An ILC scheme for a class of nonlinear continuous‐time systems with time‐iteration‐varying parameters subject to second‐order internal model

Abstract

In this paper, a new iterative learning control (ILC) scheme is proposed to deal with unknown time-iteration-varying parameters for a class of nonlinear continuous-time systems. The parametric non-repetitiveness in the iteration domain is described by a second-order internal model, which includes systems with iteration-invariant parameters as a subset. By incorporating the internal model into the parametric learning law, the proposed ILC scheme can handle more generic systems with parametric uncertainties, and includes existing ILC schemes as a special case with the first-order internal model. The conditions under which the new ILC scheme can guarantee learning convergence are delicately explored. Utilizing the information of the previous two iterations and the method of composite energy function (CEF), it is able to derive pointwise convergence along the time axis and asymptotic convergence along the iteration axis. The controller design is further extended to the case for systems with mixed parameters and unknown time-varying input gain.

Adaptive Terminal ILC for Iteration‐varying Target Points

“…Remark 8. It is noted that the proposed TILC is very different from the adaptive ILCs [14][15][16][17][18]. First, the proposed adaptive TILC merely depends on the measurement of the terminal output at the end point without requiring any intermediate states and outputs.…”

“…Second, the control law (8) utilizes the control input signal k−1 and the terminal output signal k−1 in previous iteration, and the desired output at the terminal point of the current iteration d,k together. While for the adaptive ILCs in [14][15][16][17][18], no control input signals is used explicitly.…”

“…Since V 0 is bounded, and V k is non-increasing and nonnegative, in terms of (17) and (20), one obtains that…”

Iterative Learning Control for Linear Discrete‐Time Systems with Unknown High‐Order Internal Models: A Time‐Frequency Analysis Approach

“…Therefore, the ILC design with iteration-varying factors has been frequently investigated. For example, the iteration-varying initial state [4,5], reference [6,7], parameters [8][9][10], uncertainties [11], and disturbances [12,13] have been frequently encountered. In practice, along the iterative axis, these factors can be described by high-order internal models (HOIMs) [9,14,15], for example,…”

Discrete‐time Adaptive ILC for Non‐parametric Uncertain Nonlinear Systems with Iteration‐Varying Trajectory and Random Initial Condition

“…Reference discussed the issue of adaptive ILC for different trajectories with identical resetting error for continuous parameterized systems. In , a new ILC scheme was proposed for iteration‐dependent reference trajectory with bounded initial resetting error and disturbances by incorporating a second‐order internal model. Although some discrete‐time adaptive ILC approaches were explored by considering the iteration‐varying initial error and the iteration‐varying reference trajectory together, the trade‐off requirement is that the nonlinear dynamics should be linearly parameterized and the full state should be measurable.…”