Repetitive learning control of nonlinear systems over finite intervals

Abstract

Iterative learning control requires initial repositioning, while the time functions to be learned should be of periodicity in repetitive control. However, there are cases in practice where the time-varying unknowns are not periodic but repetitive, and repetitive learning control is applicable with avoidance of initial repositioning. In this paper, repetitive learning control designs are presented for a broader class of nonlinear systems over finite intervals. The Freeman formula is modified and used for stabilization of the nominal nonlinear time-varying system undertaken. The global stability of the learning system and asymptotic convergence of the tracking error are established through analysis of both partially and fully saturated learning algorithms, respectively. The repetitive learning control method is theoretically shown to be effective in dealing with time-varying parametric uncertainties. CitationSun M X, Wang D W, Chen P N. Repetitive learning control of nonlinear systems over finite intervals.

State-Constrained Iterative Learning Control for a Class Of MIMO Systems

“…As such, we will be able to design a function , according to Assumption 1 and selected Barrier Lyapunov Function , such that systems with formulation (2) can be converted into the form of (1). This is a widely adopted approach, like in [5], [9]- [11], [16]. Nonlinear systems under alignment condition with mixed type of uncertainties that do not satisfy matching condition will be extremely difficult to handle, either in ILC scope or other control regimes.…”

“…On one hand, it is easier to handle parametric uncertainties by learning or adaptation. Hence, in this work is handled by the updating law (5). On the other hand, it is not so straightforward to handle nonparametric uncertainties.…”

“…According to the learning updating law (5), and using the above trace properties, as well as the inequality , we can derive (16) therefore (17) Notice that the term has opposite sign in (17) and (15). Last consider .…”

“…Such constraints may rise due to physical limitations of the system, or due to the requirements of safe operation. In the area of ILC, constraints on control input signals have been addressed in various works such as [5] and [6] by considering saturation, for systems with parametric and nonparametric uncertainties, respectively, where Composite Energy Function (CEF) approach is adopted in analysis. These works have practical significance, since in many applications, control inputs, like voltages or currents, cannot be arbitrarily large due to limits of the supplies.…”

Adaptive backstepping repetitive learning control for discrete-time periodic systems

“…Periodic trajectory tracking or periodic disturbance rejection is a control problem that has attracted increasing attention in recent years, among which repetitive learning control (RLC) techniques are applied to tackle this problem in continuoustime domain [1][2][3][4][5][6][7][8][9][10][11][12]. The advantageous feature of the reported control schemes is that no initial resetting is required, while perfect tracking performance can be achieved as time increases.…”