Enhanced P-Type Control: Indirect Adaptive Learning From Set-Point Updates

• Published in: IEEE transactions on automatic control Vol. 68; no. 3; pp. 1600 - 1613
• Main Authors: Chi, Ronghu, Li, Huaying, Shen, Dong, Hou, Zhongsheng, Huang, Biao
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Adaptive iterative learning control; Adaptive learning; Adaptive systems; Algorithms; Analytical models; Convergence; convergence analysis; Data models; Iterative methods; Learning; Linear systems; Nonlinear systems; Nonlinearity; P-type controller; set-point updating method; System theory; Systems theory; Tuning; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3154347

In this article, an indirect adaptive iterative learning control (iAILC) scheme is proposed for both linear and nonlinear systems to enhance the P-type controller by learning from set points. An adaptive mechanism is included in the iAILC method to regulate the learning gain using input-output measurements in real time. An iAILC method is first designed for linear systems to improve control performance by fully utilizing model information if such a linear model is known exactly. Then, an iterative dynamic linearization (IDL)-based iAILC is proposed for a nonlinear nonaffine system, whose model is completely unknown. The IDL technique is employed to deal with the strong nonlinearity and nonaffine structure of the systems such that a linear data model can be attained consequently for the algorithm design and performance analysis. The convergence of the developed iAILC schemes is proved rigorously, where contraction mapping, two-dimensional (2-D) Roesser's system theory, and mathematical induction are employed as the basic analysis tools. Simulation studies are provided to verify the developed theoretical results.