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Bellman equation

About: Bellman equation is a research topic. Over the lifetime, 5884 publications have been published within this topic receiving 135589 citations.


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01 Jan 1994
TL;DR: In this article, a general framework for hybrid control problems is proposed, which encompasses several types of hybrid phenomena considered in the literature, leading to an existence result for optimal control, and the value function associated with this problem is expected to satisfy a set of generalized quasi-variational inequalities.
Abstract: We propose a very general framework for hybrid control problems which encompasses several types of hybrid phenomena considered in the literature. A specific control problem is studied in this framework, leading to an existence result for optimal controls. The "value function" associated with this problem is expected to satisfy a set of "generalized quasi-variational inequalities" which are formally derived.

69 citations

Journal ArticleDOI
TL;DR: A new dynamic programming method for the single item capacitated dynamic lot size model with non-negative demands and no backlogging is developed, which builds the Optimal value function in piecewise linear segments.
Abstract: We develop a new dynamic programming method for the single item capacitated dynamic lot size model with non-negative demands and no backlogging. This approach builds the Optimal value function in piecewise linear segments. It works very well on the test problems, requiring less than 0.3 seconds to solve problems with 48 periods on a VAX 8600. Problems with the time horizon up to 768 periods are solved. Empirically, the computing effort increases only at a quadratic rate relative to the number of periods in the time horizon.

69 citations

Journal ArticleDOI
TL;DR: A model of hybrid control system in which both discrete and continuous controls are involved is investigated, and a quasi-variational inequality satisfied by V in the viscosity sense is derived.
Abstract: We investigate a model of hybrid control system in which both discrete and continuous controls are involved. In this general model, discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where the controller can choose to jump or not. At each jump, the trajectory can move to a different Euclidean space. We prove the continuity of the associated value function V with respect to the initial point. Using the dynamic programming principle satisfied by V, we derive a quasi-variational inequality satisfied by V in the viscosity sense. We characterize the value function V as the unique viscosity solution of the quasi-variational inequality by the comparison principle method.

69 citations

Journal ArticleDOI
TL;DR: This work considers differentiability with respect to the switch times of the value function of an optimal control problem for a non-autonomous switched system and provides a method to compute the derivative of the cost function given a nominal input.

68 citations

Journal ArticleDOI
TL;DR: In this article, the authors deal with an endogenous growth model with vintage capital and more precisely with the AK model proposed in [R. Boucekkine, O. Licandro, L. Puch, F. del Rio, and L.A.

68 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023261
2022537
2021369
2020411
2019348
2018353