ONLINE SOLUTION OF THE HAMILTON–JACOBI–BELLMAN EQUATION FOR NONLINEAR SYSTEMS WITH UNKNOWN DRIFT DYNAMICS USING NEURAL NETWORK

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MOJOODI ARMAN; NARAGHI MAHYAR; MORADI MOJTABA

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Journal: Modares Mechanical Engineering Year:2017 | Volume:16 | Issue:10 Page(s): 241-252

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Title

ONLINE SOLUTION OF THE HAMILTON–JACOBI–BELLMAN EQUATION FOR NONLINEAR SYSTEMS WITH UNKNOWN DRIFT DYNAMICS USING NEURAL NETWORK

Author(s)

MOJOODI ARMAN | NARAGHI MAHYAR | MORADI MOJTABA | Issue Writer Certificate

Keywords

HJB EQUATIONQ1

OPTIMAL CONTROLQ1

NONLINEAR SYSTEMQ1

NEURAL NETWORKQ2

ACTOR-CRITICQ1

Abstract

In this paper a method for online solution of the Hamilton-Jacobi–Bellman (HJB) equation is proposed.The method is utilized to design an OPTIMAL CONTROLler for continuous-time NONLINEAR SYSTEMs. The main concept in this approach is using experiences to reinforce the controller, which is called Reinforcement Learning (RL). The online solution is based on the ACTOR-CRITIC (AC) structure where two NEURAL NETWORKs (NNs) approximately solve the HJB EQUATION. OPTIMAL CONTROL and optimal value function are approximated by the actor and the critic, respectively. Then, employing gradient descent algorithm, accuracy of the approximation is improved. Since some items like friction and damping are difficult to model and calculate, a neural-robust identifier is used in conjunction with the AC to approximate drift dynamics. Finally, the ACTOR-CRITIC-Identifier (ACI) structure is proposed to solve the HJB EQUATION online with no prior knowledge of drift dynamics. The closed-loop stability of the overall system is assured by the Lyapunov theory employing the direct method. Then the effectiveness of the proposed method is illustrated by experiment for DC motor and simulation for a NONLINEAR SYSTEM. Results indicate satisfactory performance of the proposed method to solve the Hamilton-Jacobi-Bellman equation.

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APA: Copy

MOJOODI, ARMAN, NARAGHI, MAHYAR, & MORADI, MOJTABA. (2017). ONLINE SOLUTION OF THE HAMILTON–JACOBI–BELLMAN EQUATION FOR NONLINEAR SYSTEMS WITH UNKNOWN DRIFT DYNAMICS USING NEURAL NETWORK. MODARES MECHANICAL ENGINEERING, 16(10 ), 241-252. SID. https://sid.ir/paper/178265/en

Vancouver: Copy

MOJOODI ARMAN, NARAGHI MAHYAR, MORADI MOJTABA. ONLINE SOLUTION OF THE HAMILTON–JACOBI–BELLMAN EQUATION FOR NONLINEAR SYSTEMS WITH UNKNOWN DRIFT DYNAMICS USING NEURAL NETWORK. MODARES MECHANICAL ENGINEERING[Internet]. 2017;16(10 ):241-252. Available from: https://sid.ir/paper/178265/en

IEEE: Copy

ARMAN MOJOODI, MAHYAR NARAGHI, and MOJTABA MORADI, “ONLINE SOLUTION OF THE HAMILTON–JACOBI–BELLMAN EQUATION FOR NONLINEAR SYSTEMS WITH UNKNOWN DRIFT DYNAMICS USING NEURAL NETWORK,” MODARES MECHANICAL ENGINEERING, vol. 16, no. 10 , pp. 241–252, 2017, [Online]. Available: https://sid.ir/paper/178265/en

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