Gradient Descent-Based Adaptive Control for Time-Varying Command Following

• Published in: IEEE transactions on automatic control Vol. 70; no. 6; pp. 4069 - 4076
• Main Authors: Jaramillo, Jesse, Yucelen, Tansel
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Adaptation models; Adaptive control; Control methods; Control systems; Control theory; Dynamical systems; Effectiveness; Gradient descent; Mathematical models; model reference adaptive control; Reference signals; Regulation; Robust control; Systems theory; Time-domain analysis; time-varying command following; Time-varying systems; uncertain dynamical systems; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2025.3527289

Output regulation theory is an effective method for achieving accurate time-varying command following and can utilize adaptive internal models to follow arbitrary reference signals generated by an exosystem. However, implementing these models can still lead to complexities, particularly regarding increased controller order and the dimensionality of gain matrices. This article contributes a gradient descent-based adaptive control method for uncertain dynamical systems. This method offers an alternative approach for the time-varying command following problem by altering both reference model trajectories and the control signal. As the gain of the proposed method increases, it can enable following every potential time-varying command profile without specificity. In addition to the presented system-theoretical results, three illustrative numerical examples are included to show the efficacy of the proposed gradient descent-based term for the time-varying command following problem.