solution tools for the solution of optimal control problems where the system under study undergoes major changes when certain boundaries are crossed. The 'major changes' may be that the state jumps when crossing a boundary, or that the right-hand side of the differential equation changes. Some theoretical results are also presented. In Appendix more or less sketchy proofs of these results are given.

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“…It suffices to prove the above theorem for the particular case where the criterion is ax(t 1 ). We shall refer to the proof of Remark 2.23 in Seierstad (2008). Write v = (s, y).…”

Section: Sufficient Conditionsmentioning

confidence: 99%

Discontinuous Control Systems

Boiko¹

2009

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. By means of some simple examples from economics, we elucidate certain solution tools for the solution of optimal control problems were the system under study undergoes major changes when certain boundaries are crossed. The "major changes" may be that the state gets a jump discontinuity when crossing a boundary, or that the right hand side of the differential equation changes. Some theoretical result are presented. Among the results presented, at least the sufficient condition related to fields of extremals should be new. Terms of use: Documents in.

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Stochastic Control in Discrete and Continuous Time

Cited by 45 publications

References 1 publication

Parameterized penalties in the dual representation of Markov decision processes

Parameterized penalties in the dual representation of Markov decision processes

Control problems with surfaces triggering jumps in the state variables

Discontinuous Control Systems

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