This article addresses a multilayer neural network (MNN)-based optimal adaptive tracking of partially uncertain nonlinear discrete-time (DT) systems in affine form. By employing an actor–critic neural network (NN) to approximate the value function and optimal control policy, the critic NN is updated via a novel hybrid learning scheme, where its weights are adjusted once at a sampling instant and also in a finite iterative manner within the instants to enhance the convergence rate. Moreover, to deal with the persistency of excitation (PE) condition, a replay buffer is incorporated into the critic update law through concurrent learning. To address the vanishing gradient issue, the actor and critic MNN weights are tuned using control input and temporal difference errors (TDEs), respectively. In addition, a weight consolidation scheme is incorporated into the critic MNN update law to attain lifelong learning and overcome catastrophic forgetting, thus lowering the cumulative cost. The tracking error, and the actor and critic weight estimation errors are shown to be bounded using the Lyapunov analysis. Simulation results using the proposed approach on a two-link robot manipulator show a significant reduction in tracking error by $44\%$ and cumulative cost by $31\%$ in a multitask environment.


Electrical and Computer Engineering

Publication Status

Early Access

Keywords and Phrases

Artificial neural networks; Convergence; Discrete-time (DT) concurrent learning; experience replay; Hybrid learning; hybrid learning; Iterative methods; lifelong learning (LL); multilayer neural networks (MNNs); Optimal control; optimal tracking control (OTC); Task analysis; Trajectory

International Standard Serial Number (ISSN)

2162-2388; 2162-237X

Document Type

Article - Journal

Document Version


File Type





© 2023 Institute of Electrical and Electronics Engineers, All rights reserved.

Publication Date

01 Jan 2023