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

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...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Lock, Jonathan, McKelvey, Tomas
Format: Article
Language:English
Subjects:
Approximation
Continuity (mathematics)
Convergence
Cost function
Dynamic programming
Feedback control
Iterative methods
Nonlinear control
Numerical analysis
Numerical methods
Optimal control
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Summary: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.
ISSN:2331-8422