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

TL;DR

This paper introduces a numerical method based on approximate dynamic programming for generating control policies in undiscounted, infinite-horizon nonlinear optimal control problems with continuous states, allowing for convergence of both policy and system state.

Contribution

It extends existing methods by enabling convergence criteria that include both control policy and system state, applicable to undiscounted, bounded, continuous cost functions.

Findings

Method successfully generates control policies for complex nonlinear systems.

Convergence of policy and state is achieved without discounting.

MATLAB implementation and examples demonstrate practical applicability.

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.