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Online Lifelong Optimal Adaptive Control of Partially Uncertain Strict Feedback Discrete-Time Systems With Application to Quadrotor UAVs
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DOI：10.1109/TCST.2026.3682792.png)
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Abstract
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This article considers the infinite time horizon optimal adaptive tracking control of partially uncertain strict feedback discrete-time (DT) systems with application to quadrotor uncrewed aerial vehicles (UAVs). First, the strict feedback DT system is transformed into an equivalent affine nonlinear DT system in terms of the tracking error dynamics. The optimal adaptive tracking control problem is solved using an augmented system approach, where a horizon of future bounded reference trajectory points is used in the augmented state, when compared to using a single point. It is assumed that the internal dynamics of the strict feedback system are unknown, but the control coefficient matrix is known. By applying approximate dynamic programming (ADP) using exclusively multilayer neural networks (MNNs), the optimal control policy is obtained without any other stabilizing controller. Lastly, regularization penalties are introduced for both the actor and critic NNs to support multitask learning. Upper bounds for the multitask learning hyperparameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> are proved for the first time in the online learning regime. Under our proposed MNN weight update laws, the tracking and weight estimation errors are proved to be uniformly ultimately bounded (UUB) using Lyapunov analysis. In particular, we consider the case of a quadrotor UAV where the system drift dynamics are unknown, but the control input matrix is known, corresponding to knowledge of the mass and principal moments of inertia of the UAV. The efficacy and reliability of the method are demonstrated through computer simulations and hardware implementation on the Quanser QDrone2 UAV, where the cost is reduced as much as 68% without the regularization penalty when compared to the initial control policy. With the regularization penalty, the cost is reduced by 2% compared to without using the penalty.
Keywords:
Aerial robotics
neural networks
optimal adaptive control
optimal tracking
reinforcement learning
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