Abstract

In this paper, the Hamilton-Jacobi-Bellman equation is solved forward-in-time for the optimal control of a class of general affine nonlinear discrete-time systems without using value and policy iterations. the proposed approach, referred to as adaptive dynamic programming, uses two neural networks (NNs), to solve the infinite horizon optimal regulation control of affine nonlinear discrete-time systems in the presence of unknown internal dynamics and a known control coefficient matrix. One NN approximates the cost function and is referred to as the critic NN, while the second NN generates the control input and is referred to as the action NN. the cost function and policy are updated once at the sampling instant and thus the proposed approach can be referred to as time-Based ADP. Novel update laws for tuning the unknown weights of the NNs online are derived. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signal approaches the optimal control input with small, bounded error over time. in the absence of disturbances, an optimal control is demonstrated. Simulation results are included to show the effectiveness of the approach. the end result is the systematic design of an optimal controller with guaranteed convergence that is suitable for hardware implementation. © 2012 IEEE.

Department(s)

Electrical and Computer Engineering

Second Department

Computer Science

Comments

National Science Foundation, Grant ECCS 0621924

Keywords and Phrases

Hamilton-Jacobi-Bellman; online approximators; online nonlinear optimal control; time-based policy update

International Standard Serial Number (ISSN)

2162-2388; 2162-237X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.

Publication Date

01 Dec 2012

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