Abstract
In Sect. 1.2 of this first chapter, we formulate the infinite-horizon discrete-time optimal control problems that we study. The considered systems are governed by difference equations or by difference inequations. We define four optimality criterions on such systems. In Sect. 1.3, we describe a method that we call the reduction to finite horizon: we associate to an optimal process of an infinite-horizon problem a sequence of finite-horizon problems for which the restrictions of the optimal process are solutions. In Sect. 1.4, we begin to specify the notion of strong maximum principle and of weak maximum principle and we use the contribution of Boltyanskii to understand interesting differences between them. To obtain weak maximum principles on finite-horizon problems we use the multiplier rules of Halkin and of Clarke. To obtain strong maximum principles on finite-horizon problems we present a result of Michel and we adapt a condition of Pschenichnyi.
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© 2014 Joël Blot, Naïla Hayek
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Blot, J., Hayek, N. (2014). Presentation of the Problems and Tools of the Finite Horizon. In: Infinite-Horizon Optimal Control in the Discrete-Time Framework. SpringerBriefs in Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9038-8_1
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