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    This study introduces an adaptive tracking method for nonlinear systems using multilayer neural networks (MNNs). The approach significantly reduces tracking errors and cumulative costs in robotic systems, enabling lifelong learning.

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    Area of Science:

    • Control Engineering
    • Artificial Intelligence
    • Robotics

    Background:

    • Nonlinear discrete-time (DT) systems with partial uncertainty pose significant control challenges.
    • Adaptive tracking control requires robust methods to handle system dynamics and uncertainties.
    • Existing methods may struggle with convergence rates and catastrophic forgetting in lifelong learning scenarios.

    Purpose of the Study:

    • To develop an optimal adaptive tracking control strategy for partially uncertain nonlinear DT systems.
    • To enhance the convergence rate and stability of neural network-based control.
    • To enable lifelong learning capabilities and prevent catastrophic forgetting in control systems.

    Main Methods:

    • Utilized a multilayer neural network (MNN) with an actor-critic architecture to approximate value functions and optimal control policies.
    • Implemented a hybrid learning scheme for critic NN weight updates, combining instantaneous and iterative adjustments.
    • Incorporated a replay buffer for concurrent learning to address the persistency of excitation (PE) condition.
    • Employed control input and temporal difference errors (TDEs) to tune actor and critic MNN weights, mitigating vanishing gradients.
    • Integrated a weight consolidation scheme for lifelong learning and prevention of catastrophic forgetting.

    Main Results:

    • Demonstrated bounded tracking error and weight estimation errors using Lyapunov analysis.
    • Achieved a significant 44% reduction in tracking error on a two-link robot manipulator.
    • Showcased a 31% reduction in cumulative cost in a multitask environment.
    • Validated the effectiveness of the hybrid learning and weight consolidation schemes.

    Conclusions:

    • The proposed MNN-based optimal adaptive tracking control is effective for partially uncertain nonlinear DT systems.
    • The novel hybrid learning and concurrent learning strategies enhance convergence and stability.
    • Lifelong learning capabilities are successfully integrated, preventing catastrophic forgetting and reducing cumulative cost.