Abstract
This work addresses a pattern-moving-based partial form dynamic linearization model free adaptive control (P-PFDL-MFAC) scheme and illustrates the bounded convergence of its tracking error for a class of unknown nonaffine nonlinear discrete-time systems. The concept of pattern moving is to take the pattern class of the system output condition as a dynamic operation variable, and the control purpose is to ensure that the system outputs belong to a certain pattern class or some desired pattern classes. The P-PFDL-MFAC scheme mainly includes a modified tracking control law, a deviation estimation algorithm and a pseudo-gradient (PG) vector estimation algorithm. The classification-metric deviation is considered as an external disturbance, which is caused by the process of establishing the pattern-moving-based system dynamics description, and an improved cost function is proposed from the perspective of a two-player zero-sum game (TP-ZSG). The bounded convergence of the tracking error is rigorously proven by the contraction mapping principle, and the validity of the theoretical results is verified by simulation examples.
Highlights
Another major contribution is that the bounded convergence of the tracking error dynamics of the closed-loop control system is rigorously proven by using the contraction mapping principle
The P-partial form dynamic linearization (PFDL)-model free adaptive control (MFAC) method can be considered a novel data-driven method based on offline historical data and online real-time data, and this is a major difference from the traditional MFAC methods
Due to the existence of classification-metric deviation, an improved cost function for a deviation estimation algorithm and an adaptive tracking control law is designed based on the saddle point theory of two-player zero-sum game (TP-ZSG)
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The length of the time window corresponds to the number of PG vector elements, which is called the pseudo-order of the equivalent PFDL data model This is the most significant difference between the method proposed here and the pattern-moving-based CFDL-MFAC (P-CFDL-MFAC) scheme in [30], which considered that the output difference between time and the current time is only related to the input difference between the current time and the previous time. Actuators 2021, 10, 223 dynamics description with the traditional PFDL-MFAC method, and to design a control law algorithm based on two-player zero-sum game and saddle point theory [31,32] under the condition of classification-metric deviation Another major contribution is that the bounded convergence of the tracking error dynamics of the closed-loop control system is rigorously proven by using the contraction mapping principle. R is the real n-dimensional space; [·] T is the transpose of [·]; k · k is the Euclidean norm, and k · kv is the consistent matrix norm
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