Iterative Learning Control for Nonlinear Multi-Agent Systems With Initial Shifts

Abstract

In this paper, a discussion is made on the consensus tracking control by iterative learning method for high-order nonlinear multi-agent systems. Among them, all agents with initial state errors are enabled to perform a given repetitive task over a finite interval. The method proposed can achieve consensus tracking through a series of initial shifts correction actions. In the process of tracking, this algorithm rectifies the initial error of the state x n of each agent at first, then the error of x n−1 , and so on. All of these rectifying actions are finished in a specified interval. Furthermore, the algorithm has shown effective in the improvement of tracking performance through simulation.

Initial-Rectification Barrier Iterative Learning Control for Pneumatic Artificial Muscle Systems With Nonzero Initial Errors and Iteration-Varying Reference Trajectories

“…in which m is a proper positive number. Similarly, for a large enough m w > 0, by using the learning law (19), we obtain For a large enough m > 0, with the help of the learning law (20), we have…”

A survey of methods for handling initial state shifts in iterative learning control

“…Subsequently, Sun et al [46] , [47] focused on nonlinear systems with high relative order under the condition that the initial state shifts were fixed and used initial rectifying methods to completely track on the system within a defined interval. Meng et al [48] , [49] respectively realized complete tracking for first- and high-order linear multi-agent systems with fixed initial state shifts, whereas Li et al [50] achieved complete tracking for nonlinear multi-agent systems. In addition, for higher-order systems, rectifying strategies [46] , [47] were used to simultaneously rectify all state shifts in a specified time, while others [49] , [50] used step-by-step rectifying strategies, that is, the state shifts of the highest order were first rectified, followed by those of the next highest order, and so on, until all state shifts were rectified.…”

“…Meng et al [48] , [49] respectively realized complete tracking for first- and high-order linear multi-agent systems with fixed initial state shifts, whereas Li et al [50] achieved complete tracking for nonlinear multi-agent systems. In addition, for higher-order systems, rectifying strategies [46] , [47] were used to simultaneously rectify all state shifts in a specified time, while others [49] , [50] used step-by-step rectifying strategies, that is, the state shifts of the highest order were first rectified, followed by those of the next highest order, and so on, until all state shifts were rectified. When the initial state shift gradually approached a constant, the impulse compensation strategy ensured that the system achieved consistent tracking within a defined interval [51] .…”

Filtering-Error Constrained Angle Tracking Adaptive Learning Fuzzy Control for Pneumatic Artificial Muscle Systems Under Nonzero Initial Errors

“…The control parameters and gains in control law (22) and learning laws ( 25)-( 26 The control input at the 15th learning cycle is shown in Fig. 6.…”