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Mathematics > Optimization and Control

arXiv:2104.11093 (math)
[Submitted on 22 Apr 2021]

Title:Undiscounted Control Policy Generation for Continuous-Valued Optimal Control by Approximate Dynamic Programming

Authors:Jonathan Lock, Tomas McKelvey
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Abstract:We present a numerical method for generating the state-feedback control policy associated with general undiscounted, constant-setpoint, infinite-horizon, nonlinear optimal control problems with continuous state variables. The method is based on approximate dynamic programming, and is closely related to approximate policy iteration. Existing methods typically terminate based on the convergence of the control policy and either require a discounted problem formulation or demand the cost function to lie in a specific subclass of functions. The presented method extends on existing termination criteria by requiring both the control policy and the resulting system state to converge, allowing for use with undiscounted cost functions that are bounded and continuous. This paper defines the numerical method, derives the relevant underlying mathematical properties, and validates the numerical method with representative examples. A MATLAB implementation with the shown examples is freely available.
Comments: 12 pages, 8 figures
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
Cite as: arXiv:2104.11093 [math.OC]
  (or arXiv:2104.11093v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2104.11093

Submission history

From: Jonathan Lock [view email]
[v1] Thu, 22 Apr 2021 14:23:45 UTC (479 KB)
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