Optimal Adaptive Control of Uncertain Nonlinear Continuous-Time Systems with Input and State Delays


In this article, an actor-critic neural network (NN)-based online optimal adaptive regulation of a class of nonlinear continuous-time systems with known state and input delays and uncertain system dynamics is introduced. The temporal difference error (TDE), which is dependent upon state and input delays, is derived using actual and estimated value function and via integral reinforcement learning. The NN weights of the critic are tuned at every sampling instant as a function of the instantaneous integral TDE. A novel identifier, which is introduced to estimate the control coefficient matrices, is utilized to obtain the estimated control policy. The boundedness of the state vector, critic NN weights, identification error, and NN identifier weights are shown through the Lyapunov analysis. Simulation results are provided to illustrate the effectiveness of the proposed approach.


Electrical and Computer Engineering

Publication Status

Early Access

Keywords and Phrases

Adaptive Control; Artificial Neural Networks; Delays; Discrete-Time Systems; Mathematical Models; Multilayer Neural Network (NN); Nonlinear Dynamical Systems; Optimal Adaptive Control.; Optimal Control; System Dynamics

International Standard Serial Number (ISSN)

2162-2388; 2162-237X

Document Type

Article - Journal

Document Version


File Type





© 2021 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

29 Sep 2021