Abstract
This paper provides necessary conditions in order to guarantee the existence of an unique equilibrium point in a deterministic control system. Furthermore, under additional conditions, it is proved the convergence of the optimal control sequence to this equilibrium point. The methodology to obtain these statements is based on the Euler's equation approach. A consumption-investment problem is presented with the objective to illustrate the results exposed.
Highlights
In this document a Deterministic Control System (DCS) is considered
This paper provides necessary conditions in order to guarantee the existence of an unique equilibrium point in a deterministic control system
Under additional conditions, it is proved the convergence of the optimal control sequence to this equilibrium point
Summary
A DCS is used to modelling dynamic systems, which are observed in a discrete time by a controller with the purpose that the system performs effectively with respect to certain optimality criteria (objective function). The optimal control problems consist in determining an optimal policy, i.e. a policy that minimizes the objective function These classes of problems are included in the theory of Markov Decision Processes (Hernandez-Lerma & Jean, 1996; Hinderer, Rieder & Stieglitz, 2017). In this context, a problem of interest is analysing the asymptotic behaviour of the optimal trajectory of the system, this problem is addressed in this document
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