ISA Transactions, ( ISI ), Volume (52), No (5), Year (2013-9) , Pages (611-621)

Title : ( A policy iteration approach to online optimal control of continuous-time constrained-input systems )

Authors: Hamidreza Modares , Mohammad Bagher Naghibi Sistani , Frank L. Lewis ,

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Abstract

This paper is an effort towards developing an online learning algorithm to find the optimal control solution for continuous-time (CT) systems subject to input constraints. The proposed method is based on the policy iteration (PI) technique which has recently evolved as a major technique for solving optimal control problems. Although a number of online PI algorithms have been developed for CT systems, none of them take into account the input constraints caused by actuator saturation. In practice, however, ignoring these constraints leads to performance degradation or even system instability. In this paper, to deal with the input constraints, a suitable nonquadratic functional is employed to encode the constraints into the optimization formulation. Then, the proposed PI algorithm is implemented on an actor–critic structure to solve the Hamilton–Jacobi–Bellman (HJB) equation associated with this nonquadratic cost functional in an online fashion. That is, two coupled neural network (NN) approximators, namely an actor and a critic are tuned online and simultaneously for approximating the associated HJB solution and computing the optimal control policy. The critic is used to evaluate the cost associated with the current policy, while the actor is used to find an improved policy based on information provided by the critic. Convergence to a close approximation of the HJB solution as well as stability of the proposed feedback control law are shown. Simulation results of the proposed method on a nonlinear CT system illustrate the effectiveness of the proposed approach.

Keywords

Optimal control Reinforcement learning Policy iteration Neural networks Input constraints
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@article{paperid:1040140,
author = {Modares, Hamidreza and Naghibi Sistani, Mohammad Bagher and Frank L. Lewis},
title = {A policy iteration approach to online optimal control of continuous-time constrained-input systems},
journal = {ISA Transactions},
year = {2013},
volume = {52},
number = {5},
month = {September},
issn = {0019-0578},
pages = {611--621},
numpages = {10},
keywords = {Optimal control Reinforcement learning Policy iteration Neural networks Input constraints},
}

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%0 Journal Article
%T A policy iteration approach to online optimal control of continuous-time constrained-input systems
%A Modares, Hamidreza
%A Naghibi Sistani, Mohammad Bagher
%A Frank L. Lewis
%J ISA Transactions
%@ 0019-0578
%D 2013

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