Equivalence and convergence of two iterative learning control schemes with state feedback

Abstract

This article considers the equivalence and convergence of two iterative learning control (ILC) schemes with state feedback for a class of multi-input-multi-output discrete-time nonlinear systems in which each desired trajectory corresponds to a unique desired input or an infinite number of desired inputs. First, we strictly prove that the two ILC schemes are equivalent if they have the identical initial system inputs. Moreover, by the input space transformation method and mathematical induction we establish the necessary and sufficient criterion for the convergence of system output, input and state sequences. It is shown that the (locally Lipschitz) continuity is enough to guarantee the (exponential) convergence. Generally, the learned desired input depends on the values of the initial signals, the learning gain matrix and the state feedback item. By designing them with appropriate structures, the dependence is disappeared. Third, we show how to leverage the available information of system dynamics to design the learning gain matrix and state feedback for better tracking performance. Finally, we provide an example to illustrate the usefulness of our findings, in which we introduce the energy of learnable desired input to evaluate the learning performance.

Trajectory Tracking within a Hierarchical Primitive-Based Learning Approach

“…The L2 level learning process relies on the CLCS linearity, allowing for the application of one variant of ILC which is agnostic to the CLCS dynamics, called the experiment-driven model-free ILC (EDMFILC) [ 1 , 2 , 3 ]. This technique belongs to the popular data-driven ILC approaches [ 37 , 38 , 39 , 40 , 41 , 42 ] as part of data-driven research [ 43 , 44 , 45 , 46 , 47 ]. Here, the convergence analysis selects a conservative learning gain, based on equivalent CLCS models resulting from the actual reference model and from identified models based on the reusable input–output data.…”

A unified adaptive control approach of nonlinear continuous non‐parameterized systems with asymmetric control gains for trajectory tracking in different domains

“…For trajectory tracking tasks of dynamical systems repetitively over a finite time interval, iterative learning control (ILC) is an intelligent control strategy that updates control inputs iteratively after each cycle by utilizing the control experience at past cycles such that the current tracking performance is improved progressively. Recent three decades have witnessed considerable ILC achievements in terms of theoretical development and experimental applications 1–6 …”

“…Recent three decades have witnessed considerable ILC achievements in terms of theoretical development and experimental applications. [1][2][3][4][5][6] The ILC methods in early period have been mainly investigated under the strict repeatability assumptions that the initial state, reference trajectory, time length of trail, and model parameters and so forth of the controlled system are invariant with iterations. 6,7 Nevertheless, in many practical ILC applications, initial system outputs at different iterations often deviate irregularly from the initial value of the reference trajectory due to inaccurate initial localization of the controlled system.…”

Higher-order iterative learning control for nonlinear continuous systems with variable input trail lengths and input saturation

“…In order to achieve perfect tracking, most existing ILC studies required the trail lengths of dynamical system to be identical at each iteration [2,3,35,39]. However, in many practical circumstances, the controlled system may stop earlier or later due to external disturbances or system dynamics.…”